Related papers: Model selection for sequential designs in discrete…

We present a unified technique for sequential estimation of convex divergences between distributions, including integral probability metrics like the kernel maximum mean discrepancy, $\varphi$-divergences like the Kullback-Leibler…

A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…

Complex models are often used to understand interactions and drivers of human-induced and/or natural phenomena. It is worth identifying the input variables that drive the model output(s) in a given domain and/or govern specific model…

In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…

In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…

This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new…

In this paper, we use a probabilistic model to estimate the number of uncorrelated features in a large dataset. Our model allows for both pairwise feature correlation (collinearity) and interdependency of multiple features…

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…

We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$. We also consider estimation of highest density regions, which differs from estimating level sets in that one…

We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…

Probabilistic convolutional neural networks, which predict distributions of predictions instead of point estimates, led to recent advances in many areas of computer vision, from image reconstruction to semantic segmentation. Besides state…

Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty…

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

Interval-censored data are common in fields such as epidemiology and demography. When the failure event of interest is relatively rare and the collection of covariates is costly, researchers often adopt the case-cohort design to reduce…

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic…

The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its…

This paper deals with the stochastic control of nonlinear systems in the presence of state and control constraints, for uncertain discrete-time dynamics in finite dimensional spaces. In the deterministic case, the viability kernel is known…