Related papers: Realizable Rate Distortion Function and Bayesian F…
Motivated by the lossy compression of an active-vision video stream, we consider the problem of finding the rate-distortion function of an arbitrarily varying source (AVS) composed of a finite number of subsources with known distributions.…
Rate-distortion (R-D) function, a key quantity in information theory, characterizes the fundamental limit of how much a data source can be compressed subject to a fidelity criterion, by any compression algorithm. As researchers push for…
This PhD thesis presents a distributional view of optimization in place of a worst-case perspective. We motivate this view with an investigation of the failure point of classical optimization. Subsequently we consider the optimization of a…
The information rate-distortion-perception (RDP) function characterizes the three-way trade-off between description rate, average distortion, and perceptual quality measured by discrepancy between probability distributions and has been…
This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the…
Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…
In this letter, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the minimum of two non-central Chi-square random variables with two degrees of freedom in terms of power series. With the help of…
We introduce the concept of forward rank-dependent performance processes, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of…
A decision-maker must consider cofounding bias when attempting to apply machine learning prediction, and, while feature selection is widely recognized as important process in data-analysis, it could cause cofounding bias. A causal Bayesian…
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…
When applied in healthcare, reinforcement learning (RL) seeks to dynamically match the right interventions to subjects to maximize population benefit. However, the learned policy may disproportionately allocate efficacious actions to one…
Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings. In any numerical implementation of the FPF algorithm, the main challenge is to numerically…
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…
Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…
Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals constitute a fundamental building block in…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
The regression discontinuity design (RDD) is a quasi-experimental approach used to estimate the causal effects of an intervention assigned based on a cutoff criterion. RDD exploits the idea that close to the cutoff units below and above are…
We apply statistical mechanics to an inverse problem of linear mapping to investigate the physics of the irreversible compression. We use the replica symmetry breaking (RSB) technique with a toy model to demonstrate the Shannon's result.…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
A rate-distortion problem motivated by the consideration of semantic information is formulated and solved. The starting point is to model an information source as a pair consisting of an intrinsic state which is not observable,…