Gaussianization Machines for Non-Gaussian Function Estimation Models

Abstract

A wide range of nonparametric function estimation models have been studied individually in the literature. Among them the homoscedastic nonparametric Gaussian regression is arguably the best known and understood. Inspired by the asymptotic equivalence theory, Brown, Cai and Zhou

Estimating Stochastic Poisson Intensities Using Deep Latent Models

“…Deep latent models (DLMs) [10,Ch. 19,20] specialize this general presentation to the setting where the probability measures are parameterized by deep neural networks (DNNs). Variational autoencoders (VAEs) [15] are an example of DLMs in the multivariate setting where the sequence of prior distributions are known only up to the parameters of an appropriately chosen DNN modeling these parameters.…”

“…Let d be the number of time intervals (or 'pieces') in the regressors, representing the number of degrees of freedom. We compare our method, using intensity process dZ(t) = a(b − Z(t))dt + d −1/2 Z(t)dW (t), with the piecewise linear estimator [19] and the nonparametric 'Gaussianization machine' method from [20] ('GRP' in the table below). GRP uses a variance stabilizing transformation of the Poisson counts and Gaussian process regression on the transformed variables.…”