Image by Greg Rakozy. Unsplash.

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…

Thoughts and Theory

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…

Hands-on Tutorials

Set of all possibles 2 by 2 images with colors encoded using a single bit. Image by the author.

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…

THOUGHTS AND THEORY

Less than 3% of the 32 256 pixels, here in red, are relevant to reconstruct a face from the Extended Yale B database. Image by the author.

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…

Hands-on Tutorials

Learning by Nick Youngson CC BY-SA 3.0 Alpha Stock Images

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…

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…

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…

Although it finds its roots in statistics, logistic regression is a fairly standard approach to solve binary classification problems in machine learning. It is actually so standard that it is implemented in all major data analysis software (e.g. Excel, SPSS, or its open-source alternative PSPP) and libraries (e.g. scikit-learn, statsmodels

Machine learning and artificial intelligence have been having a transformative impact in numerous fields, from medical sciences (e.g. imaging and MRI) to real-time strategy video games (e.g. StarCraft 2). Key enablers for these successes have been deep neural networks characterized by an ever-increasing number of so-called hidden layers and artificial…

Jean-Christophe B. Loiseau

Assistant Professor in Fluid Mechanics and Applied Mathematics. Passionate about machine learning, physics and science outreach.

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