Related papers: Realizable Rate Distortion Function and Bayesian F…
In the bayesian analysis of Inverse Problems most relevant cases the forward maps (FM, or regressor function) are defined in terms of a system of (O, P)DE's with intractable solutions. These necessarily involve a numerical method to find…
Rate-distortion formulation is the information-theoretic approach to the study of signal encoding systems. Since a more general approach to model the nonstationarity exhibited by real-world signals is to use appropriately fitted time…
A scenario involving a source, a channel, and a destination, where the destination is interested in {\em both} reliably reconstructing the message transmitted by the source and estimating with a fidelity criterion the state of the channel,…
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…
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations…
Consider a discrete memoryless multiple source with $m$ components of which $k \leq m$ possibly different sources are sampled at each time instant and jointly compressed in order to reconstruct all the $m$ sources under a given distortion…
Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard RL. At the…
In several areas of optics and photonics like wave propagation, digital holography, holographic microscopy, diffraction imaging, biomedical imaging and diffractive optics, the behavior of the electromagnetic waves has to be calculated with…
The regression discontinuity (RD) design is a popular approach to causal inference in non-randomized studies. This is because it can be used to identify and estimate causal effects under mild conditions. Specifically, for each subject, the…
We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework. A set of input features is deemed relevant for a classification decision if the expected…
Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically…
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These…
In this paper, the rate-distortion theory of the Gray-Wyner lossy source coding system is investigated. For the case of jointly Gaussian distributed sources, we establish an expression for the rate-distortion function under the constraint…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…
Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical)…
A critical challenge for reinforcement learning (RL) is making decisions based on incomplete and noisy observations, especially in perturbed and partially observable Markov decision processes (P$^2$OMDPs). Existing methods fail to mitigate…
We present a new method to estimate the rate-distortion-perception function in the perfect realism regime (PR-RDPF), for multivariate continuous sources subject to a single-letter average distortion constraint. The proposed approach is not…
This paper presents a new foundational approach to information theory based on the concept of the information efficiency of a recursive function, which is defined as the difference between the information in the input and the output. The…
We study task-oriented lossy compression through the lens of rate-distortion-classification (RDC) representations. The source is Bernoulli, the distortion measure is Hamming, and the binary classification variable is coupled to the source…