Vincent Granville's Posts - AnalyticBridge2019-12-14T16:19:05ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranvillehttps://storage.ning.com/topology/rest/1.0/file/get/2191504775?profile=RESIZE_48X48&width=48&height=48&crop=1%3A1https://www.analyticbridge.datasciencecentral.com/profiles/blog/feed?user=vi0zmqyuk8ci&%3Bxn_auth=noStatistics for Data Science in One Picturetag:www.analyticbridge.datasciencecentral.com,2019-12-13:2004291:BlogPost:3957052019-12-13T01:30:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>There's no doubt about it, probability and statistics is an enormous field, encompassing topics from the familiar (like the average) to the complex (regression analysis, correlation coefficients and hypothesis testing to name but a few). If you want to be a great data scientist, you have to know some basic statistics. The following picture shows which statistics topics you must know if you're going to excel in data science.…</p>
<p></p>
<p>There's no doubt about it, probability and statistics is an enormous field, encompassing topics from the familiar (like the average) to the complex (regression analysis, correlation coefficients and hypothesis testing to name but a few). If you want to be a great data scientist, you have to know some basic statistics. The following picture shows which statistics topics you must know if you're going to excel in data science.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3767565869?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3767565869?profile=RESIZE_710x" class="align-center"/></a></p>
<p>Read the full article <a href="https://www.datasciencecentral.com/profiles/blogs/statistics-for-data-science-in-one-picture" target="_blank" rel="noopener">here</a>. For more concepts explained in one picture, follow <a href="https://www.datasciencecentral.com/page/search?q=in+one+picture" target="_blank" rel="noopener">this link</a>. For articles about statistical and machine learning concepts explained in simple English, from the same author, follow <a href="https://www.datasciencecentral.com/page/search?q=in+simple+english" target="_blank" rel="noopener">this link</a>. Or to download a book featuring many of these resources, click <a href="https://www.datasciencecentral.com/profiles/blogs/online-encyclopedia-of-statistical-science-free-1" target="_blank" rel="noopener">here</a> (free, but available to DSC members exclusively.)</p>
<p><strong>From our Sponsors</strong></p>
<ul>
<li><a href="https://dsc.news/34h27EX" target="_blank" rel="noopener">Future-proof your path to Enterprise AI</a> - Dataiku 6 Webinar Recording</li>
</ul>
<p></p>On Being a 50 Year Old Data Scientisttag:www.analyticbridge.datasciencecentral.com,2019-12-10:2004291:BlogPost:3955862019-12-10T18:51:04.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>At the time of writing, I'm a 52 year-old working in the fields of mathematics and data science. In mathematics, that makes me well-seasoned (and probably well-tenured, if I had chosen to continue in academia). In data science, some would consider me a dinosaur. In fact, many older people considering a career in data science might be put off by the thought that data science is tough to break into at a later age. But is that statement true? Should the over 50 crowd put down their textbooks…</p>
<p>At the time of writing, I'm a 52 year-old working in the fields of mathematics and data science. In mathematics, that makes me well-seasoned (and probably well-tenured, if I had chosen to continue in academia). In data science, some would consider me a dinosaur. In fact, many older people considering a career in data science might be put off by the thought that data science is tough to break into at a later age. But is that statement true? Should the over 50 crowd put down their textbooks and pick up their gardening tools?</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3764064994?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3764064994?profile=RESIZE_710x" class="align-center"/></a></p>
<p><strong>Is Math a Young Person's Game? Maybe</strong></p>
<p>As far as the mathematics portion of my career, I didn't become a mathematician until I was in my mid-thirties. Before that I dabbled with whatever venture brought in a few bob to feed the kids: computer operator, Ebay entrepreneur, aviation electrician. I was 36 when I decided to go back to school to get my master's. If Alfred Adler<span> </span>is to be believed, my "mathematical life" had already long passed by the time I graduated.</p>
<p>Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished. </p>
<p>Read the full article by Stephanie Glen, <a href="https://www.datasciencecentral.com/profiles/blogs/on-being-a-50-year-old-data-scientist" target="_blank" rel="noopener">here</a>. For other articles by Stephanie Glen, <a href="https://www.datasciencecentral.com/profiles/blog/list?user=0lahn4b4odglr" target="_blank" rel="noopener">follow this link</a>. </p>
<p><strong>Sponsored Announcement</strong></p>
<ul>
<li><span>Be Indispensable With a Master’s in Data Analytics. As technology and the marketplace change constantly, you want the skills to thrive. The UCLA Anderson Master of Science in Business Analytics is a 13-month program that will give you the tools to become a leader in this rapidly evolving field. Read more <a href="https://dsc.news/2KTpz3V" target="_blank" rel="noopener">here</a>. </span></li>
</ul>Variance, Attractors and Behavior of Chaotic Statistical Systemstag:www.analyticbridge.datasciencecentral.com,2019-11-29:2004291:BlogPost:3957632019-11-29T09:30:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><span>We study the properties of a typical chaotic system to derive general insights that apply to a large class of unusual statistical distributions. The purpose is to create a unified theory of these systems. These systems can be deterministic or random, yet due to their gentle chaotic nature, they exhibit the same behavior in both cases. They lead to new models with numerous applications in Fintech, cryptography, simulation and benchmarking tests of statistical hypotheses. They are also…</span></p>
<p><span>We study the properties of a typical chaotic system to derive general insights that apply to a large class of unusual statistical distributions. The purpose is to create a unified theory of these systems. These systems can be deterministic or random, yet due to their gentle chaotic nature, they exhibit the same behavior in both cases. They lead to new models with numerous applications in Fintech, cryptography, simulation and benchmarking tests of statistical hypotheses. They are also related to numeration systems. One of the highlights in this article is the discovery of a simple variance formula for an infinite sum of highly correlated random variables. We also try to find and characterize attractor distributions: these are the limiting distributions for the systems in question, just like the Gaussian attractor is the universal attractor with finite variance in the central limit theorem framework. Each of these systems is governed by a specific functional equation, typically a stochastic integral equation whose solutions are the attractors. This equation helps establish many of their properties. The material discussed here is state-of-the-art and original, yet presented in a format accessible to professionals with limited exposure to statistical science. Physicists, statisticians, data scientists and people interested in signal processing, chaos modeling, or dynamical systems will find this article particularly interesting. Connection to other similar chaotic systems is also discussed. </span></p>
<p>Read the full article <a href="https://www.datasciencecentral.com/profiles/blogs/chaos-attractors-in-machine-learning-systems" target="_blank" rel="noopener">here</a>. </p>
<p><span><a href="https://storage.ning.com/topology/rest/1.0/file/get/3746624910?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3746624910?profile=RESIZE_710x" class="align-center"/></a></span></p>
<p><span><strong>Content of this article</strong></span></p>
<p>1. The Geometric System: Definition and Properties</p>
<ul>
<li>A test for independence</li>
<li>Connection to the Fixed-Point Theorem</li>
</ul>
<p>2. Geometric and Uniform Attractors</p>
<ul>
<li>General formula</li>
<li>The geometric attractor</li>
<li>Not any distribution can be an attractor</li>
<li>The uniform attractor</li>
</ul>
<p>3. Discrete <em>X</em> Resulting in a Gaussian-looking Attractor</p>
<ul>
<li>Towards a numerical solution</li>
</ul>
<p>4. Special Cases with Continuous Distribution for <em>X</em></p>
<ul>
<li>An almost perfect equality</li>
<li>Is the log-normal distribution an attractor?</li>
</ul>
<p>5. Connection to Binary Digits and Singular Distributions</p>
<ul>
<li>Numbers made up of random digits</li>
<li>Singular distributions</li>
<li>Connection to Infinite Random Products</li>
</ul>
<p>6. A General Classification of Chaotic Statistical Distributions</p>
<p><em>Read the full article <a href="https://www.datasciencecentral.com/profiles/blogs/chaos-attractors-in-machine-learning-systems" target="_blank" rel="noopener">here</a>. </em></p>A Lesson in Using NLP for Hidden Feature Extractiontag:www.analyticbridge.datasciencecentral.com,2019-11-29:2004291:BlogPost:3956562019-11-29T05:00:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><strong><em>Summary:</em></strong><em> 99% of our application of NLP has to do with chatbots or translation. This is a very interesting story about expanding the bounds of NLP and feature creation to predict bestselling novels. The authors created over 20,000 NLP features, about 2,700 of which proved to be predictive with a 90% accuracy rate in predicting NYT bestsellers.…</em></p>
<p></p>
<p><strong><em>Summary:</em></strong><em> 99% of our application of NLP has to do with chatbots or translation. This is a very interesting story about expanding the bounds of NLP and feature creation to predict bestselling novels. The authors created over 20,000 NLP features, about 2,700 of which proved to be predictive with a 90% accuracy rate in predicting NYT bestsellers.</em></p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3515945869?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3515945869?profile=RESIZE_710x" width="300" class="align-right"/></a>It’s a pretty rare individual who hasn’t had a personal experience with NLP (Natural Language Processing). About 99% of those experiences are in the form of chatbots or translators, either text or speech in, and text or speech out.</p>
<p>This has proved to be one of the hottest and most economically valuable applications of deep learning but it’s not the whole story.</p>
<p>I recently picked up a copy of a 2016 book entitled<span> </span><em>“The Bestseller Code – Anatomy of the Blockbuster Novel”</em><span> </span>which promised a story about using NLP and machine learning to predict which US fiction novels would make the New York Times Best Sellers list and which would not.</p>
<p>There are about 55,000 new works of fiction published each year (and that doesn’t count self-published). Less than 0.5% or about 200 to 220 make the NYT Bestseller list in a year. Only 3 or 4 of those will sell more than a million copies.</p>
<p>The authors, Jodie Archer (background in publishing), and Matt Jockers (cofounder of the Stanford Literary Lab) write about their model which has an astounding 90% success rate in predicting which books will make the NYT list using a corpus of 5,000 novels from the last 30 years which included 500 NYT Bestsellers.</p>
<p>The book, which I heartily recommend, is not a data science book, nor is it a how-to-write-a-bestseller. And while it has elements of both it’s mostly reporting about the most interesting finds among the 20,000 extracted features they developed, about 2,800 of which proved to be predictive. More on that later.</p>
<p>What struck me was the potential this field of ‘stylometrics’ has for extracting hidden features for almost any problem which has a large amount of text as one of its data sources. Could be CSR logs of customer interaction, could be doctor’s notes, blogs, or warranty repair descriptions where we’re really only scratching the surface with word clouds and sentiment analysis.</p>
<p></p>
<p><em>Read full article <a href="https://www.datasciencecentral.com/profiles/blogs/nlp-picks-bestsellers-a-lesson-in-using-nlp-for-hidden-feature-ex" target="_blank" rel="noopener">here</a>.</em></p>New Family of Generalized Gaussian Distributionstag:www.analyticbridge.datasciencecentral.com,2019-11-28:2004291:BlogPost:3957602019-11-28T06:14:46.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><span>In this article, we explore a new type of generalized univariate normal distributions that satisfies useful statistical properties, with interesting applications. This new class of distributions is defined by its characteristic function, and applications are discussed in the last section. These distributions are semi-stable (we define what this means below). In short it is a much wider class than the stable distributions</span><span> (the only stable distribution with a finite variance…</span></p>
<p><span>In this article, we explore a new type of generalized univariate normal distributions that satisfies useful statistical properties, with interesting applications. This new class of distributions is defined by its characteristic function, and applications are discussed in the last section. These distributions are semi-stable (we define what this means below). In short it is a much wider class than the stable distributions</span><span> (the only stable distribution with a finite variance being the Gaussian one) and it encompasses all stable distributions as a subset. It is a sub-class of the divisible distributions. </span></p>
<p><span><a href="https://storage.ning.com/topology/rest/1.0/file/get/3744926698?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3744926698?profile=RESIZE_710x" class="align-center"/></a></span></p>
<p><strong>Content of this article:</strong></p>
<ul>
<li>New two-parameter distribution <em>G</em>(<em>a</em>, <em>b</em>): introduction, properties</li>
<li>Generalized central limit theorem</li>
<li>Characteristic function</li>
<li>Density: special cases, moments, mathematical conjecture</li>
<li>Simulations</li>
<li>Weakly semi-stable distributions</li>
<li>Counter-example</li>
<li>Applications and conclusions</li>
</ul>
<p><em>Read the full article <a href="https://www.datasciencecentral.com/profiles/blogs/new-family-of-generalized-gaussian-distributions" target="_blank" rel="noopener">here</a>. </em></p>
<p></p>10 Machine Learning Methods that Every Data Scientist Should Knowtag:www.analyticbridge.datasciencecentral.com,2019-11-27:2004291:BlogPost:3957572019-11-27T17:58:33.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw" id="a572">Machine learning is a hot topic in research and industry, with new methodologies developed all the time. The speed and complexity of the field makes keeping up with new techniques difficult even for experts — and potentially overwhelming for beginners.</p>
<p class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw" id="0d4d">To demystify machine learning and to offer a learning path for those who are new to the core…</p>
<p id="a572" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw">Machine learning is a hot topic in research and industry, with new methodologies developed all the time. The speed and complexity of the field makes keeping up with new techniques difficult even for experts — and potentially overwhelming for beginners.</p>
<p id="0d4d" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw">To demystify machine learning and to offer a learning path for those who are new to the core concepts, let’s look at ten different methods, including simple descriptions, visualizations, and examples for each one.</p>
<p id="64a5" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw">A machine learning algorithm, also called model, is a mathematical expression that represents data in the context of a problem, often a business problem. The aim is to go from data to insight. For example, if an online retailer wants to anticipate sales for the next quarter, they might use a machine learning algorithm that predicts those sales based on past sales and other relevant data. Similarly, a windmill manufacturer might visually monitor important equipment and feed the video data through algorithms trained to identify dangerous cracks.</p>
<p class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw"><a href="https://storage.ning.com/topology/rest/1.0/file/get/3744174486?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3744174486?profile=RESIZE_710x" class="align-center"/></a></p>
<p id="00c2" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw">The ten methods described offer an overview — and a foundation you can build on as you hone your machine learning knowledge and skill:</p>
<ol class="">
<li id="b886" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw nx ny nz">Regression</li>
<li id="2763" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Classification</li>
<li id="54dd" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Clustering</li>
<li id="c007" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Dimensionality Reduction</li>
<li id="1af1" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Ensemble Methods</li>
</ol>
<p><em>Read the rest of the list, with description for all the 10 algorithms, <a href="https://www.datasciencecentral.com/profiles/blogs/10-machine-learning-methods-that-every-data-scientist-should-know" target="_blank" rel="noopener">here</a>. </em></p>10 Visualizations Every Data Scientist Should Knowtag:www.analyticbridge.datasciencecentral.com,2019-11-12:2004291:BlogPost:3954782019-11-12T17:00:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><em>This article is by Jorge Castañón, Ph.D., Senior Data Scientist at the IBM Machine Learning Hub.</em></p>
<p class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv" id="5920">Data visualization plays two key roles:</p>
<p class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv" id="085d">1.<span> </span><em class="op">Communicating results clearly to a general audience.</em></p>
<p class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv" id="c440">2.<span> …</span></p>
<p><em>This article is by Jorge Castañón, Ph.D., Senior Data Scientist at the IBM Machine Learning Hub.</em></p>
<p id="5920" class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv">Data visualization plays two key roles:</p>
<p id="085d" class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv">1.<span> </span><em class="op">Communicating results clearly to a general audience.</em></p>
<p id="c440" class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv">2.<span> </span><em class="op">Organizing a view of data that suggests a new hypothesis or a next step in a project.</em></p>
<p id="f14e" class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv">It’s no surprise that most people prefer visuals to large tables of numbers. That’s why clearly labeled plots with meaningful interpretation always make it to the front of academic papers.</p>
<p class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv"><a href="https://storage.ning.com/topology/rest/1.0/file/get/3709852824?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3709852824?profile=RESIZE_710x" class="align-center"/></a></p>
<p id="6028" class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv">This post looks at the 10 visualizations you can bring to bear on your data — whether you want to convince the wider world of your theories or crack open your own project and take the next step:</p>
<ol class="">
<li id="53c6" class="ni nj en ao nk b nl nm nn no np nq nr ns nt nu nv oq or os">Histograms</li>
<li id="ddc7" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">Bar/Pie charts</li>
<li id="6fcc" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">Scatter/Line plots</li>
<li id="3613" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">Time series</li>
<li id="6263" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">Relationship maps</li>
<li id="c7df" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">Heat maps</li>
<li id="d07c" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">Geo Maps</li>
<li id="8f76" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">3-D Plots</li>
<li id="3965" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">Higher-Dimensional Plots</li>
<li id="ec17" class="ni nj en ao nk b nl ot nn ou np ov nr ow nt ox nv oq or os">Word clouds</li>
</ol>
<p>Read the full article, with descriptions and illustrations for these visualizations, <a href="https://www.datasciencecentral.com/profiles/blogs/10-visualizations-every-data-scientist-should-know" target="_blank" rel="noopener">here</a>.</p>More Weird Statistical Distributionstag:www.analyticbridge.datasciencecentral.com,2019-10-27:2004291:BlogPost:3951392019-10-27T00:00:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>Some original and very interesting material is presented here, with possible applications in Fintech. No need for a PhD in math to understand this article: I tried to make the presentation as simple as possible, focusing on high-level results rather than technicalities. Yet, professional statisticians and mathematicians, even academic researchers, will find some deep and fascinating results worth further exploring.…</p>
<p></p>
<p>Some original and very interesting material is presented here, with possible applications in Fintech. No need for a PhD in math to understand this article: I tried to make the presentation as simple as possible, focusing on high-level results rather than technicalities. Yet, professional statisticians and mathematicians, even academic researchers, will find some deep and fascinating results worth further exploring.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3681849077?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3681849077?profile=RESIZE_710x" class="align-center"/></a></p>
<p style="text-align: center;"><em>Can you identify patterns in this chart? (see section 2.2. in the article for an answer)</em></p>
<p>Let's start with </p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3681308901?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3681308901?profile=RESIZE_710x" class="align-center"/></a></p>
<p>Here the<span> </span><em>X</em>(<em>k</em>)'s are random variable identically and independently distributed, commonly referred to as <em>X</em>. We are trying to find the distribution of<span> </span><em>Z</em>.</p>
<p><strong>Contents</strong></p>
<p>1. Using a Simple Discrete Distribution for <em>X</em></p>
<p>2. Towards a Better Model</p>
<ul>
<li>Approximate Solution</li>
<li>The Fractal, Brownian-like Error Term</li>
</ul>
<p>3. Finding <em>X</em> and <em>Z</em> Using Characteristic Functions</p>
<ul>
<li>Test with Log-normal Distribution for <em>X</em></li>
<li>Playing with the Characteristic Functions</li>
<li>Generalization to Continued Fractions and Nested Cubic Roots</li>
</ul>
<p>4. Exercises</p>
<p><em>Read this article <a href="https://www.datasciencecentral.com/profiles/blogs/math-fun-infinite-nested-radicals-of-random-variables" target="_blank" rel="noopener">here</a>. </em></p>
<p></p>Complete Hands-Off Automated Machine Learningtag:www.analyticbridge.datasciencecentral.com,2019-10-22:2004291:BlogPost:3948882019-10-22T20:30:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>By Bill Vorhies. </p>
<p><strong><em>Summary:</em></strong><em> Here’ a proposal for real ‘zero touch’, ‘set-em-and-forget-em’ machine learning from the researchers at Amazon. If you have an environment as fast changing as e-retail and a huge number of models matching buyers and products you could achieve real cost savings and revenue increases by making the refresh cycle faster and more accurate with automation. This capability likely will be coming soon to your favorite AML…</em></p>
<p>By Bill Vorhies. </p>
<p><strong><em>Summary:</em></strong><em> Here’ a proposal for real ‘zero touch’, ‘set-em-and-forget-em’ machine learning from the researchers at Amazon. If you have an environment as fast changing as e-retail and a huge number of models matching buyers and products you could achieve real cost savings and revenue increases by making the refresh cycle faster and more accurate with automation. This capability likely will be coming soon to your favorite AML platform.</em></p>
<p><em><a href="https://storage.ning.com/topology/rest/1.0/file/get/3674974988?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3674974988?profile=RESIZE_710x" class="align-center"/></a></em></p>
<p>Is there a future in which we can really ‘set-em-and-forget-em’ machine learning? So far Automated Machine Learning (AML) is delivering on vastly simplifying the creation of models but the maintenance, refresh, and update still require manual intervention.</p>
<p>Not that we’re trying to talk ourselves out of a job. But after all, once the model is built and implemented it’s more fun to move on to the next opportunity. If the maintenance and refresh cycle could be truly automated that would be a good thing.</p>
<p>Much of the effort so far has been put into simplifying getting the model out of its AML environment and into its production environment. Facebook’s FBLearner is an example of this. A number of platforms claim to ease this process for the rest of us. At least once we manually refresh the model it’s easier to update it in production.</p>
<p><em>Read full article <a href="https://www.datasciencecentral.com/profiles/blogs/complete-hands-off-automated-machine-learning" target="_blank" rel="noopener">here</a>. </em></p>40+ Modern Tutorials Covering All Aspects of Machine Learningtag:www.analyticbridge.datasciencecentral.com,2019-10-13:2004291:BlogPost:3947202019-10-13T17:00:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><span>This list of lists contains books, notebooks, presentations, cheat sheets, and tutorials covering all aspects of data science, machine learning, deep learning, statistics, math, and more, with most documents featuring Python or R code and numerous illustrations or case studies. All this material is available for free, and consists of content mostly created in 2019 and 2018, by various top experts in their respective fields. A few of these documents are available on LinkedIn: see last…</span></p>
<p><span>This list of lists contains books, notebooks, presentations, cheat sheets, and tutorials covering all aspects of data science, machine learning, deep learning, statistics, math, and more, with most documents featuring Python or R code and numerous illustrations or case studies. All this material is available for free, and consists of content mostly created in 2019 and 2018, by various top experts in their respective fields. A few of these documents are available on LinkedIn: see last section on how to download them. </span></p>
<p><span><a href="https://storage.ning.com/topology/rest/1.0/file/get/3660371847?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3660371847?profile=RESIZE_710x" class="align-center"/></a></span></p>
<p><span>Below are the first two sections.</span></p>
<p><strong>General References</strong></p>
<ul>
<li>Free Deep Learning Book (639 pages) by Prof. Gilles Louppe</li>
<li>Python Crash Course (562 pages) by Eric Matthes</li>
<li>Free Book: Applied Data Science (141 pages) - Columbia University</li>
<li>Data Science in Practice</li>
<li>Machine Learning 101 - By Jason Mayes, Google</li>
<li>The Ultimate guide to AI, Data Science & Machine Learning</li>
<li>Free Handbooks for Data Science Professionals</li>
<li>Free Book: Natural Language Processing with Python</li>
<li>Data Visualization Resources</li>
<li>Textbook: Probability Course - Harvard University</li>
<li>Textbook: The Math of Machine Learning - Berkeley University</li>
<li>Comprehensive Guide to Machine Learning - Berkeley University</li>
<li>Free Book: Foundations of Data Science - by Microsoft Research</li>
<li>Comprehensive Guide on Machine Learning - by J.P. Morgan</li>
<li>Gentle Approach to Linear Algebra - by Vincent Granville</li>
</ul>
<p><strong>Data Science Central Books, Booklets and References</strong></p>
<ul>
<li>Statistics: New Foundations, Toolbox, and Machine Learning Recipes</li>
<li>Deep Learning and Computer Vision with CNNs</li>
<li>Getting Started with TensorFlow 2.0</li>
<li>Classification and Regression in a Weekend</li>
<li>Online Encyclopedia of Statistical Science</li>
<li>Azure Machine Learning in a Weekend</li>
<li>Enterprise AI - An Application Perspective</li>
<li>Applied Stochastic Processes</li>
<li>Comprehensive Repository of Data Science and ML Resources</li>
<li>Foundations of ML and Data Science for Developers</li>
<li>Elegant Representation of Forward/Back Propagation in Neural Networks</li>
<li>Learning the Math of Data Science</li>
</ul>
<p>To access all these documents and more, <a href="https://www.datasciencecentral.com/profiles/blogs/40-tutorials-covering-all-aspects-of-machine-learning" target="_blank" rel="noopener">follow this link</a>.</p>Surprising Uses of Synthetic Random Data Setstag:www.analyticbridge.datasciencecentral.com,2019-10-02:2004291:BlogPost:3947462019-10-02T23:00:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>I have used synthetic data sets many times for simulation purposes, most recently in my articles<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/six-degrees-of-separation-between-any-two-data-sets" rel="noopener" target="_blank">Six degrees of Separations between any two Datasets</a><span> </span>and<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/how-to-lie-with-p-values" rel="noopener" target="_blank">How to Lie with p-values</a>. Many…</p>
<p>I have used synthetic data sets many times for simulation purposes, most recently in my articles<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/six-degrees-of-separation-between-any-two-data-sets" target="_blank" rel="noopener">Six degrees of Separations between any two Datasets</a><span> </span>and<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/how-to-lie-with-p-values" target="_blank" rel="noopener">How to Lie with p-values</a>. Many applications (including the data sets themselves) can be found in my books<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/fee-book-applied-stochastic-processes" target="_blank" rel="noopener">Applied Stochastic Processes</a><span> </span>and<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/free-book-statistics-new-foundations-toolbox-and-machine-learning" target="_blank" rel="noopener">New Foundations of Statistical Science</a>. For instance, these data sets can be used to benchmark some statistical tests of hypothesis (the null hypothesis known to be true or false in advance) and to assess the power of such tests or confidence intervals. In other cases, it is used to simulate clusters and test cluster detection / pattern detection algorithms, see<span> </span><a href="https://www.analyticbridge.datasciencecentral.com/profiles/blogs/how-to-detect-a-pattern-problem-and-solution" target="_blank" rel="noopener">here</a>. I also used such data sets to discover two new deep conjectures in number theory (see<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/two-new-deep-conjectures-in-probabilistic-number-theory" target="_blank" rel="noopener">here</a>), to design new Fintech models such as<span> </span><em>bounded Brownian motions</em>, and find new families of statistical distributions (see<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/a-strange-family-of-statistical-distributions" target="_blank" rel="noopener">here</a>).</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3641314354?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3641314354?profile=RESIZE_710x" class="align-center"/></a></p>
<p style="text-align: center;"><em>Goldbach's comet </em></p>
<p>In this article, I focus on peculiar random data sets to prove -- heuristically -- two of the most famous math conjectures in number theory, related to prime numbers: the Twin Prime conjecture, and the Goldbach conjecture. The methodology is at the intersection of probability theory, experimental math, and probabilistic number theory. It involves working with infinite data sets, dwarfing any data set found in any business context.</p>
<p>Read full article <a href="https://www.datasciencecentral.com/profiles/blogs/surprising-uses-of-synthetic-random-data-sets?xg_source=activity" target="_blank" rel="noopener">here</a>. </p>Six Degrees of Separation Between Any Two Data Setstag:www.analyticbridge.datasciencecentral.com,2019-09-09:2004291:BlogPost:3943772019-09-09T16:30:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>This is an interesting data science conjecture, inspired by the well known<span> </span><a href="https://www.bigdatanews.datasciencecentral.com/profiles/blogs/graph-theory-six-degrees-of-separation-problem" rel="noopener" target="_blank">six degrees of separation problem</a>, stating that there is a link involving no more than 6 connections between any two people on Earth, say between you and anyone living (say) in North Korea. </p>
<p>Here the link is between any two univariate data sets…</p>
<p>This is an interesting data science conjecture, inspired by the well known<span> </span><a href="https://www.bigdatanews.datasciencecentral.com/profiles/blogs/graph-theory-six-degrees-of-separation-problem" target="_blank" rel="noopener">six degrees of separation problem</a>, stating that there is a link involving no more than 6 connections between any two people on Earth, say between you and anyone living (say) in North Korea. </p>
<p>Here the link is between any two univariate data sets of the same size, say Data A and Data B. The claim is that there is a chain involving no more than 6 intermediary data sets, each highly correlated to the previous one (with a correlation above 0.8), between Data A and Data B. The concept is illustrated in the example below, where only 4 intermediary data sets (labeled Degree 1, Degree 2, Degree 3, and Degree 4) are actually needed. </p>
<p><img src="https://storage.ning.com/topology/rest/1.0/file/get/3547469050?profile=RESIZE_710x" class="align-center"/></p>
<p style="text-align: center;"><em>Correlation table for the 6 data sets</em></p>
<p>The view the (random) data sets, understand how the chain of intermediary data sets was built, and access the spreadsheets to reproduce the results or test on different data, <a href="https://www.datasciencecentral.com/profiles/blogs/six-degrees-of-separation-between-any-two-data-sets" target="_blank" rel="noopener">follow this link</a>. I<span>t makes for an interesting theoretical data science research project, for people with too much free time on their hands. </span></p>Two New Deep Conjectures in Probabilistic Number Theorytag:www.analyticbridge.datasciencecentral.com,2019-09-08:2004291:BlogPost:3941282019-09-08T10:09:38.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>The material discussed here is also of interest to machine learning, AI, big data, and data science practitioners, as much of the work is based on heavy data processing, algorithms, efficient coding, testing, and experimentation. Also, it's not just two new conjectures, but paths and suggestions to solve these problems. The last section contains a few new, original exercises, some with solutions, and may be useful to students, researchers, and instructors offering math and statistics classes…</p>
<p>The material discussed here is also of interest to machine learning, AI, big data, and data science practitioners, as much of the work is based on heavy data processing, algorithms, efficient coding, testing, and experimentation. Also, it's not just two new conjectures, but paths and suggestions to solve these problems. The last section contains a few new, original exercises, some with solutions, and may be useful to students, researchers, and instructors offering math and statistics classes at the college level: they range from easy to very difficult. Some great probability theorems are also discussed, in layman's terms: see section 1.2. </p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3546311327?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3546311327?profile=RESIZE_710x" class="align-center"/></a></p>
<p>The two deep conjectures highlighted in this article (conjectures B and C) are related to the digit distribution of well known math constants such as Pi or log 2, with an emphasis on binary digits of SQRT(2). This is an old problem, one of the most famous ones in mathematics, still unsolved today.</p>
<p><strong>Content of this article</strong></p>
<p>A Strange Recursive Formula</p>
<ul>
<li>Conjecture A</li>
<li>A deeper result</li>
<li>Conjecture B</li>
<li>Connection to the Berry-Esseen theorem</li>
<li>Potential path to solving this problem</li>
</ul>
<p>Potential Solution Based on Special Rational Number Sequences</p>
<ul>
<li>Interesting statistical result</li>
<li>Conjecture C</li>
<li>Another curious statistical result</li>
</ul>
<p>Exercises</p>
<p><em>Read the full article <a href="https://www.datasciencecentral.com/profiles/blogs/two-new-deep-conjectures-in-probabilistic-number-theory" target="_blank" rel="noopener">here</a>. </em></p>10 Machine Learning Methods that Every Data Scientist Should Knowtag:www.analyticbridge.datasciencecentral.com,2019-08-30:2004291:BlogPost:3944382019-08-30T17:08:12.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw" id="a572">Machine learning is a hot topic in research and industry, with new methodologies developed all the time. The speed and complexity of the field makes keeping up with new techniques difficult even for experts — and potentially overwhelming for beginners.</p>
<p class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw" id="0d4d">To demystify machine learning and to offer a learning path for those who are new to the core…</p>
<p id="a572" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw">Machine learning is a hot topic in research and industry, with new methodologies developed all the time. The speed and complexity of the field makes keeping up with new techniques difficult even for experts — and potentially overwhelming for beginners.</p>
<p id="0d4d" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw">To demystify machine learning and to offer a learning path for those who are new to the core concepts, let’s look at ten different methods, including simple descriptions, visualizations, and examples for each one.</p>
<p class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw"><a href="https://storage.ning.com/topology/rest/1.0/file/get/3487793979?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3487793979?profile=RESIZE_710x" class="align-center"/></a></p>
<p id="64a5" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw">A machine learning algorithm, also called model, is a mathematical expression that represents data in the context of a problem, often a business problem. The aim is to go from data to insight. For example, if an online retailer wants to anticipate sales for the next quarter, they might use a machine learning algorithm that predicts those sales based on past sales and other relevant data. Similarly, a windmill manufacturer might visually monitor important equipment and feed the video data through algorithms trained to identify dangerous cracks.</p>
<p id="00c2" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw">The ten methods described offer an overview — and a foundation you can build on as you hone your machine learning knowledge and skill:</p>
<ol class="">
<li id="b886" class="nj nk eo ao nl b nm nn no np nq nr ns nt nu nv nw nx ny nz">Regression</li>
<li id="2763" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Classification</li>
<li id="54dd" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Clustering</li>
<li id="c007" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Dimensionality Reduction</li>
<li id="1af1" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Ensemble Methods</li>
<li id="91ed" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Neural Nets and Deep Learning</li>
<li id="5128" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Transfer Learning</li>
<li id="2251" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Reinforcement Learning</li>
<li id="6975" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Natural Language Processing</li>
<li id="429f" class="nj nk eo ao nl b nm ob no oc nq od ns oe nu of nw nx ny nz">Word Embeddings</li>
</ol>
<p><em>Read the full article, with detailed description for each method, <a href="https://www.datasciencecentral.com/profiles/blogs/10-machine-learning-methods-that-every-data-scientist-should-know" target="_blank" rel="noopener">here</a>. </em></p>A Strange Family of Statistical Distributionstag:www.analyticbridge.datasciencecentral.com,2019-08-30:2004291:BlogPost:3943402019-08-30T16:11:16.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><span>I introduce here a family of very peculiar statistical distributions governed by two parameters: </span><em>p</em><span>, a real number in [0, 1], and </span><em>b</em><span>, an integer > 1. </span></p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3487729021?profile=original" rel="noopener" target="_blank"><img class="align-center" src="https://storage.ning.com/topology/rest/1.0/file/get/3487729021?profile=RESIZE_710x"></img></a></p>
<p><span>Potential applications are found in cryptography, Fintech (stock market modeling), Bitcoin, number theory, random number…</span></p>
<p><span>I introduce here a family of very peculiar statistical distributions governed by two parameters: </span><em>p</em><span>, a real number in [0, 1], and </span><em>b</em><span>, an integer > 1. </span></p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3487729021?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3487729021?profile=RESIZE_710x" class="align-center"/></a></p>
<p><span>Potential applications are found in cryptography, Fintech (stock market modeling), Bitcoin, number theory, random number generation, benchmarking statistical tests (see </span><a href="https://www.datasciencecentral.com/profiles/blogs/fascinating-new-results-in-the-theory-of-randomness" target="_blank" rel="noopener">here</a><span>) and even gaming (see </span><a href="https://www.datasciencecentral.com/profiles/blogs/data-science-foundations-for-a-new-stock-market" target="_blank" rel="noopener">here</a><span>.) However, the most interesting application is probably to gain insights about how non-normal numbers look like, especially their chaotic nature. It is a fundamental tool to help solve one of the most intriguing mathematical conjectures of all times (yet unsolved): are the digits of standard constants such as Pi or SQRT(2) uniformly distributed or not? For instance, when </span><em>b</em><span> = 2, any departure from </span><em>p</em><span> = 0.5 (a normal seed) results in a strong discontinuity for </span><em>f</em><span>(</span><em>x</em><span>) at </span><em>x</em><span> = 0.5. If you look at the above chart, </span><em>f(</em><span>0) = </span><em>f(</em><span>1/2) = </span><em>f</em><span>(1) regardless of </span><em>p</em><span>, but discontinuities are masking this fact. </span></p>
<p><span><a href="https://www.datasciencecentral.com/profiles/blogs/a-strange-family-of-statistical-distributions" target="_blank" rel="noopener">Read full article here</a>. </span></p>Extreme Events Modeling Using Continued Fractionstag:www.analyticbridge.datasciencecentral.com,2019-08-30:2004291:BlogPost:3943242019-08-30T15:42:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>Continued fractions are usually considered as a beautiful, curious mathematical topic, but with applications mostly theoretical and limited to math and number theory. Here we show how it can be used in applied business and economics contexts, leveraging the mathematical theory developed for continued fraction, to model and explain natural phenomena. …</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3487696331?profile=original" rel="noopener" target="_blank"><img class="align-center" src="https://storage.ning.com/topology/rest/1.0/file/get/3487696331?profile=RESIZE_710x"></img></a></p>
<p>Continued fractions are usually considered as a beautiful, curious mathematical topic, but with applications mostly theoretical and limited to math and number theory. Here we show how it can be used in applied business and economics contexts, leveraging the mathematical theory developed for continued fraction, to model and explain natural phenomena. </p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3487696331?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3487696331?profile=RESIZE_710x" class="align-center"/></a></p>
<p>The interest in this project started when analyzing sequences such as<span> </span><em>x</em>(<em>n</em>) = {<span> </span><em>nq</em><span> </span>} =<span> </span><em>nq</em><span> </span>- INT(<em>nq</em>) where<span> </span><em>n</em>= 1, 2, and so on, and<span> </span><em>q</em><span> </span>is an irrational number in [0, 1] called the<span> </span><em>seed</em>. The brackets denote the fractional part function. The values<span> </span><em>x</em>(<em>n</em>) are also in [0, 1] and get arbitrarily close to 0 and 1 infinitely often, and indeed arbitrarily close to any number in [0, 1] infinitely often. I became interested to see what happens when it gets very close to 1, and more precisely, about the distribution of the arrival times<span> </span><em>t</em>(<em>n</em>) of successive records. I was curious to compare these arrival times with those from truly random numbers, or from real-life time series such as temperature, stock market or gaming/sports data. Such arrival times are known to have an infinite expectation under stable conditions, though their medians always exist: after all, any record could be the final one, never to be surpassed again in the future. This always happens at some point with the sequence<span> </span><em>x</em>(<em>n</em>), if<span> </span><em>q</em><span> </span>is a rational number -- thus our focus on irrational seeds: they yield successive records that keep growing over and over, without end, although the gaps between successive records eventually grow very large, in a chaotic, unpredictable way, just like records in traditional time series.</p>
<p><a href="https://www.datasciencecentral.com/profiles/blogs/extreme-events-modeling-using-continued-fractions" target="_blank" rel="noopener">Read the full article here</a>.</p>
<p><strong>Content</strong>:</p>
<ul>
<li>Theoretical background (simplified)</li>
<li>Generalization and potential applications to real life problems</li>
<li>Original applications in music and probabilistic number theory</li>
</ul>Comparing Model Evaluation Techniquestag:www.analyticbridge.datasciencecentral.com,2019-08-08:2004291:BlogPost:3936612019-08-08T16:37:43.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>In my previous posts, I compared model evaluation techniques using Statistical Tools & Tests and commonly used Classification and Clustering evaluation techniques</p>
<p>In this post, I'll take a look at how you can compare regression models. Comparing regression models is perhaps one of the trickiest tasks to complete in the "comparing models" arena; The reason is that there are literally dozens of statistics you can calculate to compare regression models, including:</p>
<p><strong>1.…</strong></p>
<p>In my previous posts, I compared model evaluation techniques using Statistical Tools & Tests and commonly used Classification and Clustering evaluation techniques</p>
<p>In this post, I'll take a look at how you can compare regression models. Comparing regression models is perhaps one of the trickiest tasks to complete in the "comparing models" arena; The reason is that there are literally dozens of statistics you can calculate to compare regression models, including:</p>
<p><strong>1. Error measures in the estimation period (in-sample testing) or validation period (out-of-sample testing):</strong></p>
<ul>
<li>Mean Absolute Error (MAE),</li>
<li>Mean Absolute Percentage Error (MAPE),</li>
<li>Mean Error,</li>
<li>Root Mean Squared Error (RMSE),</li>
</ul>
<p><br/><strong>2. Tests on Residuals and Goodness-of-Fit:</strong></p>
<ul>
<li>Plots: actual vs. predicted value; cross correlation; residual autocorrelation; residuals vs. time/predicted values,</li>
<li>Changes in mean or variance,</li>
<li>Tests: normally distributed errors; excessive runs (e.g. of positives or negatives); outliers/extreme values/ influential observations.</li>
</ul>
<p>This list isn't exhaustive--there are many other tools, tests and plots at your disposal. Rather than discuss the statistics in detail, I chose to focus this post on comparing a few of the most popular regression model evaluation techniques and discuss when you might want to use them (or when you might not want to). The techniques listed below tend to be on the "easier to use and understand" end of the spectrum, so if you're new to model comparison it's a good place to start.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3414342046?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3414342046?profile=RESIZE_710x" class="align-center"/></a></p>
<p></p>
<p>The above picture (comparing models) was originally posted <a href="https://www.datasciencecentral.com/profiles/blogs/model-evaluation-techniques-in-one-picture" target="_blank" rel="noopener">here</a>. </p>
<p><em>Read full article <a href="https://www.datasciencecentral.com/profiles/blogs/comparing-model-evaluation-techniques-part-3-regression-models" target="_blank" rel="noopener">here</a>. </em></p>Elegant Representation of Forward and Back Propagation in Neural Networkstag:www.analyticbridge.datasciencecentral.com,2019-08-08:2004291:BlogPost:3934122019-08-08T16:29:52.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>Sometimes, you see a diagram and it gives you an ‘aha ha’ moment. Here is one representing forward propagation and back propagation in a neural network:<br></br><a href="https://storage.ning.com/topology/rest/1.0/file/get/3388408048?profile=original" rel="noopener" target="_blank"><img class="align-center" src="https://storage.ning.com/topology/rest/1.0/file/get/3388408048?profile=RESIZE_710x"></img></a></p>
<p>A brief explanation is:</p>
<ul>
<li>Using the input variables x and y, The forwardpass (left half of the figure) calculates output z as a function of x and y i.e. f(x,y)</li>
<li>The right side…</li>
</ul>
<p>Sometimes, you see a diagram and it gives you an ‘aha ha’ moment. Here is one representing forward propagation and back propagation in a neural network:<br/><a href="https://storage.ning.com/topology/rest/1.0/file/get/3388408048?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3388408048?profile=RESIZE_710x" class="align-center"/></a></p>
<p>A brief explanation is:</p>
<ul>
<li>Using the input variables x and y, The forwardpass (left half of the figure) calculates output z as a function of x and y i.e. f(x,y)</li>
<li>The right side of the figures shows the backwardpass.</li>
<li>Receiving dL/dz (the derivative of the total loss with respect to the output z) , we can calculate the individual gradients of x and y on the loss function by applying the chain rule, as shown in the figure.</li>
</ul>
<p>A more detailed explanation below from me.</p>
<p><em>Read full article <a href="https://www.datasciencecentral.com/profiles/blogs/an-elegant-way-to-represent-forward-propagation-and-back" target="_blank" rel="noopener">here</a>. </em></p>Decision Tree vs Random Forest vs Gradient Boosting Machinestag:www.analyticbridge.datasciencecentral.com,2019-08-08:2004291:BlogPost:3934102019-08-08T16:25:09.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>Decision Trees, Random Forests and Boosting are among the top 16 data science and machine learning tools used by data scientists. The three methods are similar, with a significant amount of overlap. In a nutshell:</p>
<ul>
<li>A decision tree is a simple, decision making-diagram.</li>
<li>Random forests are a large number of trees, combined (using averages or "majority rules") at the end of the process.</li>
<li>Gradient boosting machines also combine decision trees, but start the combining…</li>
</ul>
<p>Decision Trees, Random Forests and Boosting are among the top 16 data science and machine learning tools used by data scientists. The three methods are similar, with a significant amount of overlap. In a nutshell:</p>
<ul>
<li>A decision tree is a simple, decision making-diagram.</li>
<li>Random forests are a large number of trees, combined (using averages or "majority rules") at the end of the process.</li>
<li>Gradient boosting machines also combine decision trees, but start the combining process at the beginning, instead of at the end.</li>
</ul>
<p><strong>Decision Trees and Their Problems</strong></p>
<p>Decision trees are a series of sequential steps designed to answer a question and provide probabilities, costs, or other consequence of making a particular decision.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3414325027?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3414325027?profile=RESIZE_710x" class="align-center"/></a></p>
<p>They are simple to understand, providing a clear visual to guide the decision making progress. However, this simplicity comes with a few serious disadvantages, including overfitting, error due to bias and error due to variance.</p>
<ul>
<li>Overfitting happens for many reasons, including presence of noise and lack of representative instances. It's possible for overfitting with one large (deep) tree.</li>
<li>Bias error happens when you place too many restrictions on target functions. For example, restricting your result with a restricting function (e.g. a linear equation) or by a simple binary algorithm (like the true/false choices in the above tree) will often result in bias.</li>
<li>Variance error refers to how much a result will change based on changes to the training set. Decision trees have high variance, which means that tiny changes in the training data have the potential to cause large changes in the final result.</li>
</ul>
<p><strong>Random Forest vs Decision Trees</strong></p>
<p>As noted above, decision trees are fraught with problems. A tree generated from 99 data points might differ significantly from a tree generated with just one different data point. If there was a way to generate a very large number of trees, averaging out their solutions, then you'll likely get an answer that is going to be very close to the true answer.</p>
<p><em>Read full article <a href="https://www.datasciencecentral.com/profiles/blogs/decision-tree-vs-random-forest-vs-boosted-trees-explained" target="_blank" rel="noopener">here</a>. </em></p>How the Mathematics of Fractals Can Help Predict Stock Markets Shiftstag:www.analyticbridge.datasciencecentral.com,2019-07-08:2004291:BlogPost:3930292019-07-08T16:25:57.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>In financial markets, two of the most common trading strategies used by investors are the momentum and mean reversion strategies. If a stock exhibits momentum (or trending behavior as shown in the figure below), its price on the current period is more likely to increase (decrease) if it has already increased (decreased) on the previous period.</p>
<p>When the return of a stock at time t depends in some way on the return at the previous time t-1, the returns are said to be autocorrelated. In…</p>
<p>In financial markets, two of the most common trading strategies used by investors are the momentum and mean reversion strategies. If a stock exhibits momentum (or trending behavior as shown in the figure below), its price on the current period is more likely to increase (decrease) if it has already increased (decreased) on the previous period.</p>
<p>When the return of a stock at time t depends in some way on the return at the previous time t-1, the returns are said to be autocorrelated. In the momentum regime, returns are positively correlated.</p>
<p>In contrast, the price of a mean-reverting stock fluctuates randomly around its historical mean and displays a tendency to revert to it. When there is mean reversion, if the price increased (decreased) in the current period, it is more likely to decrease (increase) in the next one.</p>
<p>A section of the time series of log returns of the Apple stock (adjusted closing price), shown below, is an example of mean-reverting behavior.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3211474393?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3211474393?profile=RESIZE_710x" class="align-center"/></a></p>
<p>Note that, since the two regimes occur in different time frames (trending behavior usually occurs in larger timescales), they can, and often do, coexist.</p>
<p>In both regimes, the current price contains useful information about the future price. In fact, trading strategies can only generate profit if asset prices are either trending or mean-reverting since, otherwise, prices are following what is known as a random walk (see the animation below).</p>
<p>Read full (long) article <a href="https://www.datasciencecentral.com/profiles/blogs/how-the-mathematics-of-fractals-can-help-predict-stock-markets" target="_blank" rel="noopener">here</a>. <span>For free books about machine learning and data science, </span><a href="https://www.datasciencecentral.com/profiles/blogs/new-books-and-resources-for-dsc-members" target="_blank" rel="noopener">follow this link</a><span>. </span></p>Where’s the Love – Trends in Data Science Career Opportunitiestag:www.analyticbridge.datasciencecentral.com,2019-07-08:2004291:BlogPost:3933392019-07-08T16:18:23.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><strong><em>Summary:</em></strong><span> </span><em> The annual Burtch Works salary survey tells us a lot about which industries are using the most data scientists and the difference between higher and lower skilled data scientists. Salary increases show us whether demand is increasing, and finally we take a shot at determining which skills are most in demand.</em></p>
<p> What a difference a few years can make. We used to say that everyone loves a data scientist – and wants to be one. …</p>
<p><strong><em>Summary:</em></strong><span> </span><em> The annual Burtch Works salary survey tells us a lot about which industries are using the most data scientists and the difference between higher and lower skilled data scientists. Salary increases show us whether demand is increasing, and finally we take a shot at determining which skills are most in demand.</em></p>
<p> What a difference a few years can make. We used to say that everyone loves a data scientist – and wants to be one. That’s still true. But as data science has increasingly been adopted by businesses at all levels, industries, and geographies the nature of the opportunities available to data science have also changed.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3211466047?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3211466047?profile=RESIZE_710x" class="align-center"/></a></p>
<p>Yes it’s still one of the most interesting and rewarding career choices you can make. I wouldn’t trade it for anything. Where else can you create value out of previously unvalued data while basically predicting the future? Of course I’m talking about what customers will do, what prices or values will be, or whether something is abnormal. All the things we’re involved with on a day-to-day basis.</p>
<p>Read the full article <a href="https://www.datasciencecentral.com/profiles/blogs/where-s-the-love-trends-in-data-science-career-opportunities" target="_blank" rel="noopener">here</a>. For free books about machine learning and data science, <a href="https://www.datasciencecentral.com/profiles/blogs/new-books-and-resources-for-dsc-members" target="_blank" rel="noopener">follow this link</a>. </p>How to learn the maths of Data Science using your high school maths knowledgetag:www.analyticbridge.datasciencecentral.com,2019-06-27:2004291:BlogPost:3931012019-06-27T18:22:15.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>By Ajit Jaokar. This post is a part of my forthcoming book on Mathematical foundations of Data Science. In this post, we use the Perceptron algorithm to bridge the gap between high school maths and deep learning. </p>
<p><strong>Background</strong></p>
<p>As part of my role as course director of the Artificial Intelligence: Cloud and Edge Computing at the University of Oxford, I see more students who are familiar with programming than with mathematics.</p>
<p>They have last learnt maths…</p>
<p>By Ajit Jaokar. This post is a part of my forthcoming book on Mathematical foundations of Data Science. In this post, we use the Perceptron algorithm to bridge the gap between high school maths and deep learning. </p>
<p><strong>Background</strong></p>
<p>As part of my role as course director of the Artificial Intelligence: Cloud and Edge Computing at the University of Oxford, I see more students who are familiar with programming than with mathematics.</p>
<p>They have last learnt maths years ago at University. And then, suddenly they find that they encounter matrices, linear algebra etc when they start learning Data Science.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/3138240717?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/3138240717?profile=RESIZE_710x" class="align-center"/></a></p>
<p>Ideas they thought they would not face again after college! Worse still, in many cases, they do not know where precisely these concepts apply to data science.</p>
<p>If you consider the maths foundations needed to learn data science, you could divide them into four key areas</p>
<ul>
<li>Linear Algebra</li>
<li>Probability Theory and Statistics</li>
<li>Multivariate Calculus</li>
<li>Optimization</li>
</ul>
<p>All of these are taught (at least partially) in high schools (14 to 17 years of age). In this book, we start with these ideas and co-relate them to data science and AI.</p>
<p>Read full article <a href="https://www.datasciencecentral.com/profiles/blogs/how-to-learn-the-maths-of-data-science-using-your-high-school" target="_blank" rel="noopener">here</a>. </p>Machine Learning and Data Science Cheat Sheettag:www.analyticbridge.datasciencecentral.com,2019-06-07:2004291:BlogPost:3931312019-06-07T02:27:48.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>Originally published in 2014 and viewed more than 200,000 times, this is the oldest data science cheat sheet - the mother of all the numerous cheat sheets that are so popular nowadays. I decided to update it in June 2019. While the first half, dealing with installing components on your laptop and learning UNIX, regular expressions, and file management hasn't changed much, the second half, dealing with machine learning, was rewritten entirely from scratch. It is amazing how things changed in…</p>
<p>Originally published in 2014 and viewed more than 200,000 times, this is the oldest data science cheat sheet - the mother of all the numerous cheat sheets that are so popular nowadays. I decided to update it in June 2019. While the first half, dealing with installing components on your laptop and learning UNIX, regular expressions, and file management hasn't changed much, the second half, dealing with machine learning, was rewritten entirely from scratch. It is amazing how things changed in just five years!</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/2802101885?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/2802101885?profile=RESIZE_710x" class="align-center"/></a></p>
<p>Written for people who have never seen a computer in their life, it starts with the very beginning: buying a laptop! You can skip the first half and jump to sections 5 and 6 if you are already familiar with UNIX. This new cheat sheet will be included in my upcoming book<span> </span><em>Machine Learning: Foundations, Toolbox, and Recipes</em><span> </span>to be published in September 2019, and available (for free) to Data Science Central members exclusively. This cheat sheet is 14 pages long.</p>
<p><strong>Content</strong></p>
<p>1. Hardware</p>
<p>2. Linux environment on Windows laptop</p>
<p>3. Basic UNIX commands</p>
<p>4. Scripting languages</p>
<p>5. Python, R, Hadoop, SQL, DataViz</p>
<p>6. Machine Learning</p>
<ul>
<li>Algorithms</li>
<li>Getting started</li>
<li>Applications</li>
<li>Data sets and sample projects</li>
</ul>
<p>This new cheat sheet is available <a href="https://www.datasciencecentral.com/profiles/blogs/data-science-cheat-sheet" target="_blank" rel="noopener">here</a>. </p>7 Simple Tricks to Handle Complex Machine Learning Issuestag:www.analyticbridge.datasciencecentral.com,2019-06-04:2004291:BlogPost:3925262019-06-04T18:00:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>We propose simple solutions to important problems that all data scientists face almost every day. In short, a toolbox for the handyman, useful to busy professionals in any field.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/2760849159?profile=original" rel="noopener" target="_blank"><img class="align-center" src="https://storage.ning.com/topology/rest/1.0/file/get/2760849159?profile=RESIZE_710x"></img></a></p>
<p><strong>1. Eliminating sample size effects</strong>. <span>Many statistics, such as correlations or R-squared, depend on the sample size, making it difficult to…</span></p>
<p>We propose simple solutions to important problems that all data scientists face almost every day. In short, a toolbox for the handyman, useful to busy professionals in any field.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/2760849159?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/2760849159?profile=RESIZE_710x" class="align-center"/></a></p>
<p><strong>1. Eliminating sample size effects</strong>. <span>Many statistics, such as correlations or R-squared, depend on the sample size, making it difficult to compare values computed on two data sets of different sizes. Based on re-sampling techniques, use this easy trick, to compare apples with other apples, not with oranges. Read more <a href="https://www.datasciencecentral.com/profiles/blogs/simple-trick-to-normalize-correlations-r-squared-and-so-on" target="_blank" rel="noopener">here</a>. </span></p>
<p><span><strong>2. Sample size determination, and simple, model-free confidence intervals</strong>. We propose a generic methodology, also based on re-sampling techniques, to compute any confidence interval and for testing hypotheses, without using any statistical theory. Also, it is easy to implement, even in Excel. Read more <a href="https://www.datasciencecentral.com/profiles/blogs/modern-re-sampling-and-statistical-recipes" target="_blank" rel="noopener">here</a>. </span></p>
<p><span><strong>3. Determining the number of clusters in non-supervised clustering</strong>. This modern version of the elbow rule also tells you how strong the global optimum is, and can help you identify local optima too. It can also be automated. Read more <a href="https://www.datasciencecentral.com/profiles/blogs/how-to-automatically-determine-the-number-of-clusters-in-your-dat" target="_blank" rel="noopener">here</a>. </span></p>
<p><span><strong>4. Fixing issues in regression models when the assumptions are violated</strong>. If your data has serial correlation, unequal variances and other similar problems, this simple trick will remove the issue and allows you to perform more meaningful regressions, or to detect flaws in your data set. Read more <a href="https://www.datasciencecentral.com/profiles/blogs/simple-trick-to-remove-serial-correlation-in-regression-models" target="_blank" rel="noopener">here</a>. </span></p>
<p><strong>5. Performing joins on poor quality data</strong>. This 40 year old trick allows you to perform a join when your data is infested with typos, multiple names representing the same entity, and other similar issues. In short, it performs a fuzzy join. Read more <a href="https://www.datasciencecentral.com/forum/topics/40-year-old-trick-to-clean-data-efficiently" target="_blank" rel="noopener">here</a>. </p>
<p><strong>6. Scale invariant techniques</strong>. Sometimes, transforming your data, even changing the scale of one feature, say from meters to feet, have a dramatic impact on the results. Sometimes, you want your conclusions to be scale-independent. This trick solves this problem. Read more <a href="https://www.datasciencecentral.com/profiles/blogs/scale-invariant-clustering-and-regression" target="_blank" rel="noopener">here</a>. </p>
<p><strong>7. Blending data sets with incompatible data, adding consistency to your metrics</strong>. We are all too familiar with metrics that change over time and result in inconsistencies when comparing the past to the present, or when comparing different segments with incompatible measurements. This trick will allow you to design systems where again, apples are compared to other apples, not to oranges. Read more <a href="https://www.datasciencecentral.com/profiles/blogs/how-to-stabilize-data-to-avoid-decay-in-model-performance" target="_blank" rel="noopener">here</a>.</p>
<p><em>To not miss this type of content in the future,<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/check-out-our-dsc-newsletter">subscribe</a><span> </span>to our newsletter. For related articles from the same author, <a href="http://www.datasciencecentral.com/profiles/blogs/my-data-science-machine-learning-and-related-articles" target="_blank" rel="noopener">click here</a><span> </span>or visit<span> </span><a href="http://www.vincentgranville.com/" target="_blank" rel="noopener">www.VincentGranville.com</a>. Follow me on<span> </span><a href="https://www.linkedin.com/in/vincentg/" target="_blank" rel="noopener">on LinkedIn</a>, or visit my old web page<span> </span><a href="http://www.datashaping.com">here</a>.</em></p>
<p><span style="font-size: 12pt;"><strong>Resources from our sponsors</strong></span></p>
<ul>
<li dir="ltr"><a href="https://dsc.news/2WFHJ0q" target="_blank" rel="noopener">The State of Data Preparation in 2019</a> - June 25</li>
<li dir="ltr"><a href="https://dsc.news/2JWn6XR" target="_blank" rel="noopener">AI in Action: Real-time Anomaly Detection</a> - June 18</li>
<li dir="ltr"><a href="https://dsc.news/2GZmBtn" target="_blank" rel="noopener">Balancing AI Endeavors with Analytic Talent</a> - DSC Podcast</li>
</ul>
<p></p>Gentle Approach to Linear Algebra, with Machine Learning Applicationstag:www.analyticbridge.datasciencecentral.com,2019-05-29:2004291:BlogPost:3925052019-05-29T03:00:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><span>This simple introduction to matrix theory offers a refreshing perspective on the subject. Using a basic concept that leads to a simple formula for the power of a matrix, we see how it can solve time series, Markov chains, linear regression, data reduction, principal components analysis (PCA) and other machine learning problems. These problems are usually solved with more advanced matrix calculus, including eigenvalues, diagonalization, generalized inverse matrices, and other types of…</span></p>
<p><span>This simple introduction to matrix theory offers a refreshing perspective on the subject. Using a basic concept that leads to a simple formula for the power of a matrix, we see how it can solve time series, Markov chains, linear regression, data reduction, principal components analysis (PCA) and other machine learning problems. These problems are usually solved with more advanced matrix calculus, including eigenvalues, diagonalization, generalized inverse matrices, and other types of matrix normalization. Our approach is more intuitive and thus appealing to professionals who do not have a strong mathematical background, or who have forgotten what they learned in math textbooks. It will also appeal to physicists and engineers. Finally, it leads to simple algorithms, for instance for matrix inversion. The classical statistician or data scientist will find our approach somewhat intriguing. </span></p>
<p><span><a href="https://storage.ning.com/topology/rest/1.0/file/get/2716936013?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/2716936013?profile=RESIZE_710x" class="align-center"/></a></span></p>
<p><strong>Content</strong></p>
<p>1. Power of a matrix</p>
<p>2. Examples, Generalization, and Matrix Inversion</p>
<ul>
<li>Example with a non-invertible matrix</li>
<li>Fast computations</li>
</ul>
<p>3. Application to Machine Learning Problems</p>
<ul>
<li>Markov chains</li>
<li>Time series</li>
<li>Linear regression</li>
</ul>
<p><span><a href="https://www.datasciencecentral.com/profiles/blogs/new-approach-to-linear-algebra-in-machine-learning" target="_blank" rel="noopener">Read the full article</a>. </span></p>New Book: Classification and Regression In a Weekend (in Python)tag:www.analyticbridge.datasciencecentral.com,2019-05-17:2004291:BlogPost:3927002019-05-17T00:24:08.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>We have added a new free book in our selection exclusively for DSC members. See the first entry below, to get started with machine learning with Python.</p>
<p><strong>1. Book: Classification and Regression In a Weekend</strong></p>
<p>This tutorial began as a series of weekend workshops created by Ajit Jaokar and Dan Howarth. The idea was to work with a specific (longish) program such that we explore as much of it as possible in one weekend. This book is an attempt to take this idea online.…</p>
<p>We have added a new free book in our selection exclusively for DSC members. See the first entry below, to get started with machine learning with Python.</p>
<p><strong>1. Book: Classification and Regression In a Weekend</strong></p>
<p>This tutorial began as a series of weekend workshops created by Ajit Jaokar and Dan Howarth. The idea was to work with a specific (longish) program such that we explore as much of it as possible in one weekend. This book is an attempt to take this idea online. The best way to use this book is to work with the Python code as much as you can. The code has comments. But you can extend the comments by the concepts explained here.</p>
<p>The table of contents is available<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/free-book-classification-and-regression-in-a-weekend" target="_blank" rel="noopener">here</a>. The book can be accessed<span> </span><a href="https://www.datasciencecentral.com/page/free-books-1" target="_blank" rel="noopener">here</a><span> </span>(members only.)</p>
<p></p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/2626374029?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/2626374029?profile=RESIZE_710x" class="align-center"/></a></p>
<p><strong>2. Book: Enterprise AI - An Application Perspective</strong> </p>
<p>Enterprise AI: An applications perspective takes a use case driven approach to understand the deployment of AI in the Enterprise. Designed for strategists and developers, the book provides a practical and straightforward roadmap based on application use cases for AI in Enterprises. The authors (Ajit Jaokar and Cheuk Ting Ho) are data scientists and AI researchers who have deployed AI applications for Enterprise domains. The book is used as a reference for Ajit and Cheuk's new course on Implementing Enterprise AI.</p>
<p>The table of content is available<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/free-ebook-enterprise-ai-an-applications-perspective" target="_blank" rel="noopener">here</a>. The book can be accessed<span> </span><a href="https://www.datasciencecentral.com/page/free-books-1" target="_blank" rel="noopener">here</a><span> </span>(members only.)</p>
<p><strong>3. Book: Applied Stochastic Processes</strong></p>
<p>Full title:<span> </span><em>Applied Stochastic Processes, Chaos Modeling, and Probabilistic Properties of Numeration Systems</em>. Published June 2, 2018. Author: Vincent Granville, PhD. (104 pages, 16 chapters.)</p>
<p>This book is intended to professionals in data science, computer science, operations research, statistics, machine learning, big data, and mathematics. In 100 pages, it covers many new topics, offering a fresh perspective on the subject. It is accessible to practitioners with a two-year college-level exposure to statistics and probability. The compact and tutorial style, featuring many applications (Blockchain, quantum algorithms, HPC, random number generation, cryptography, Fintech, web crawling, statistical testing) with numerous illustrations, is aimed at practitioners, researchers and executives in various quantitative fields.</p>
<p>New ideas, advanced topics, and state-of-the-art research are discussed in simple English, without using jargon or arcane theory. It unifies topics that are usually part of different fields (data science, operations research, dynamical systems, computer science, number theory, probability) broadening the knowledge and interest of the reader in ways that are not found in any other book. This short book contains a large amount of condensed material that would typically be covered in 500 pages in traditional publications. Thanks to cross-references and redundancy, the chapters can be read independently, in random order.</p>
<p>The table of content is available<span> </span><a href="https://www.datasciencecentral.com/profiles/blogs/fee-book-applied-stochastic-processes" target="_blank" rel="noopener">here</a>. The book (PDF) can be accessed<span> </span><a href="https://www.datasciencecentral.com/page/free-books-1" target="_blank" rel="noopener">here</a><span> </span>(members only.) </p>Confidence Intervals Without Pain, with Exceltag:www.analyticbridge.datasciencecentral.com,2019-05-09:2004291:BlogPost:3924682019-05-09T17:30:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>We propose a simple model-free solution to compute any confidence interval and to extrapolate these intervals beyond the observations available in your data set. In addition we propose a mechanism to sharpen the confidence intervals, to reduce their width by an order of magnitude. The methodology works with any estimator (mean, median, variance, quantile, correlation and so on) even when the data set violates the classical requirements necessary to make traditional statistical techniques…</p>
<p>We propose a simple model-free solution to compute any confidence interval and to extrapolate these intervals beyond the observations available in your data set. In addition we propose a mechanism to sharpen the confidence intervals, to reduce their width by an order of magnitude. The methodology works with any estimator (mean, median, variance, quantile, correlation and so on) even when the data set violates the classical requirements necessary to make traditional statistical techniques work. In particular, our method also applies to observations that are auto-correlated, non identically distributed, non-normal, and even non-stationary. </p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/2383098025?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/2383098025?profile=RESIZE_710x" class="align-center"/></a></p>
<p>No statistical knowledge is required to understand, implement, and test our algorithm, nor to interpret the results. Its robustness makes it suitable for black-box, automated machine learning technology. It will appeal to anyone dealing with data on a regular basis, such as data scientists, statisticians, software engineers, economists, quants, physicists, biologists, psychologists, system and business analysts, and industrial engineers. </p>
<p>In particular, we provide a confidence interval (CI) for the width of confidence intervals without using Bayesian statistics. The width is modeled as<span> </span><em>L</em><span> </span>=<span> </span><em>A</em><span> </span>/<span> </span><em>n^B</em> and we compute, using Excel alone, a 95% CI for<span> </span><em>B</em><span> </span>in the classic case where<span> </span><em>B</em><span> </span>= 1/2. We also exhibit an artificial data set where<span> </span><em>L</em><span> </span>= 1 / (log<span> </span><em>n</em>)^Pi. Here<span> </span><em>n</em><span> </span>is the sample size.</p>
<p><span>Despite the apparent simplicity of our approach, we are dealing here with martingales. But you don't need to know what a martingale is to understand the concepts and use our methodology. </span></p>
<p><a href="https://www.datasciencecentral.com/profiles/blogs/confidence-intervals-without-pain" target="_blank" rel="noopener">Read the full article here</a>.</p>Re-sampling: Amazing Results and Applicationstag:www.analyticbridge.datasciencecentral.com,2019-05-04:2004291:BlogPost:3925562019-05-04T18:30:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>This crash course features a new fundamental statistics theorem -- even more important than the central limit theorem -- and a new set of statistical rules and recipes. We discuss concepts related to determining the optimum sample size, the optimum<span> </span><em>k</em><span> </span>in<span> </span><em>k</em>-fold cross-validation, bootstrapping, new re-sampling techniques, simulations, tests of hypotheses, confidence intervals, and statistical inference using a unified, robust, simple…</p>
<p>This crash course features a new fundamental statistics theorem -- even more important than the central limit theorem -- and a new set of statistical rules and recipes. We discuss concepts related to determining the optimum sample size, the optimum<span> </span><em>k</em><span> </span>in<span> </span><em>k</em>-fold cross-validation, bootstrapping, new re-sampling techniques, simulations, tests of hypotheses, confidence intervals, and statistical inference using a unified, robust, simple approach with easy formulas, efficient algorithms and illustration on complex data.</p>
<p>Little statistical knowledge is required to understand and apply the methodology described here, yet it is more advanced, more general, and more applied than standard literature on the subject. The intended audience is beginners as well as professionals in any field faced with data challenges on a daily basis. This article presents statistical science in a different light, hopefully in a style more accessible, intuitive, and exciting than standard textbooks, and in a compact format yet covering a large chunk of the traditional statistical curriculum and beyond.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/2301106250?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/2301106250?profile=RESIZE_710x" class="align-center"/></a></p>
<p>In particular, the concept of<span> </span><em>p</em>-value is not explicitly included in this tutorial. Instead, following the new trend after the recent <em>p</em>-value debacle (addressed<span> </span>by the president of the American Statistical Association), it is replaced with a range of values computed on multiple sub-samples. </p>
<p>Our algorithms are suitable for inclusion in black-box systems, batch processing, and automated data science. Our technology is data-driven and model-free. Finally, our approach to this problem shows the contrast between the data science unified, bottom-up, and computationally-driven perspective, and the traditional top-down statistical analysis consisting of a collection of disparate results that emphasizes the theory. </p>
<p><a href="https://www.datasciencecentral.com/profiles/blogs/modern-re-sampling-and-statistical-recipes" target="_blank" rel="noopener">Read the full article here</a>.</p>
<p><span><strong>Contents</strong></span></p>
<p><span>1. Re-sampling and Statistical Inference</span></p>
<ul>
<li><span>Main Result</span></li>
<li><span>Sampling with or without Replacement</span></li>
<li><span>Illustration</span></li>
<li><span>Optimum Sample Size </span></li>
<li><span>Optimum <em>K</em> in <em>K</em>-fold Cross-Validation</span></li>
<li><span>Confidence Intervals, Tests of Hypotheses</span></li>
</ul>
<p><span>2. Generic, All-purposes Algorithm</span></p>
<ul>
<li><span>Re-sampling Algorithm with Source Code</span></li>
<li><span>Alternative Algorithm</span></li>
<li><span>Using a Good Random Number Generator</span></li>
</ul>
<p><span>3. Applications</span></p>
<ul>
<li><span>A Challenging Data Set</span></li>
<li><span>Results and Excel Spreadsheet</span></li>
<li><span>A New Fundamental Statistics Theorem</span></li>
<li><span>Some Statistical Magic</span></li>
<li><span>How does this work?</span></li>
<li><span>Does this contradict entropy principles?</span></li>
</ul>
<p><span>4. Conclusions</span></p>Some Fun with Gentle Chaos, the Golden Ratio, and Stochastic Number Theorytag:www.analyticbridge.datasciencecentral.com,2019-04-25:2004291:BlogPost:3923832019-04-25T13:30:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p>So many fascinating and deep results have been written about the number (1 + SQRT(5)) / 2 and its related sequence - the Fibonacci numbers - that it would take years to read all of them. This number has been studied both for its applications (population growth, architecture) and its mathematical properties, for over 2,000 years. It is still a topic of active research.…</p>
<p></p>
<p>So many fascinating and deep results have been written about the number (1 + SQRT(5)) / 2 and its related sequence - the Fibonacci numbers - that it would take years to read all of them. This number has been studied both for its applications (population growth, architecture) and its mathematical properties, for over 2,000 years. It is still a topic of active research.</p>
<p><a href="https://storage.ning.com/topology/rest/1.0/file/get/2197458362?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/2197458362?profile=RESIZE_710x" class="align-center"/></a></p>
<p style="text-align: center;"><em>Lag-1 auto-correlation in digit distribution of good seeds, for b-processes</em></p>
<p>I show here how I used the golden ratio for a new number guessing game (to generate chaos and randomness in ergodic time series) as well as new intriguing results, in particular:</p>
<ul>
<li>Proof that the<span> </span><a href="http://mathworld.wolfram.com/RabbitConstant.html" target="_blank" rel="noopener">rabbit constant</a><span> </span>it is not normal in any base; this might be the first instance of a non-artificial mathematical constant for which the normalcy status is formally established.</li>
<li>Beatty sequences, pseudo-periodicity, and infinite-range auto-correlations for the digits of irrational numbers in the numeration system derived from perfect stochastic processes</li>
<li>Properties of multivariate<span> </span><em>b</em>-processes, including integer or non-integer bases.</li>
<li>Weird behavior of auto-correlations for the digits of normal numbers (good seeds) in the numeration system derived from stochastic<span> </span><em>b</em>-processes</li>
<li>A strange recursion that generates all the digits of the rabbit constant</li>
</ul>
<p><strong>Content of this article</strong></p>
<p>1. Some Definitions</p>
<p>2. Digits Distribution in b-processes</p>
<p>3. Strange Facts and Conjectures about the Rabbit Constant</p>
<p>4. Gaming Application</p>
<ul>
<li>De-correlating Using Mapping and Thinning Techniques</li>
<li>Dissolving the Auto-correlation Structure Using Multivariate b-processes</li>
</ul>
<p>5. Related Articles</p>
<p><em>Read full articles, <a href="https://www.datasciencecentral.com/profiles/blogs/some-fun-with-the-golden-ratio-time-series-and-number-theory" target="_blank" rel="noopener">here</a>. </em></p>Causality – The Next Most Important Thing in AI/MLtag:www.analyticbridge.datasciencecentral.com,2019-04-25:2004291:BlogPost:3923012019-04-25T01:30:00.000ZVincent Granvillehttps://www.analyticbridge.datasciencecentral.com/profile/VincentGranville
<p><strong><em>Summary:</em></strong><em> Finally there are tools that let us transcend ‘correlation is not causation’ and<span> </span><strong>identify true causal factors</strong><span> </span>and their relative strengths in our models. This is what prescriptive analytics was meant to be.</em></p>
<p> <a href="https://storage.ning.com/topology/rest/1.0/file/get/2132982369?profile=original" rel="noopener" target="_blank"><img class="align-center" src="https://storage.ning.com/topology/rest/1.0/file/get/2132982369?profile=RESIZE_710x" width="400"></img></a></p>
<p>Just when I thought we’d figured it all out,…</p>
<p><strong><em>Summary:</em></strong><em> Finally there are tools that let us transcend ‘correlation is not causation’ and<span> </span><strong>identify true causal factors</strong><span> </span>and their relative strengths in our models. This is what prescriptive analytics was meant to be.</em></p>
<p> <a href="https://storage.ning.com/topology/rest/1.0/file/get/2132982369?profile=original" target="_blank" rel="noopener"><img src="https://storage.ning.com/topology/rest/1.0/file/get/2132982369?profile=RESIZE_710x" width="400" class="align-center"/></a></p>
<p>Just when I thought we’d figured it all out, something comes along to make me realize I was wrong. And that something in AI/ML is as simple as realizing that everything we’ve done so far is just curve-fitting. Whether it’s a scoring model or a CNN to recognize cats, it’s all about association; reducing the error between the distribution of two data sets. </p>
<p>What we should have had our eye on is CAUSATION. How many times have you repeated ‘correlation is not causation’. Well it seems we didn’t stop to ask how AI/ML can actually determine causality. And now it turns out it can.</p>
<p>But to achieve an understanding of causality requires us to cast loose of many of the common tools and techniques we’ve been trained to apply and to understand the data from a wholly new perspective. Fortunately the constant advance of research and ever increasing compute capability now makes it possible for us to use new relatively friendly tools to measure causality. </p>
<p>However, make no mistake, you’ll need to master the concepts of causal data analysis or you will most likely misunderstand what these tools can do.</p>
<p><em>Read the full article by Bill Vorhies, <a href="https://www.datasciencecentral.com/profiles/blogs/causality-the-next-most-important-thing-in-ai-ml" target="_blank" rel="noopener">here</a>. </em></p>