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Causal effect estimation from observational data is a crucial but challenging task. Currently, only a limited number of data-driven causal effect estimation methods are available. These methods either provide only a bound estimation of the…
Many analysis and machine learning tasks require the availability of marginal statistics on multidimensional datasets while providing strong privacy guarantees for the data subjects. Applications for these statistics range from finding…
Count data, for example the number of observed cases of a disease in a city, often arise in the fields of healthcare analytics and epidemiology. In this paper, we consider performing regression on multivariate data in which our outcome is a…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
Data privacy has increasingly become a daunting challenge because it limits data availability, which is essential in estimating statistical models such as generalized linear mixed models. Access to personal data often involves considerable…
The US Decennial Census provides valuable data for both research and policy purposes. Census data are subject to a variety of disclosure avoidance techniques prior to release in order to preserve respondent confidentiality. While many are…
This article introduces an algorithm to draw random discrete uniform variables within a given range of size n from a source of random bits. The algorithm aims to be simple to implement and optimal both with regards to the amount of random…
In the present work we have selected a collection of statistical and mathematical tools useful for the exploration of multivariate data and we present them in a form that is meant to be particularly accessible to a classically trained…
In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision…
We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…
Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting…
It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…
Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
The development of high-dimensional generative models has recently gained a great surge of interest with the introduction of variational auto-encoders and generative adversarial neural networks. Different variants have been proposed where…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…
We introduce the Poisson Binomial mechanism (PBM), a discrete differential privacy mechanism for distributed mean estimation (DME) with applications to federated learning and analytics. We provide a tight analysis of its privacy guarantees,…
Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…