$\alpha $-variational inference with statistical guarantees

Statistical Inference in Autoregressive Models with Non-negative Residuals

Normal residual is one of the usual assumptions of autoregressive models but in practice sometimes we are faced with non-negative residuals case. In this paper we consider some autoregressive models with non-negative residuals as competing models and we have derived the maximum likelihood estimators of parameters based on the modified approach and EM algorithm for the competing models. Also,...

Variational Inference with Rényi Divergence

This paper introduces the variational Rényi bound (VR) that extends traditional variational inference to Rényi’s α-divergences. This new family of variational methods unifies a number of existing approaches, and enables a smooth interpolation from the evidence lower-bound to the log (marginal) likelihood that is controlled by the value of α that parametrises the divergence. The reparameterizati...

Variational inference with copula augmentation

Robust Inference with Variational Bayes

In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior and likelihood, since this choice is made by the modeler and is necessarily somewhat subjective. For example, the process of prior elicitation may be prohibitively time-consuming, two practitioners may have irre...

Procrustean statistical inference of deformations

A two step method has been devised for the statistical inference of deformation changes. In the first step of this method and based on Procrustes analysis of deformation tensors, the significance of the change in a time or space series of deformation tensors is statistically analyzed. In the second step significant change(s) in deformations are localized. In other words, they are assigned to ce...