Related papers: Consistency Analysis for the Doubly Stochastic Dir…
The Dirichlet process mixture (DPM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as…
We address the problem of retrieving relevant experiments given a query experiment, motivated by the public databases of datasets in molecular biology and other experimental sciences, and the need of scientists to relate to earlier work on…
In this paper, our goal is solving backward doubly stochastic differential equation (BDSDE for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic…
Double descent is a surprising phenomenon in machine learning, in which as the number of model parameters grows relative to the number of data, test error drops as models grow ever larger into the highly overparameterized (data…
Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…
In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
Time series data may exhibit clustering over time and, in a multiple time series context, the clustering behavior may differ across the series. This paper is motivated by the Bayesian non--parametric modeling of the dependence between the…
We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…
This paper gives an elementary proof for the following theorem: a renewal process can be represented by a doubly-stochastic Poisson process (DSPP) if and only if the Laplace-Stieltjes transform of the inter-arrival times is of the following…
Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been…
In answer set programming, inconsistencies arise when the constraints placed on a program become unsatisfiable. In this paper, we introduce a technique for dynamic consistency checking for our goal-directed method for computing answer sets,…
The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep…
In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…
Nowadays, algorithms with fast convergence, small memory footprints, and low per-iteration complexity are particularly favorable for artificial intelligence applications. In this paper, we propose a doubly stochastic algorithm with a novel…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…
We introduce topological differential testing (TDT), an approach to extracting the consensus behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a simplicial complex (and implicitly draws on richer…
In this paper, we obtain stability results for backward stochastic differential equations with jumps (BSDEs) in a very general framework. More specifically, we consider a convergent sequence of standard data, each associated to their own…
In this article, we present data-subsetting algorithms that allow for the approximate and scalable implementation of the Bayesian bootstrap. They are analogous to two existing algorithms in the frequentist literature: the bag of little…