Related papers: Maximal-entropy driven determination of weights in…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
In the paper we consider the problem of multivariate function approximation in polynomial basis. In order to solve this problem, we adjust the least squares method (LSM) by adding information about derivatives of the function. This…
We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame- work. Our method is motivated by generalized Polynomial…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
This paper is concerned with the approximation of a function $u$ in a given approximation space $V_m$ of dimension $m$ from evaluations of the function at $n$ suitably chosen points. The aim is to construct an approximation of $u$ in $V_m$…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
From a machine learning point of view, identifying a subset of relevant features from a real data set can be useful to improve the results achieved by classification methods and to reduce their time and space complexity. To achieve this…
We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…
In this paper, we present a novel maximum entropy formulation of the Differential Dynamic Programming algorithm and derive two variants using unimodal and multimodal value functions parameterizations. By combining the maximum entropy…
Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…
The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker's preferences. In order to obtain such utility values it is necessary to establish an analogy between…
(Jaynes') Method of (Shannon-Kullback's) Relative Entropy Maximization (REM or MaxEnt) can be - at least in the discrete case - according to the Maximum Probability Theorem (MPT) viewed as an asymptotic instance of the Maximum Probability…
We provide a robust and general algorithm for computing distribution functions associated to induced orthogonal polynomial measures. We leverage several tools for orthogonal polynomials to provide a spectrally-accurate method for a broad…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
We propose and analyze a weighted greedy scheme for computing deterministic sample configurations in multidimensional space for performing least-squares polynomial approximations on $L^2$ spaces weighted by a probability density function.…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…
This review describes recent advances by the authors and others on the topic of incorporating experimental data into molecular simulations through maximum entropy methods. Methods which incorporate experimental data improve accuracy in…