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This is another interesting problem, off-the-beaten-path. It ends up with a formula to compute the integral of a function, based on its derivatives solely.

For simplicity, I'll start with some notations used in the context of matrix theory, familiar to everyone: T(*f*) = *g*, where *f* and *g* are vectors, and T a square matrix. The notation T(*f*) represents the product between the matrix T, and the vector *f*. Now, imagine that the…

Added by Vincent Granville on February 3, 2019 at 5:30pm — 1 Comment

First days after the celebration of the New Year is the time when looking back we can analyze our actions, promises and draw conclusions whether our predictions and expectations came true. As 2018 came to its end, it is perfect time to analyze it and to set trends for the next year. The amount of data generated every minute is enormous. Therefore new approaches, techniques, and solutions have been developed.…

ContinueAdded by Vincent Granville on January 29, 2019 at 11:43am — No Comments

Extract from the upcoming Monday newsletter published by Data Science Central. Previous editions can be found here. The contribution flagged with a + is our selection for the picture of the week. To subscribe, …

ContinueAdded by Vincent Granville on January 27, 2019 at 3:20pm — No Comments

Extract from the upcoming Monday newsletter published by Data Science Central. Previous editions can be found here. The contribution flagged with a + is our selection for the picture of the week. To subscribe, …

ContinueAdded by Vincent Granville on January 20, 2019 at 12:15pm — No Comments

This article was written by Ajit Joakar.

In this longish post, I have tried to explain Deep Learning starting from familiar ideas like machine learning. This approach forms a part of my forthcoming book. I have used this approach in my teaching. It is based on ‘learning by exception,' i.e. understanding one concept and it’s limitations and then understanding how the subsequent concept…

ContinueAdded by Vincent Granville on January 16, 2019 at 9:48am — No Comments

*Summary:** Here are our 5 predictions for data science, machine learning, and AI for 2019. We also take a look back at last year’s predictions to see how we did.*

It’s that time of year again when we do a look back in order to offer a look forward. What trends will speed up, what things will actually happen,…

ContinueAdded by Vincent Granville on December 20, 2018 at 6:30pm — No Comments

We are in the process of writing and adding new material (compact eBooks) exclusively available to our members, and written in simple English, by world leading experts in AI, data science, and machine learning. In the upcoming months, the following will be added:

- The Machine Learning Coding Book
- Off-the-beaten-path Statistics and Machine Learning Techniques
- Encyclopedia of Statistical Science
- Original Math, Stat and Probability Problems - with…

Added by Vincent Granville on December 1, 2018 at 6:26pm — No Comments

*Summary:** This may be the golden age of deep learning but a lot can be learned by looking at where deep neural nets aren’t working yet. This can be a guide to calming the hype. It can also be a roadmap to future opportunities once these barriers are behind us. The full article is accessible here, below is a…*

Added by Vincent Granville on November 21, 2018 at 10:00am — No Comments

**Summary**: There are several approaches to reducing the cost of training data for AI, one of which is to get it for free. Here are some excellent sources.

Recently we wrote that training data (not just data in general) is the new oil. It’s the difficulty and expense of acquiring labeled training data that causes many deep learning projects to be abandoned.

It also matters a great deal just how good you want your new deep learning app to be. A 2016 study by…

ContinueAdded by Vincent Granville on October 3, 2018 at 10:49am — No Comments

*Guest blog post by Zied HY. Zied is Senior Data Scientist at Capgemini Consulting. He is specialized in building predictive models utilizing both traditional statistical methods (Generalized Linear Models, Mixed Effects Models, Ridge, Lasso, etc.) and modern machine learning techniques (XGBoost, Random Forests, Kernel Methods, neural networks, etc.). Zied run some workshops for university students (ESSEC, HEC, Ecole polytechnique) interested in Data…*

Added by Vincent Granville on September 21, 2018 at 12:00pm — No Comments

*Summary:** The role of Analytics Translator was recently identified by McKinsey as the most important new role in analytics, and a key factor in the failure of analytic programs when the role is absent.*

The role of Analytics Translator was recently identified by McKinsey as the most important new role in…

ContinueAdded by Vincent Granville on September 12, 2018 at 5:30pm — No Comments

You won't learn this in textbooks, college classes, or data camps. Some of the material in this article is very advanced yet presented in simple English, with an Excel implementation for various statistical tests, and no arcane theory, jargon, or obscure theorems. It has a number of applications, in finance in particular. This article covers several topics under a unified approach, so it was not easy to find a title. In particular, we discuss:

- When the central limit theorem…

Added by Vincent Granville on September 10, 2018 at 9:07pm — No Comments

Full title: *Applied Stochastic Processes, Chaos Modeling, and Probabilistic Properties of Numeration Systems*. Published June 2, 2018. Author: Vincent Granville, PhD. (104 pages, 16 chapters.)

This book is intended for 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…

ContinueAdded by Vincent Granville on September 8, 2018 at 11:16am — No Comments

Join the largest community of machine learning (ML), deep learning, AI, data science, business analytics, BI, operations research, mathematical and statistical professionals: Sign up here. If instead, you are only interested in receiving our newsletter, you can subscribe here. There is no…

ContinueAdded by Vincent Granville on September 8, 2018 at 11:14am — No Comments

Let us consider the following equation:

Prove that

*x*= log(Pi) = 1.14472988584... is a very good approximation of a solution, up to 10 digits.- Using high performance computing or other means, prove that it is…

Added by Vincent Granville on August 30, 2018 at 11:00pm — 1 Comment

*Here is Rafael Knuth's story.*

In 1992, I entered the job market and landed a job as an advertising copywriter for McDonald’s. I was tasked with ideating radio, TV and print advertisements to curb burger, fries and soft drink sales. The internet did not exist in the public domain back then, and my first laptop was actually a mechanical type writer. Around 2000, I became a freelance…

ContinueAdded by Vincent Granville on August 30, 2018 at 5:00pm — No Comments

Here is our selection of recently featured articles and resources:

**Featured Resources and Technical Contributions**

Added by Vincent Granville on August 25, 2018 at 6:45pm — No Comments

For a person being from a non-statistical background the most confusing aspect of statistics, are always the fundamental statistical tests, and when to use which. This blog post is an attempt to mark out the difference between the most common tests, the use of null value hypothesis in these tests and outlining the conditions under which a particular test should be used.

**Null Hypothesis and Testing**

Before we venture on the difference between different tests, we…

ContinueAdded by Vincent Granville on August 22, 2018 at 11:00am — No Comments

I have been involved in teaching Data Science for a few years now (Oxford University - Data Science for Internet of Things and also online). Over the years, I have tried to improve my teaching .. and adopt ideas from other domains into my teaching

One such technique is Deliberate practice a technique which probably originated in the former Soviet Union to train world class athletes. Deliberate practise is also used in learning complex skills like playing the violin – which require…

ContinueAdded by Vincent Granville on August 21, 2018 at 5:01pm — No Comments

Here is our selection of featured articles and resources posted recently:

**Resources**

- Solving Image Processing Problems with Python - Part 1
- Getting Started with NLP: Simple Topic Modeling in…

Added by Vincent Granville on August 18, 2018 at 8:52pm — No Comments

- Statistics for Data Science in One Picture
- On Being a 50 Year Old Data Scientist
- Variance, Attractors and Behavior of Chaotic Statistical Systems
- A Lesson in Using NLP for Hidden Feature Extraction
- New Family of Generalized Gaussian Distributions
- 10 Machine Learning Methods that Every Data Scientist Should Know
- 10 Visualizations Every Data Scientist Should Know

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