Septimia Sârbu

Septimia Sarbu, Abdellatif Zaidi

We consider the problem of learning parametric distributions from their quantized samples in a network. Specifically, $n$ agents or sensors observe independent samples of an unknown parametric distribution; and each of them uses $k$ bits to describe its observed sample to a central processor whose goal is to estimate the unknown distribution. First, we establish a generalization of the well-known van Trees inequality to general $L_p$-norms, with $p > 1$, in terms of Generalized Fisher information. Then, we develop minimax lower bounds on the estimation error for two losses: general $L_p$-norms and the related Wasserstein loss from optimal transport.

Septimia Sârbu, Riccardo Volpi, Alexandra Peşte et al.

In this paper we propose two novel bounds for the log-likelihood based on Kullback-Leibler and the Rényi divergences, which can be used for variational inference and in particular for the training of Variational AutoEncoders. Our proposal is motivated by the difficulties encountered in training VAEs on continuous datasets with high contrast images, such as those with handwritten digits and characters, where numerical issues often appear unless noise is added, either to the dataset during training or to the generative model given by the decoder. The new bounds we propose, which are obtained from the maximization of the likelihood of an interval for the observations, allow numerically stable training procedures without the necessity of adding any extra source of noise to the data.