Samuel I. Berchuck

Youngsoo Baek, Samuel I. Berchuck, Sayan Mukherjee

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the variance of the posterior predictive distribution (Bayesian model average) and compare its asymptotics to that of the risk of the MAP estimator. In the regime where the model dimensions grow faster than any constant multiple of the number of samples, asymptotic agreement between these two quantities is governed by the phase transition in the signal-to-noise ratio. They also asymptotically agree with each other when the number of samples grow faster than any constant multiple of model dimensions. Numerical simulations illustrate finer distributional properties of the two quantities for finite dimensions. We conjecture they have Gaussian fluctuations and exhibit similar properties as found by previous authors in a Gaussian sequence model, which is of independent theoretical interest.

Samuel I. Berchuck, Felipe A. Medeiros, Sayan Mukherjee

As big spatial data becomes increasingly prevalent, classical spatiotemporal (ST) methods often do not scale well. While methods have been developed to account for high-dimensional spatial objects, the setting where there are exceedingly large samples of spatial observations has had less attention. The variational autoencoder (VAE), an unsupervised generative model based on deep learning and approximate Bayesian inference, fills this void using a latent variable specification that is inferred jointly across the large number of samples. In this manuscript, we compare the performance of the VAE with a more classical ST method when analyzing longitudinal visual fields from a large cohort of patients in a prospective glaucoma study. Through simulation and a case study, we demonstrate that the VAE is a scalable method for analyzing ST data, when the goal is to obtain accurate predictions. R code to implement the VAE can be found on GitHub: https://github.com/berchuck/vaeST.

Matthew Engelhard, Samuel Berchuck, Joshua D'Arcy et al.

Event time models predict occurrence times of an event of interest based on known features. Recent work has demonstrated that neural networks achieve state-of-the-art event time predictions in a variety of settings. However, standard event time models suppose that the event occurs, eventually, in all cases. Consequently, no distinction is made between a) the probability of event occurrence, and b) the predicted time of occurrence. This distinction is critical when predicting medical diagnoses, equipment defects, social media posts, and other events that or may not occur, and for which the features affecting a) may be different from those affecting b). In this work, we develop a conditional event time model that distinguishes between these components, implement it as a neural network with a binary stochastic layer representing finite event occurrence, and show how it may be learned from right-censored event times via maximum likelihood estimation. Results demonstrate superior event occurrence and event time predictions on synthetic data, medical events (MIMIC-III), and social media posts (Reddit), comprising 21 total prediction tasks.