Related papers: Kullback Leibler property of kernel mixture priors…
In this work, we present formulations for regularized Kullback-Leibler and R\'enyi divergences via the Alpha Log-Determinant (Log-Det) divergences between positive Hilbert-Schmidt operators on Hilbert spaces in two different settings,…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
The Kullback-Leibler (KL) divergence is a fundamental equation of information theory that quantifies the proximity of two probability distributions. Although difficult to understand by examining the equation, an intuition and understanding…
Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
We propose a method to fuse posterior distributions learned from heterogeneous datasets. Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple…
We give a short proof of the $L^{1}$ criterion for Beurling generalized integers to have a positive asymptotic density. We actually prove the existence of density under a weaker hypothesis. We also discuss related sufficient conditions for…
In 1997 H.G.Diamond gave a condition on Beurling's generalized prime numbers in order that the corresponding generalized integers have a density. We give a new proof of this condition (Theorem 1) and a proof that it is not necessary…
A common failure mode of density models trained as variational autoencoders is to model the data without relying on their latent variables, rendering these variables useless. Two contributing factors, the underspecification of the model and…
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…
In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive…
In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are…
An initial screening experiment may lead to ambiguous conclusions regarding the factors which are active in explaining the variation of an outcome variable: thus adding follow-up runs becomes necessary. We propose a fully Bayes objective…
This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into…
Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…
In this work, we are concerned with the estimation of the predictive density of a Gaussian random vector where both the mean and the variance are unknown. In such a context, we prove the inadmissibility of the best equivariant predictive…
We study classes of reproducing kernels $K$ on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
Estimating the marginal likelihoods is an essential feature of model selection in the Bayesian context. It is especially crucial to have good estimates when assessing the number of planets orbiting stars when the models explain the noisy…
We study frequentist properties of Bayesian and $L_0$ model selection, with a focus on (potentially non-linear) high-dimensional regression. We propose a construction to study how posterior probabilities and normalized $L_0$ criteria…