Related papers: Maximal-entropy driven determination of weights in…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are…
We extend the problem of obtaining an estimator for the finite population mean parameter incorporating complete auxiliary information through calibration estimation in survey sampling but considering a functional data framework. The…
We consider the problem of approximating a function from $L^2$ by an element of a given $m$-dimensional space $V_m$, associated with some feature map $\boldsymbol{\varphi}$, using evaluations of the function at random points $x_1,…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
We use the method of Maximum (relative) Entropy to process information in the form of observed data and moment constraints. The generic "canonical" form of the posterior distribution for the problem of simultaneous updating with data and…
Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
Least-squares approximation is one of the most important methods for recovering an unknown function from data. While in many applications the data is fixed, in many others there is substantial freedom to choose where to sample. In this…
In this paper, we propose a maximum entropy method for predicting disease risks. It is based on a patient's medical history with diseases coded in ICD-10 which can be used in various cases. The complete algorithm with strict mathematical…
A maximum entropy-based framework is presented for the synthesis of projections from multiple Earth climate models. This identifies the most representative (most probable) model from a set of climate models -- as defined by specified…
We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a…
We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
This paper presents a novel systematic methodology to obtain new simple and tight approximations, lower bounds, and upper bounds for the Gaussian Q-function, and functions thereof, in the form of a weighted sum of exponential functions.…
The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…