They say journal acceptances are like buses¹–for a long while you don’t see any, and then two come along at once. To be more specific, this week two of my papers were accepted to the journals NMR in Biomedicine (NMRB) and SIAM Multiscale Modeling and Simulation (SIAM MMS) respectively. These papers are about:

1. Input Layer Regularization (NMRB): How much information do classical statistical estimators hold about the underlying random variable, and can a neural network extract this information? We study this problem in the context of Myelin Water Imaging and empirically demonstrate that sometimes classical statistical estimators (like Generalized Cros Validation) can work better than copious amounts of deep learning. Read the paper, jointly authored with Richard Spencer’s group at the NIH, here on arXiv.

2. Collective variables that reproduce rates (SIAM MMS): A case study paper on the butane molecule, where we turn Legoll and Lelievre’s quantitative coarse-graining theory into an algorithm for learning collective variables that preserve dynamics of molecular systems. This paper has lots of independent insights on group invariant machine learning and manifold learning. Read the paper, jointly authored with Arnav Mehta and Maria Cameron here.

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.