Related papers: Empirical Process of Multivariate Gaussian under G…
Theoretical results for importance sampling rely on the existence of certain moments of the importance weights, which are the ratios between the proposal and target densities. In particular, a finite variance ensures square root convergence…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
This paper deals with the problem of quantifying the approximation a probability measure by means of an empirical (in a wide sense) random probability measure, depending on the first n terms of a sequence of random elements. In Section 2,…
In this paper we propose and study a general class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter in the context of long-range dependent multivariate time series. We establish large sample properties of…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
The posterior variance of Gaussian processes is a valuable measure of the learning error which is exploited in various applications such as safe reinforcement learning and control design. However, suitable analysis of the posterior variance…
Some scenarios require the computation of a predictive distribution of a new value evaluated on an objective function conditioned on previous observations. We are interested on using a model that makes valid assumptions on the objective…
Multi-output regression seeks to borrow strength and leverage commonalities across different but related outputs in order to enhance learning and prediction accuracy. A fundamental assumption is that the output/group membership labels for…
In observational studies, causal inference relies on several key identifying assumptions. One identifiability condition is the positivity assumption, which requires the probability of treatment be bounded away from 0 and 1. That is, for…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several…
We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…
Learning joint probability distributions on n random variables requires exponential sample size in the generic case. Here we consider the case that a temporal (or causal) order of the variables is known and that the (unknown) graph of…
Conditional independence in a multivariate normal (or Gaussian) distribution is characterized by the vanishing of subdeterminants of the distribution's covariance matrix. Gaussian conditional independence models thus correspond to algebraic…
Let $(X_{\underline{\ell}})_{\underline{\ell} \in \mathbb Z^d}$ be a real random field (r.f.) indexed by $\mathbb Z^d$ with common probability distribution function $F$. Let $(z_k)_{k=0}^\infty$ be a sequence in $\mathbb Z^d$. The empirical…
In this paper we propose a generalization of a class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter for long-range dependent multivariate time series. We generalize a known GSE-type estimator by…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…