Related papers: Superresolution in the maximum entropy approach to…
This paper considers the problem of steering an arbitrary initial probability density function to an arbitrary terminal one, where the system dynamics is governed by a first-order linear stochastic difference equation. It is a…
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…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…
The density deconvolution problem involves recovering a target density g from a sample that has been corrupted by noise. From the perspective of Le Cam's local asymptotic normality theory, we show that non-parametric density deconvolution…
We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
We consider the problem of learning a target probability distribution over a set of $N$ binary variables from the knowledge of the expectation values (with this target distribution) of $M$ observables, drawn uniformly at random. The space…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
We present a new method to investigate a class of diagrams which generalizes the sunset topology to any number of massive internal lines. Our attention is focused on the computation of the spectral density of these diagrams which is related…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…
Laplace's method is used to approximate intractable integrals in a statistical problems. The relative error rate of the approximation is not worse than $O_p(n^{-1})$. We provide the first statistical lower bounds showing that the $n^{-1}$…
Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this…
We introduce a method for analyzing radio interferometry data which produces maps which are optimal in the Bayesian sense of maximum posterior probability density, given certain prior assumptions. It is similar to maximum entropy…
To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…