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We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite…

Lossy compression plays a growing role in scientific simulations where the cost of storing their output data can span terabytes. Using error bounded lossy compression reduces the amount of storage for each simulation; however, there is no…

We propose TAROT, a targeted data selection framework grounded in optimal transport theory. Previous targeted data selection methods primarily rely on influence-based greedy heuristics to enhance domain-specific performance. While effective…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

We derive lower bounds on the Bayes risk in decentralized estimation, where the estimator does not have direct access to the random samples generated conditionally on the random parameter of interest, but only to the data received from…

Heavy-tailed impact distributions, intrinsic uncertainty, and the high costs of proposal-based peer review increasingly challenge research funding decisions. Using large-scale bibliometric data, we show that past scientific performance…

We formulate the problem of performing optimal data compression under the constraints that compressed data can be used for accurate classification in machine learning. We show that this translates to a problem of minimizing the mutual…

When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…

Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…

Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…

We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in…

Inferring the causal direction and causal effect between two discrete random variables X and Y from a finite sample is often a crucial problem and a challenging task. However, if we have access to observational and interventional data, it…

A probabilistic expert system emulates the decision-making ability of a human expert through a directional graphical model. The first step in building such systems is to understand data generation mechanism. To this end, one may try to…

We propose a new method of discovering causal relationships in temporal data based on the notion of causal compression. To this end, we adopt the Pearlian graph setting and the directed information as an information theoretic tool for…

We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates. We show that the theoretical capacity of algorithms built from standard parity-check gates converges exponentially fast to…

We introduce a simple and efficient algorithm for stochastic linear bandits with finitely many actions that is asymptotically optimal and (nearly) worst-case optimal in finite time. The approach is based on the frequentist…

We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes;…

As data-driven predictive models are increasingly used to inform decisions, it has been argued that decision makers should provide explanations that help individuals understand what would have to change for these decisions to be beneficial…

We study the compressive diffusion strategies over distributed networks based on the diffusion implementation and adaptive extraction of the information from the compressed diffusion data. We demonstrate that one can achieve a comparable…

This paper investigates the investment problem of constructing an optimal no-short sequential portfolio strategy in a market with a latent dependence structure between asset prices and partly unobservable side information, which is often…