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Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…

This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover,…

The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…

We study computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded factor size and bounded connectivity can be learned in polynomial time…

Just as semantic hashing can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for…

In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim we…

In situations where the sampling units in a study can be more easily ranked based on the measurement of an auxiliary variable, ranked set sampling provide unbiased estimators for the mean of a population that they are more efficient than…

Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…

In this work, we present a probabilistic model for directed graphs where nodes have attributes and labels. This model serves as a generative classifier capable of predicting the labels of unseen nodes using either maximum likelihood or…

When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the…

This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling…

Pair-wise Markov random fields (MRF) are considered for application to the development of low complexity, iterative MIMO detection. Specifically, we consider two types of MRF, namely, the fully-connected and ring-type. For the edge…

This paper studies the asymptotic distribution of a constrained lasso-type estimator for denoising signals defined on the nodes of a graph, where the underlying structure encodes relationships between variables. We show that, under suitable…

We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints.For discrete distributions, we assume that the two-dimensional array to estimate is a low-rank probability matrix. In the…

We propose a semiparametric model for dyadic link formations in directed networks. The model contains a set of degree parameters that measure different effects of popularity or outgoingness across nodes, a regression parameter vector that…

We introduce a new predictive mechanism that operates in the presence of hidden confounding across distributionally diverse data sources while ensuring consistent estimation of causal parameters-despite their recognized suboptimality for…

Training generative models that capture rich semantics of the data and interpreting the latent representations encoded by such models are very important problems in un-/self-supervised learning. In this work, we provide a simple algorithm…

Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a…

We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…

A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…