相关论文: Entropic Projections and Dominating Points
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision…
As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from signal and data acquisition to modeling and prediction. The optimization…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
This paper studies the notion of computational entropy. Using techniques from convex optimization, we investigate the following problems: (a) Can we derandomize the computational entropy? More precisely, for the computational entropy, what…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
We introduce a novel generalization of entropy and conditional entropy from which most definitions from the literature can be derived as particular cases. Within this general framework, we investigate the problem of designing…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
Given a set $P$ of $n$ points in the plane, its unit-disk graph $G(P)$ is a graph with $P$ as its vertex set such that two points of $P$ are connected by an edge if their (Euclidean) distance is at most $1$. We consider several classical…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex…
We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic equations as the entropic parameter vanishes. Convergence is…
We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization.…
Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}$), arise as redundancies under…