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…

For decades, the intelligence community has been collecting and analyzing information to produce timely and actionable insights for intelligence consumers. But as the amount of information collected increases, analysts are facing new challenges in terms of data processing and analysis. In this article, we explore the possibilities that graph technology is offering for intelligence analysis.

Intelligence collection and analysis in the age of…

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…

This picture speaks more than words. It explains the concept or false positive and false negative, that is, what is referred to by statisticians as Type I and Type II errors.

Other great pictures summarizing data science and statistical concepts, can be found…

There is no need to get confused with multiple linear regression, generalized linear model or general linear methods. The general linear model or multivariate regression model is a statistical linear model and is written as Y = XB + U.

Usually, a linear model includes a number of different statistical models such as ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The GLM is a generalization of multiple…

Here we discuss an application of HPC (not high performance computing, instead high precision computing, which is a special case of HPC)  applied to dynamical systems such as  the logistic map in chaos theory. defined as X(k) = 4 X(k) (1 - X(k-1)). 

For all these systems, the loss of precision propagates exponentially, to the point that after 50 iterations, all generated values are completely wrong. Tons of articles have been written on this subject - none of them acknowledging the…

One of the first lessons you’ll receive in machine learning is that there are two broad categories: supervised and unsupervised learning. Supervised learning is usually explained as the one to which you provide the correct answers, training data, and the machine learns the patterns to apply to new data. Unsupervised learning is (apparently) where the machine figures out the correct answer on its own.

Supposedly, unsupervised learning can discover something new that has not been found…

Stochastic Signal Analysis is a field of science concerned with the processing, modification and analysis of (stochastic) signals.

Anyone with a background in Physics or Engineering knows to some degree about signal analysis techniques, what these technique are and how they can be used to analyze, model and classify signals.

Data Scientists coming from a different fields, like Computer Science or Statistics, might not be aware of the analytical power these techniques bring with…

It is crucial to ask the right questions and/or understand the problem, prior to beginning data analysis. Below is a list of 20 questions you need to ask before delving into analysis:

1. Who is the…

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…

PHP, known as the most popular server-side scripting language in the world, has evolved a lot since the first inline code snippets appeared in static HTML files.

These days developers need to build complex websites and web apps, and above a certain complexity level it can take too much time and hassle to always start from scratch, hence came the need for a more structured natural way of development. PHP frameworks provide developers with an adequate solution for that.

Choosing…

Mathematical Olympiads are popular among high school students. However, there is nothing similar for college students, except maybe IMC. Even IMC is not popular. It focuses mostly on the same kind of problems as high school Olympiads, and you can not participate if you are over 23 years old. In addition, it is organized by country, as opposed to globally, thus favoring countries with a large population. Topics such as…

Predictive analytics uses current and historical data in order to determine the probability of a particular outcome. This is a particularly powerful approach when it is applied to medical diagnosis. In an effort to reduce misdiagnosis, historical data of former patient’s symptoms may be applied to the assessment of a new patient.

While doctors are the ultimate experts and decision-makers, using predictive analytics as a means of establishing precedent for…

This article is intended for practitioners who might not necessarily be statisticians or statistically-savvy. The mathematical level is kept as simple as possible, yet I present an original, simple approach to test for randomness, with an interesting application to illustrate the methodology. This material is not something usually discussed in textbooks or classrooms (even for statistical students), offering a fresh perspective, and out-of-the-box tools that are useful in many contexts, as…

Today, enterprises recognize the critical value of advanced analytics within the organization and they are implementing data democratization initiatives. As these initiatives evolve, new roles emerge in the organization. The newest of these analysis-related roles is the 'analytics translator'. As the enterprise considers the relevance of this new role within the business, it is important to understand the responsibilities of an Analytics…

The concept of Clickless Analytics is one that will be happily embraced by business users and by the business enterprise. The reason is simple! Clickless Analytics allows users to find and analyze information without specialized skills, by using natural language.

In this, the first of a three-part series we discuss Clickless Analytics and how it can simplify user adoption of augmented analytics.

What is Clickless Analytics?

Clickless Analytics…

The Waring conjecture - actually a problem associated with a number of conjectures, many now being solved - is one of the most fascinating mathematical problems. This article covers new aspects of this problem, with a generalization and new conjectures, some with a tentative solution, and a new framework to tackle the problem. Yet it is written in simple English and accessible to the layman.

I also review a number of famous related mathematical conjectures, including one with a $1…

Summary:  Here are our 6 predictions for data science, machine learning, and AI for 2018.  Some are fast track and potentially disruptive, some take the hype off over blown claims and set realistic expectations for the coming year.

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, and what things won’t in the coming year for data science, machine…

Introduction:

In this post, we learn about building a basic search engine or document retrieval system using Vector space model. This use case is widely used in information retrieval systems. Given a set of documents and search term(s)/query we need to retrieve relevant documents that are similar to the search query. 

Problem statement:

The problem statement explained above is represented as in below image. …