Part 1: Setting up the stage — Reinforcement learning is one of the three basic machine learning paradigms, alongside supervised and unsupervised learning. In the past decade, it has established itself as one of the most successful approaches to tackling complex engineering tasks. This is best exemplified by the successes DeepMind has achieved with AlphaGo or AlphaFold…

Perspectives from classical physics: the Ptolemaic geocentric model — Parsimony is an overarching goal in modern science. Scientists describe and explain complex phenomena all over the world. To do so, they combine experimental observations and mathematical models. Following Occam’s razor, It is futile to do with more things that which can be done with fewer, the most successful scientific…

How to use linear dimensionality reduction for time series. — We all use PCA for linear dimensionality reduction. All the time and for everything, from image processing to unstructured data. We even use it for time-series analysis, although better techniques exist. In this post, I’d like to introduce you to Dynamic Mode Decomposition (DMD), a linear dimensionality reduction technique for…

Leveraging low-rank structures and sparsity to classify an image — My daughter is two years old. Like most kids her age, she’s already pretty good at distinguishing a large variety of animals. She can even make the difference between cats and dogs when I draw them, and boy, I am terrible at drawing! If you think about it, this is…

A quick introduction to Compressive Sensing — Image-space is vast, incredibly vast, and yet so small. Think about it for a second. You can create 18 446 744 073 709 551 616 different images by considering a grid as small as 8 by 8 black and white pixels. Yet, among these 18 quintillion images, very few make…

Leveraging low-rank structures to find pixels that matter most in images. — Image-space is incredibly vast. Think about it for a second. If you consider a simple grid of 8 by 8 pixels with colors encoded using a single bit (i.e. either black or white), you can construct 18 446 744 073 709 551 616 images. If you now encode shades of…

Ever wondered how to implement a simple baseline model for multi-class problems? Here is one example (code included) — Although it finds its roots in statistics, logistic regression is a fairly standard approach to solve binary classification problems in machine learning and is by far the most commonly used algorithm for such classification tasks in real-life applications. By design, it can, however, handle only binary classification problems, i.e. problems…

Some insights from simple mathematical models. — Disclaimer: I am not a medical doctor nor an epidemiologist. I’m just an applied mathematician. The sole aim of this new series is to provide a better understanding of (fairly simplified) epidemiological models to an audience as large as possible as well as illustrating some of the challenges a disease…

How simple mathematical models can help us get a better understanding of the current situation. — Disclaimer: I am not a medical doctor nor an epidemiologist. I’m just an applied mathematician. The sole aim of this new series is to provide a better understanding of (fairly simplified) epidemiological models to an audience as large as possible as well as illustrating some of the challenges a disease…