#### A Synthetic Stock Exchange Played with Real Money

- Vincent Granville
- May 15, 2023

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 […]

Read More#### Smart Grid Search for Faster Hyperparameter Tuning

- Vincent Granville
- March 30, 2023

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 […]

Read More#### New Book: Gentle Introduction To Chaotic Dynamical Systems

- Vincent Granville
- March 21, 2023

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 […]

Read More#### Random Walks, Brownian Motions, and Related Stochastic Processes

- Vincent Granville
- February 11, 2023

Entitled “Random Walks, Brownian Motions, and Related Stochastic Processes”, 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. In about 15 pages, this scratch course covers a lot more material than expected in such […]

Read More#### Military-grade Fast Random Number Generator Based on Quadratic Irrationals

- Vincent Granville
- December 13, 2022

This article is an extract from my book “Synthetic Data and Generative AI”, available here. There are very few serious articles in the literature dealing with digits of irrational numbers to build a pseudo-random number generator (PRNG). It seems that this idea was abandoned long ago due to the computational complexity and the misconception that such […]

Read More#### Machine Learning Cloud Regression: The Swiss Army Knife of Optimization

- Vincent Granville
- August 25, 2022

Entitled “Machine Learning Cloud Regression: The Swiss Army Knife of Optimization”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. Also discussed in details with Python code in chapter 1 in my book “Intuitive Machine Learning and Explainable AI”, available here. Many machine learning and statistical techniques exist as seemingly unrelated, […]

Read More#### Weird Random Walks: Synthetizing, Testing and Leveraging Quasi-randomness

- Vincent Granville
- August 11, 2022

Entitled “Weird Random Walks: Synthetizing, Testing and Leveraging Quasi-randomness”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. I discuss different types of synthetized random walks that are almost perfectly random, in one and two dimensions. Besides the theoretical interest, it provides new modeling tools, especially for physicists, engineers, natural […]

Read More#### New Perspective on the Riemann Hypothesis

- Vincent Granville
- July 29, 2022

Entitled “New Perspective on the Riemann Hypothesis”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. In about 10 pages (plus Python code, exercises and figures), this article constitutes a scratch course on the subject. It covers a large range of topics, both recent as well as unpublished, in a […]

Read More#### Synthetic Data in Machine Learning: What, Why, How?

- Vincent Granville
- July 24, 2022

In this episode, Nicolai Baldin (CEO) and Simon Swan (Machine Learning Lead) of Synthesized are welcoming the founder of Data Science Central and MLTechniques.com Vincent Granville to discuss synthetic data generation, share secrets about Machine Learning on synthetic data, key challenges with synthetic data, and using generative models to solve issues related to fairness and […]

Read More#### 2nd Edition of My Book Now Published, with Python Code

- Vincent Granville
- June 23, 2022

The book covers supervised classification, including fractal classification, as well as unsupervised clustering, using an innovative approach. Datasets are first mapped onto an image, then processed using image filtering techniques. I discuss the analogy with neural networks, comparing very deep but sparse neural networks, with standard networks. Sponsors The free distribution of our content would […]

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