Related papers: Maximum Entropy Reconstruction for Discrete Distri…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…
How to find unknown distributions is questioned in many pieces of research. There are several ways to figure them out, but the main question is which acts more reasonably than others. In this paper, we focus on the maximum entropy principle…
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…
The purpose of this paper is to study the problem of estimating a compactly supported density of probability from noisy observations of its moments. In fact, we provide a statistical approach to the famous Hausdorff classical moment…
This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomials in decision variables. We reformulate the DRO with…
Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
Contextual MDPs are powerful tools with wide applicability in areas from biostatistics to machine learning. However, specializing them to offline datasets has been challenging due to a lack of robust, theoretically backed methods. Our work…
Trajectory optimization and model predictive control are essential techniques underpinning advanced robotic applications, ranging from autonomous driving to full-body humanoid control. State-of-the-art algorithms have focused on data-driven…
Maximum-entropy distributions are shown to appear in the probability calculus as approximations of a model by exchangeability or a model by sufficiency, the former model being preferable. The implications of this fact are discussed,…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
The maximum entropy technique (MENT) is used to determine the distribution functions of physical values. MENT naturally combines required maximum entropy, the properties of a system and connection conditions in the form of restrictions…
We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
It is well known that open dynamical systems can admit an uncountable number of (absolutely continuous) conditionally invariant measures (ACCIMs) for each prescribed escape rate. We propose and illustrate a convex optimisation based…
Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…