Computing the optimal keyboard through a geometric analysis of the English language

In the context of a group project for the course COMSW4995 002 - Geometric Data Analysis, we bring our attention to the design of fast-typing keyboards. Leveraging some geometric tools in an optimization framework allowed us to propose novel keyboard layouts that offer a faster typing.

Parametric information geometry with the package Geomstats

We introduce the information geometry module of the Python package Geomstats. The module first implements Fisher-Rao Riemannian manifolds of widely used parametric families of probability distributions, such as normal, gamma, beta, Dirichlet distributions, and more. The module further gives the Fisher-Rao Riemannian geometry of any parametric family of distributions of interest, given a parameterized probability density function as input. The implemented Riemannian geometry tools allow users to compare, average, interpolate between distributions inside a given family. Importantly, such capabilities open the door to statistics and machine learning on probability distributions. We present the object-oriented implementation of the module along with illustrative examples and show how it can be used to perform learning on manifolds of parametric probability distributions.