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Related papers: Gaussian Rate-Distortion-Perception Coding and Ent…

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Approximate inference techniques are the cornerstone of probabilistic methods based on Gaussian process priors. Despite this, most work approximately optimizes standard divergence measures such as the Kullback-Leibler (KL) divergence, which…

Machine Learning · Computer Science 2020-11-06 Rui Zhang , Christian J. Walder , Edwin V. Bonilla , Marian-Andrei Rizoiu , Lexing Xie

In the theory of lossy compression, the rate-distortion (R-D) function $R(D)$ describes how much a data source can be compressed (in bit-rate) at any given level of fidelity (distortion). Obtaining $R(D)$ for a given data source establishes…

Information Theory · Computer Science 2023-10-31 Yibo Yang , Stephan Eckstein , Marcel Nutz , Stephan Mandt

We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we…

Machine Learning · Computer Science 2026-02-02 Binshuai Wang , Peng Wei

It is shown that under suitable regularity conditions, differential entropy is a Lipschitz functional on the space of distributions on $n$-dimensional Euclidean space with respect to the quadratic Wasserstein distance. Under similar…

Information Theory · Computer Science 2016-02-03 Yury Polyanskiy , Yihong Wu

We derive a class of divergences measuring the difference between probability density functions on the one-dimensional sample space. This divergence is a one-parameter variation of the Itakura--Saito divergence between quantile density…

Information Theory · Computer Science 2026-02-20 Wuchen Li

We revisit the Gray-Wyner lossy source coding problem and derive the first-order asymptotic optimal rate-distortion-perception region when additional perception constraints are imposed on reproduced source sequences. The optimal trade-off…

Information Theory · Computer Science 2026-01-19 Yu Yang , Yingxin Zhang , Weijie Yuan , Lin Zhou

This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in the Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional Hilbert space,…

Machine Learning · Statistics 2021-02-16 Minh Ha Quang

In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…

Numerical Analysis · Mathematics 2014-08-11 Frank J. Pinski , Gideon Simpson , Andrew M. Stuart , Hendrik Weber

We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those…

Information Theory · Computer Science 2007-07-13 Nan Liu , Sennur Ulukus

The rate-distortion saddle-point problem considered by Lapidoth (1997) consists in finding the minimum rate to compress an arbitrary ergodic source when one is constrained to use a random Gaussian codebook and minimum (Euclidean) distance…

Information Theory · Computer Science 2018-09-03 Lin Zhou , Vincent Y. F. Tan , Mehul Motani

Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some…

Machine Learning · Statistics 2022-07-28 Mingxuan Yi , Song Liu

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Optimization and Control · Mathematics 2018-05-21 Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani

I introduce rate-distortion theory for quantum coding, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to encode a quantum source with a given maximum level of distortion per source…

Quantum Physics · Physics 2007-05-23 Howard Barnum

This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…

Machine Learning · Statistics 2022-03-29 Borja Rodríguez-Gálvez , Germán Bassi , Ragnar Thobaben , Mikael Skoglund

We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account,…

Quantum Physics · Physics 2012-09-19 Rafal Demkowicz-Dobrzanski , Jan Kolodynski , Madalin Guta

When we consider canonical averages for classical discrete systems, typically referred to as substitutional alloys, the map phi from many-body interatomic interactions to thermodynamic equilibrium configurations generally exhibits…

Statistical Mechanics · Physics 2026-05-12 Koretaka Yuge

Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns…

Quantum Physics · Physics 2015-02-13 Ioannis Kogias , Antony R. Lee , Sammy Ragy , Gerardo Adesso

We consider lossy compression of a binary symmetric source by means of a low-density generator-matrix code. We derive two lower bounds on the rate distortion function which are valid for any low-density generator-matrix code with a given…

Information Theory · Computer Science 2008-04-11 Shrinivas Kudekar , Ruediger Urbanke

Score-based generative models are shown to achieve remarkable empirical performances in various applications such as image generation and audio synthesis. However, a theoretical understanding of score-based diffusion models is still…

Machine Learning · Computer Science 2022-12-14 Dohyun Kwon , Ying Fan , Kangwook Lee

A new source model, which consists of an intrinsic state part and an extrinsic observation part, is proposed and its information-theoretic characterization, namely its rate-distortion function, is defined and analyzed. Such a source model…

Information Theory · Computer Science 2022-06-02 Jiakun Liu , Shuo Shao , Wenyi Zhang , H. Vincent Poor