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A privacy-constrained information extraction problem is considered where for a pair of correlated discrete random variables $(X,Y)$ governed by a given joint distribution, an agent observes $Y$ and wants to convey to a potentially public…
We show how rate-distortion theory provides a mechanism for automated theory building by naturally distinguishing between regularity and randomness. We start from the simple principle that model variables should, as much as possible, render…
This paper investigates a lossy source coding problem in which two decoders can access their side-information respectively. The correlated sources are a product of two component correlated sources, and we exclusively investigate the case…
Rate-distortion theory provides bounds for compressing data produced by an information source to a specified encoding rate that is strictly less than the source's entropy. This necessarily entails some loss, or distortion, between the…
Blau and Michaeli recently introduced a novel concept for inverse problems of signal processing, that is, the perception-distortion tradeoff. We introduce their tradeoff into the rate distortion theory of lossy source coding in information…
For a number of lossy source coding problems it is shown that even if the usual single-letter sum-rate-distortion expressions may become invalid for non-infinite distortion functions, they can be approached, to any desired accuracy, via the…
This paper investigates the rate-distortion function, under a squared error distortion $D$, for an $n$-dimensional random vector uniformly distributed on an $(n-1)$-sphere of radius $R$. First, an expression for the rate-distortion function…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…
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 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…
Finite abstractions are discrete approximations of dynamical systems, such that the set of abstraction trajectories contains all system trajectories. There is a consensus that abstractions suffer from the curse of dimensionality: for the…
The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to…
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…
The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the…
In many, if not most, machine learning applications the training data is naturally heterogeneous (e.g. federated learning, adversarial attacks and domain adaptation in neural net training). Data heterogeneity is identified as one of the…
A general rate theory for resonance energy transfer is formulated to incorporate any degrees of freedom (e.g., rotation, vibration, exciton, and polariton) as well as coherently-coupled composite states. The compact rate expression allows…
A composite source, consisting of multiple subsources and a memoryless switch, outputs one symbol at a time from the subsource selected by the switch. If some data should be encoded more accurately than other data from an information…
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…
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…
Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…