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Scientific fields such as insider-threat detection and highway-safety planning often lack sufficient amounts of time-series data to estimate statistical models for the purpose of scientific discovery. Moreover, the available limited data…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…
The paper describes a new class of capture-recapture models for closed populations when individual covariates are available. The novelty consists in combining a latent class model for the distribution of the capture history, where the class…
Several approaches have been proposed in the literature for clustering multivariate ordinal data. These methods typically treat missing values as absent information, rather than recognizing them as valuable for profiling population…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
We study a non-parametric approach to multivariate density estimation. The estimators are piecewise constant density functions supported by binary partitions. The partition of the sample space is learned by maximizing the likelihood of the…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…
We introduce a density-based clustering method called skeleton clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large…
Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…
We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…
We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions. Following the method of moments, we tackle an…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on…
Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…