Related papers: Reliable Estimation of KL Divergence using a Discr…
Generative Flow Networks (GFlowNets) are amortized inference models designed to sample from unnormalized distributions over composable objects, with applications in generative modeling for tasks in fields such as causal discovery, NLP, and…
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…
Suppose that $Y$ is a scalar and $X$ is a second-order stochastic process, where $Y$ and $X$ are conditionally independent given the random variables $\xi_1,...,\xi_p$ which belong to the closed span $L_X^2$ of $X$. This paper investigates…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
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…
Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
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…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
This short note is on a property of the Kullback-Leibler (KL) divergence which indicates that independent Gaussian distributions minimize the KL divergence from given independent Gaussian distributions. The primary purpose of this note is…
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…
Recently in [1, 2], Ali-Akbar Bromideh introduced the Kullback-Leibler Divergence (KLD) test statistic in discrim- inating between two models. It was found that the Ratio Minimized Kulback-Leibler Divergence (RMKLD) works better than the…
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed…
The learning of the region proposal in object detection using the deep neural networks (DNN) is divided into two tasks: binary classification and bounding box regression task. However, traditional RPN (Region Proposal Network) defines these…
This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…
The Kullback-Leibler divergence, the Kullback-Leibler variation, and the Bernstein "norm" are used to quantify discrepancies among probability distributions in likelihood models such as nonparametric maximum likelihood and nonparametric…
We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel…
We consider learning with possibilistic supervision for multi-class classification. For each training instance, the supervision is a normalized possibility distribution that expresses graded plausibility over the classes. From this…