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Here we introduce probabilistic weighted and unweighted multilayer networks as derived from information theoretical correlation measures on large multidimensional datasets. We present the fundamentals of the formal application of…

Adverse selection is a version of the principal-agent problem that includes monopolist nonlinear pricing, where a monopolist with known costs seeks a profit-maximizing price menu facing a population of potential consumers whose preferences…

In this paper, we analyze the behavior of the multivariate symmetric uncertainty (MSU) measure through the use of statistical simulation techniques under various mixes of informative and non-informative randomly generated features.…

A natural link between the notions of majorization and strongly Sperner posets is elucidated. It is then used to obtain a variety of consequences, including new R\'enyi entropy inequalities for sums of independent, integer-valued random…

Generalized linear models, such as logistic regression, are widely used to model the association between a treatment and a binary outcome as a function of baseline covariates. However, the coefficients of a logistic regression model…

We study the assignment problem of objects to agents with heterogeneous preferences under distributional constraints. Each agent is associated with a publicly known type and has a private ordinal ranking over objects. We are interested in…

In many public health problems, an important goal is to identify the effect of some treatment/intervention on the risk of failure for the whole population. A marginal proportional hazards regression model is often used to analyze such an…

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…

We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…

Multi-agent systems (MAS) composed of large language models often exhibit improved problem-solving performance despite operating on identical information. In this work, we provide a formal explanation for this phenomenon grounded in…

Causal influence measures for machine learnt classifiers shed light on the reasons behind classification, and aid in identifying influential input features and revealing their biases. However, such analyses involve evaluating the classifier…

We study a general class of Principal-Agent problems in continuous time under hidden action. By formulating the model as a coupled stochastic optimal control problem we are able to find a set of necessary conditions characterizing optimal…

We investigate the power of censoring techniques, first developed for learning {\em fair representations}, to address domain generalization. We examine {\em adversarial} censoring techniques for learning invariant representations from…

TheMinority Game (MG) has become a paradigm to probe complex social and economical phenomena where adaptive agents compete for a limited resource, and it finds applications in statistical and nonlinear physics as well. In the traditional MG…

Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…

We consider learning from labeled data collected across multiple environments, where the data distribution may vary across these environments. This problem is commonly approached from a causal perspective, seeking invariant representations…

In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…

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…

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…

We use the Minority Game as a testing frame for the problem of the emergence of diversity in socio-economic systems. For the MG with heterogeneous impacts, we show that the direct generalization of the usual agents' profit does not fit some…