Related papers: Rate distortion dimension and ergodic decompositio…

Quantum random variable, distortion operator are introduced based on canonical operators. As the lower bound of rate distortion, the entanglement information rate distortion is achieved by Gaussian map for Gaussian source. General Gaussian…

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…

Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the…

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…

Since Shannon's foundational work, rate-distortion theory has defined the fundamental limits of lossy compression. Classical results, derived for memoryless and stationary ergodic sources in the asymptotic regime, have shaped both transform…

We characterize the rate-distortion function for zero-mean stationary Gaussian sources under the MSE fidelity criterion and subject to the additional constraint that the distortion is uncorrelated to the input. The solution is given by two…

We derive fundamental accuracy limits for distributed localization when a fusion center has access only to independently rate-distortion (RD)-optimally compressed versions of multi-sensor observations, under a line-of-sight propagation…

In this paper we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of…

We show the existence of variable-rate rate-distortion codes that meet the disortion constraint almost surely and are minimax, i.e., strongly, universal with respect to an unknown source distribution and a distortion measure that is…

The rate-distortion function (RDF) has long been an information-theoretic benchmark for data compression. As its natural extension, the indirect rate-distortion function (iRDF) corresponds to the scenario where the encoder can only access…

Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…

Many images and videos are primarily processed by computer vision algorithms, involving only occasional human inspection. When this content requires compression before processing, e.g., in distributed applications, coding methods must…

Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…

This paper investigates the joint compression problem of a vector Gaussian source, where an individual distortion constraint is imposed on each source component. It is known that the rate-distortion function (RDF) is lower-bounded by the…

A variational principle for the rate distortion (RD) theory with Bregman divergences is formulated within the ambit of the generalized (nonextensive) statistics of Tsallis. The Tsallis-Bregman RD lower bound is established. Alternate…

We describe a method to derive the expansion and acceleration rates directly from the data, without the need for the specification of a theory of gravity, and without adopting an a priori parameterization of the form or redshift evolution…

The paper systematically classifies rings based on the dominant metric dimensions (Ddim) of their associated CZDG, establishing consequential bounds for the Ddim of these compressed zero-divisor graphs. The authors investigate the interplay…

We derive a lower bound on the differential entropy of a log-concave random variable $X$ in terms of the $p$-th absolute moment of $X$. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds…

In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…

Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…