相关论文: Hellinger vs. Kullback-Leibler multivariable spect…
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…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
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 establish the well-posedness of the generalized moment problems recently studied by Byrnes-Georgiou-Lindquist and coworkers, and by Ferrante-Pavon-Ramponi. We then apply these continuity results to prove almost sure…
We study the problem of nonnegative rank-one approximation of a nonnegative tensor, and show that the globally optimal solution that minimizes the generalized Kullback-Leibler divergence can be efficiently obtained, i.e., it is not NP-hard.…
In this paper, we extend the Beta divergence family to multivariate power spectral densities. Similarly to the scalar case, we show that it smoothly connects the multivariate Kullback-Leibler divergence with the multivariate Itakura-Saito…
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…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
Given a matrix $A$, a matrix nearness problem seeks an $X$ that most closely approximates $A$ in the sense of minimizing $\lVert A - X\rVert$ under a variety of constraints on $X$. A generalized matrix nearness problem seeks the same but…
A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this…
We derive, similar to Lau and Riha, a matrix formulation of a general best approximation theorem of Singer for the special case of spectral approximations of a given matrix from a given subspace. Using our matrix formulation we describe the…
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…
In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
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)…
Maximizing the Kullback-Leibler divergence (KLD) is a fundamental problem in waveform design for active sensing and hypothesis testing, as it directly relates to the error exponent of detection probability. However, the associated…
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…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…