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Although Shannon mutual information has been widely used, its effective calculation is often difficult for many practical problems, including those in neural population coding. Asymptotic formulas based on Fisher information sometimes…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
Multi-physics simulations play a crucial role in understanding complex systems. However, their computational demands are often prohibitive due to high dimensionality and complex interactions, such that actual calculations often rely on…
The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…
We propose an entropy-based information measure, namely the Discounted Least Information Theory of Entropy (DLITE), which not only exhibits important characteristics expected as an information measure but also satisfies conditions of a…
Let psi: R^n --> R^k be a map defined by k positive definite quadratic forms on R^n. We prove that the relative entropy (Kullback-Leibler) distance from the convex hull of the image of psi to the image of psi is bounded above by an absolute…
Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…
Modern software systems are typically configurable, a fundamental prerequisite for wide applicability and reusability. This flexibility poses an extraordinary challenge for quality assurance, as the enormous number of possible…
We consider zero-sum repeated games in which the players are restricted to strategies that require only a limited amount of randomness. Let $v_n$ be the max-min value of the $n$ stage game; previous works have characterized…
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
The accurate asymptotic evaluation of marginal likelihood integrals is a fundamental problem in Bayesian statistics. Following the approach introduced by Watanabe, we translate this into a problem of computational algebraic geometry,…
Now that Bayesian Networks (BNs) have become widely used, an appreciation is developing of just how critical an awareness of the sensitivity and robustness of certain target variables are to changes in the model. When time resources are…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…