Schedule

This session introduces the basic ideas of Topological Data Analysis (TDA), focusing on the concepts of homotopy and homotopy equivalence as tools for understanding data shape. We also discuss planar graphs as a way to visualize topological structures. 

Poisson regression is a useful and practical technique for modeling count or frequency data, such as the number of deaths per year, insurance claims per year, or rainfall events per month. It is widely applicable to a variety of industrial problems where the outcome involves discrete counts, including demand forecasting, resource planning, and event monitoring.

In this talk, I will introduce generalized linear models (GLMs) in scikit-learn and explain how they relate to Poisson regression. I will also cover tree-based models, focusing on the algorithm behind scikit-learn’s HistGradientBoostingRegressor, with an emphasis on Poisson deviance as a loss function.

The presentation includes theoretical background to build intuition for these models, followed by a practical demonstration using Poisson regression techniques in scikit-learn on a bike-share dataset. This talk is adapted from a presentation originally given at the SciPy conference under the same title.

We explore geometric constructions for data representation, including the simplex and simplicial complex. Concepts such as alpha hull, Voronoi diagram, and filtered structure are introduced as foundations for multi-scale analysis. 

This session covers the algebraic framework of homology, introducing chains, chain complexes, and homology groups. We conclude with persistence homology, which captures topological features across scales. 

This course provides hands-on experience with topological data analysis (TDA) using Python. Through coding exercises, participants will develop practical skills to analyze and interpret complex datasets using TDA techniques. 

We examine TDA-based approaches to clustering, and introduce the mapper algorithm, a method for extracting and visualizing the shape of high-dimensional data.