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Several scalable sample-based methods to compute the Kullback Leibler (KL) divergence between two distributions have been proposed and applied in large-scale machine learning models. While they have been found to be unstable, the…
The t-distributed Stochastic Neighbor Embedding (t-SNE) is a powerful and popular method for visualizing high-dimensional data. It minimizes the Kullback-Leibler (KL) divergence between the original and embedded data distributions. In this…
AI computation in healthcare faces significant challenges when clinical datasets are limited and heterogeneous. Integrating datasets from multiple sources and different equipments is critical for effective AI computation but is complicated…
This paper addresses the problem of distributed detection in fixed and switching networks. A network of agents observe partially informative signals about the unknown state of the world. Hence, they collaborate with each other to identify…
Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some…
A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state tomography, is also applicable to…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
The Kullback-Leibler (KL) divergence plays a central role in probabilistic machine learning, where it commonly serves as the canonical loss function. Optimization in such settings is often performed over the probability simplex, where the…
Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $\alpha$-divergence face analytical challenges due to the $\alpha$-power…
Kullback Leibler (KL) control problems allow for efficient computation of optimal control by solving a principal eigenvector problem. However, direct applicability of such framework to continuous state-action systems is limited. In this…
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.…
Causal discovery from observational data underpins applications in finance, climate modeling, and machine learning. Constraint-based causal discovery reduces structure learning to a sequence of conditional independence (CI) tests, where…
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…
Transmission electron microscopes (TEMs) enable atomic-scale imaging but suffer from aberrations caused by lens imperfections and environmental conditions, reducing image quality. These aberrations can be compensated by adjusting…
We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to…
Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…
Many two-sample problems call for a comparison of two distributions from an exponential family. Density ratio estimation methods provide ways to solve such problems through direct estimation of the differences in natural parameters. The…
Computed tomography (CT) is an important imaging technique used in medical analysis of the internal structure of the human body. Previously, image segmentation methods were required after acquiring reconstructed CT images to obtain…
We consider the problem of constructing a least conservative estimator of the expected value $\mu$ of a non-negative heavy-tailed random variable. We require that the probability of overestimating the expected value $\mu$ is kept…
In Simulation-based Inference, the goal is to solve the inverse problem when the likelihood is only known implicitly. Neural Posterior Estimation commonly fits a normalized density estimator as a surrogate model for the posterior. This…