相关论文: Gaussian Rate-Distortion-Perception Coding and Ent…

We consider the question of estimating multi-dimensional Gaussian mixtures (GM) with compactly supported or subgaussian mixing distributions. Minimax estimation rate for this class (under Hellinger, TV and KL divergences) is a long-standing…

We consider the transmission of a memoryless bivariate Gaussian source over an average-power-constrained one-to-two Gaussian broadcast channel. The transmitter observes the source and describes it to the two receivers by means of an…

Wasserstein distortion is a one-parameter family of distortion measures that was recently proposed to unify fidelity and realism constraints. After establishing continuity results for Wasserstein in the extreme cases of pure fidelity and…

Density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. Many quantum systems of physical interest can be represented as high-dimensional low rank density matrices. A…

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

In this article we study generalization of the classical Talagrand transport-entropy inequality in which the Wasserstein distance is replaced by the entropic transportation cost. This class of inequalities has been introduced in the recent…

This paper investigates system identification problems with Gaussian inputs and quantized observations under fixed thresholds. By reinterpreting the nonlinear effects induced by quantization as the product of the unknown parameter and an…

In lossy compression, Wang et al. [1] recently introduced the rate-distortion-perception-classification function, which supports multi-task learning by jointly optimizing perceptual quality, classification accuracy, and reconstruction…

Recently, Tian et al. [1] considered joint source-channel coding of transmitting a Gaussian source over $K$-user Gaussian broadcast channel, and derived an outer bound on the admissible distortion region. In [1], they stated "due to its…

In this work we investigate the behavior of the minimal rate needed in order to guarantee a given probability that the distortion exceeds a prescribed threshold, at some fixed finite quantization block length. We show that the excess coding…

Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an…

We study the rate-distortion problem for both scalar and vector memoryless heavy-tailed $\alpha$-stable sources ($0 < \alpha < 2$). Using a recently defined notion of ``strength" as a power measure, we derive the rate-distortion function…

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-)Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In…

We establish asymptotic upper and lower bounds for the Wasserstein distance of any order $p\ge 1$ between the empirical measure of a fractional Brownian motion on a flat torus and the uniform Lebesgue measure. Our inequalities reveal an…

We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\nu$ and $\mu$ supported on $\mathbb{R}^d$ such that $\mu$ is the reversible measure of a diffusion process. In order to…

The purpose of this paper is to estimate the limiting variance of asymptotically stationary Gaussian processes observed at high frequency, using the second moment estimator (SME). We study rates of convergence of the central limit theorem…

Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed…

In this paper, we consider the rate-distortion-perception (RDP) trade-off for the lossy compression of a Bernoulli vector source, which is a finite collection of independent binary random variables. The RDP function quantifies in a way the…

Boundary discontinuity and its inconsistency to the final detection metric have been the bottleneck for rotating detection regression loss design. In this paper, we propose a novel regression loss based on Gaussian Wasserstein distance as a…