Author: Vincent Granville

Vincent Granville is a pioneering data scientist and machine learning expert, founder of, co-founder of Data Science Central (acquired by TechTarget in 2020), former VC-funded executive, author and patent owner. Vincent's past corporate experience includes Visa, Wells Fargo, eBay, NBC, Microsoft, CNET. Vincent is also a former post-doc at Cambridge University, and the National Institute of Statistical Sciences (NISS). Vincent published in Journal of Number Theory, Journal of the Royal Statistical Society (Series B), and IEEE Transactions on Pattern Analysis and Machine Intelligence. He is also the author of multiple books, available here. He lives in Washington state, and enjoy doing research on stochastic processes, dynamical systems, experimental math and probabilistic number theory.
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High-value AI and Machine Learning Certifications Under $50

If you thought certifications and training for advanced AI/Machine Learning specializations was out of reach due to the steep price, prerequisites and time commitment, read on. now offers two paths to certification: Automatic qualification for busy professionals with 2+ years of relevant industry experience and fluent in analyzing data. Read more here to see […]

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Featured Posts Machine Learning Statistical Science Stochastic Systems Synthetic Data Time Series

A Synthetic Stock Exchange Played with Real Money

Not only that, but you can predict — more precisely compute with absolute certainty — what the value of any stock will be tomorrow. Transaction fees are well below 0.05% and the market, at least in the version presented here, is fair: in other words, a zero-sum game if you play by luck. If instead […]

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Generating and Videolizing Agglomerative Processes

This short article explains how to efficiently simulate the evolution of agglomerative processes, and visualize their behavior with data animations. I use a generic, simple model for illustration purposes: atoms, initially consisting of one electron, collide and merge over time, with a pre-specified maximum number of electrons per atom: the maximum limit. Given enough time, […]

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Massively Speed-Up your Learning Algorithm, with Stochastic Thinning

Dramatically Speed-Up your Learning Algorithm, with Stochastic Thinning. Includes use case, Python code, regression and neural network illustrations.

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Smart Grid Search for Faster Hyperparameter Tuning

The objective is two-fold. First, I introduce a 2-parameter generalization of the discrete geometric and zeta distributions. Indeed, a combination of both. It allows you to simultaneously match the variance and mean in observed data, thanks to the two parameters p and α. To the contrary, each distribution taken separately only has one parameter, and […]

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New Book: Gentle Introduction To Chaotic Dynamical Systems

In less than 100 pages, the book covers all important topics about discrete chaotic dynamical systems and related time series and stochastic processes, ranging from introductory to advanced, in one and two dimensions. State-of-the art methods and new results are presented in simple English. Yet, some mathematical proofs appear for the first time in this […]

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Feature Clustering: A Simple Solution to Many Machine Learning Problems

Feature clustering is an unsupervised machine learning technique to separate the features of a dataset into homogeneous groups. In short, it is a clustering procedure, but performed on the features rather than on the observations. Such techniques often rely on a similarity metric, measuring how close two features are to each other. In this article, […]

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Data Synthetization: enhanced GANs vs Copulas

Using case studies, I compare generative adversarial networks (GANs) with copulas to synthesize tabular data. I discuss back-end and front-end improvements to help GANs better replicate the correlation structure present in the real data. Likewise, I discuss methods to further improve copulas, including transforms, the use of separate copulas for each population segment, and parametric […]

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Data Synthetization Explained in One Picture

The diagram is organized as follows. Dashed blue lines are associated to GANs (generative adversarial networks), where the goal is to produce a sequence of synthetic datasets that get better and better at mimicking the structure present in the real data, over successive iterations. The diagram features 5 such iterations, with the synthetized datasets denoted […]

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Introduction to Discrete Chaotic Dynamical Systems

Entitled “Introduction to Discrete Chaotic Dynamical Systems”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. This article is an extract from my book “Gentle Introduction to Chaotic Dynamical Systems”, available here. This is chapter 2 of my upcoming book on dynamical systems and related stochastic processes, expected to be […]

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