Last month marked the culmination of a two major projects regarding collective variable discovery, a fundamental interdisciplinary problem in drug discovery, computational statistical physics, and stochastic processes. From a probabilistic perpsective, this problem asks: how can we map a stochastic process to low dimensions and still preserve its statistics? In two case study-style papers on the butane molecule and Lennard-Jones clusters we provide some answers by resorting to quantitive coarse graining theory and proposing algorithms that use some of my favourite tools from geometric data science.

Two papers I’ve been working on are out. One tells a story about how you can combine classical and deep learning methods for magnetic resonance imaging in the brain. The other one shows how to use the Neumann eigenvectors of subgraphs for dimension reduction–with nearly isometric embeddings!

Our paper on Short Time Fourier Transform (STFT) phase retrieval was recently published at the 34th European Signal Processing Conference! We showed that neural networks can perform speech phase retreival given far fewer samples than what is mathematically required. Read it here.