A Variational Characterization of Rényi Divergences
نویسندگان
چکیده
منابع مشابه
A variational characterization of Rényi divergences
Atar, Chowdhary and Dupuis have recently exhibited a variational formula for exponential integrals of bounded measurable functions in terms of Rényi divergences. We develop a variational characterization of the Rényi divergences between two probability distributions on a measurable space in terms of relative entropies. When combined with the elementary variational formula for exponential integr...
متن کاملRényi Divergence Variational Inference
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...
متن کاملVariational 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...
متن کاملAPPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES.
In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist.38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show c...
متن کاملAlpha-Divergences in Variational Dropout
We investigate the use of alternative divergences to Kullback-Leibler (KL) in variational inference(VI), based on the Variational Dropout [10]. Stochastic gradient variational Bayes (SGVB) [9] is a general framework for estimating the evidence lower bound (ELBO) in Variational Bayes. In this work, we extend the SGVB estimator with using Alpha-Divergences, which are alternative to divergences to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2018
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2018.2861013