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We are interested in modeling networks in which the connectivity among the nodes and node attributes are random variables and interact with each other. We propose a probabilistic model that allows one to formulate jointly a probability…
We use neutron star mass and radius measurements to constrain the spontaneous scalarization phenomenon in scalar-tensor theories using Bayesian analysis. Neutron star structures in this scenario can be significantly different from the case…
We treat projective dependency trees as latent variables in our probabilistic model and induce them in such a way as to be beneficial for a downstream task, without relying on any direct tree supervision. Our approach relies on Gumbel…
Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
We construct a tree-based dependence structure for the representation of binomial, Poisson and Gaussian random vectors having a given covariance matrix, using sums of independent random variables. This construction allows us to characterize…
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the…
Estimating the unconstrained mean and covariance matrix is a popular topic in statistics. However, estimation of the parameters of $N_p(\mu,\Sigma)$ under joint constraints such as $\Sigma\mu = \mu$ has not received much attention. It can…
We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
Motivated by the problem of testing tetrad constraints in factor analysis, we study the large-sample distribution of Wald statistics at parameter points at which the gradient of the tested constraint vanishes. When based on an…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
Graph alignment - identifying node correspondences between two graphs - is a fundamental problem with applications in network analysis, biology, and privacy research. While substantial progress has been made in aligning correlated…
We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…
Recently, Sturma, Drton, and Leung proposed a general-purpose stochastic method for hypothesis testing in models defined by polynomial equality and inequality constraints. Notably, the method remains theoretically valid even near irregular…
There are many high dimensional function classes that have fast agnostic learning algorithms when assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be confident that…
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…
Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical…