Related papers: Lossy Compression of General Random Variables
This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…
Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting…
We examine the coordinated and universal rate-efficient sampling of a subset of correlated discrete memoryless sources followed by lossy compression of the sampled sources. The goal is to reconstruct a predesignated subset of sources within…
Classical rate-distortion theory requires knowledge of an elusive source distribution. Instead, we analyze rate-distortion properties of individual objects using the recently developed algorithmic rate-distortion theory. The latter is based…
Recent research has shown a strong theoretical connection between variational autoencoders (VAEs) and the rate-distortion theory. Motivated by this, we consider the problem of lossy image compression from the perspective of generative…
Variational principles for the rate distortion (RD) theory in lossy compression are formulated within the ambit of the generalized nonextensive statistics of Tsallis, for values of the nonextensivity parameter satisfying $ 0 < q < 1 $ and $…
We investigate lossy compression (source coding) of data in the form of permutations. This problem has direct applications in the storage of ordinal data or rankings, and in the analysis of sorting algorithms. We analyze the rate-distortion…
Realism constraints (or constraints on perceptual quality) have received considerable recent attention within the context of lossy compression, particularly of images. Theoretical studies of lossy compression indicate that high-rate common…
Rate-distortion (RD) theory is at the heart of lossy data compression. Here we aim to model the generalized RD (GRD) trade-off between the visual quality of a compressed video and its encoding profiles (e.g., bitrate and spatial…
We study the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of data points is unknown. Our analysis is based on…
The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all second-order information are derived…
Consider the problem of estimating a latent signal from a lossy compressed version of the data when the compressor is agnostic to the relation between the signal and the data. This situation arises in a host of modern applications when data…
Generalization to novel visual conditions remains a central challenge for both human and machine vision, yet standard robustness metrics offer limited insight into how systems trade accuracy for robustness. We introduce a…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
In lossy image compression, the objective is to achieve minimal signal distortion while compressing images to a specified bit rate. The increasing demand for visual analysis applications, particularly in classification tasks, has emphasized…
Living organisms rely on internal models of the world to act adaptively. These models, because of resource limitations, cannot encode every detail and hence need to compress information. From a cognitive standpoint, information compression…
We present a novel systematic theoretical framework to analyze the rate-distortion (R-D) limits of learned image compression. While recent neural codecs have achieved remarkable empirical results, their distance from the…
Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations,…
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 image compression, with recent advances in generative modeling, the existence of a trade-off between the rate and the perceptual quality (realism) has been brought to light, where the realism is measured by the closeness of the output…