相关论文: A new family of high-resolution multivariate spect…
In this technical note, we deal with a spectrum approximation problem arising in THREE-like multivariate spectral estimation approaches. The solution to the problem minimizes a suitable divergence index with respect to an a priori spectral…
We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by minimizing a suitable distance from the given spectrum and under the constraints…
This paper deals with M$^2$-signals, namely multivariate (or vector-valued) signals defined over a multidimensional domain. In particular, we propose an optimization technique to solve the covariance extension problem for stationary random…
In this paper, we study a matricial version of the Byrnes-Georgiou-Lindquist generalized moment problem with complexity constraint. We introduce a new metric on multivariable spectral densities induced by the family of their spectral…
This paper introduces a variational approximation framework using direct optimization of what is known as the {\it scale invariant Alpha-Beta divergence} (sAB divergence). This new objective encompasses most variational objectives that use…
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…
We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy…
This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…
In this paper, we establish optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal processing, image processing, and computer vision, among…
We propose a closed-form spectral framework for relative log-density estimation in linearly parameterized probabilistic models, including unnormalized and conditional models. This is achieved by representing the Kullback-Leibler (KL)…
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…
This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations…
The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications but doing so naively is intractable. Computing the alpha-beta divergence -- a family of divergences that includes the…
We introduce a new transformation called \emph{relative differential-escort}, which extends the usual differential-escort transformation by relating the change of variable to a reference probability density. As an application of it, we…
There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in…
In this paper, we consider an infinite dimensional exponential family, $\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a…
Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have primarily centered…
We derive a new variational formula for the R\'enyi family of divergences, $R_\alpha(Q\|P)$, between probability measures $Q$ and $P$. Our result generalizes the classical Donsker-Varadhan variational formula for the Kullback-Leibler…
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically…