#### 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 It covers a large range of topics, both recent as well as unpublished, in a […]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#### Detecting Subtle Departures from Randomness

- Vincent Granville
- July 23, 2022

Entitled “Detecting Subtle Departures from Randomness”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. Figure 1 below shows two plots arising from two different, non-periodic pseudo-random sequences of +1 and -1 in about equal proportions, distributed seemingly randomly. The left one is associated to prime numbers, assumed to be […]

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 […]

Read More#### Fast Classification and Clustering via Image Convolution Filters

- Vincent Granville
- June 19, 2022

Subtitled “Alternative to Generative Mixture Models”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. I explain, with Python code and numerous illustrations, how to turn traditional tabular data into images, to perform both clustering and supervised classification using simple image filtering techniques. I also explain how to generalize the […]

Read More#### The Art of Visualizing High Dimensional Data

- Vincent Granville
- June 9, 2022

Entitled “The Art of Visualizing High Dimensional Data”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. This article discusses enriched visualizations, with a focus on animated gifs and videos built in Python. For instance, the comet video displayed below can feature several dimensions that are difficult to show in […]

Read More#### Gentle Introduction to Linear Algebra, with Spectacular Applications

- Vincent Granville
- May 31, 2022

This is not a traditional tutorial on linear algebra. The material presented here, in a compact style, is rarely taught in college classes. It covers a wide range of topics, while avoiding excessive use of jargon or advanced math. The fundamental tool is the power of a matrix, and its byproduct, the characteristic polynomial. It […]

Read More#### Fuzzy Regression: A Generic, Model-free, Math-free Machine Learning Technique

- Vincent Granville
- May 22, 2022

Some people climb Mount Everest solo in winter, with no oxygen. Some mathematicians prove difficult theorems using only elementary arithmetic. The proof, despite labeled as “elementary” is typically far more complicated than those based on advanced mathematical theory. The people accomplishing these feasts are very rare. Introduction For years, I have developed machine learning techniques […]

Read More#### Little Known Secrets about Interpretable Machine Learning on Synthetic Data

- Vincent Granville
- May 7, 2022

This first article in a new series on synthetic data and explainable AI, focuses on making linear regression more meaningful and controllable. Includes synthetic data, advanced machine learning with Excel, combinatorial feature selection, parametric bootstrap, cross-validation, and alternatives to R-squared to measure model performance. The full technical article (PDF, 13 pages, with detailed explanations and […]

Read More#### Amazing Neural Network Video Demonstration

- Vincent Granville
- April 12, 2022

I recently posted an article featuring a very deep neural network in action (250 layers), see here. Each frame in the video represented one layer, with the signal propagating from one layer to the next. In the last layer, the whole space was classified, in the sense that any new observation was immediately assigned to […]

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