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Various events in the nature, economics and in other areas force us to combine the study of extremes with regression and other methods. A useful tool for reducing the role of nuisance regression, while we are interested in the shape or…
We construct Nash-equilibria in mean-field portfolio games of optimal investment and hedging under relative performance concerns with exponential (CARA) utility preferences. Common noise dynamics are modeled by integer-valued random…
Estimating causal quantities (CQs) typically requires large datasets, which can be expensive to obtain, especially when measuring individual outcomes is costly. This challenge highlights the importance of sample-efficient active learning…
The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations, usual empirical averages may fail to provide reliable…
In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…
This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation,…
Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…
Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…
We address a fundamental problem that is systematically encountered when modeling complex systems: the limitedness of the information available. In the case of economic and financial networks, privacy issues severely limit the information…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…
We propose a general error analysis related to the low-rank approximation of a given real matrix in both the spectral and Frobenius norms. First, we derive deterministic error bounds that hold with some minimal assumptions. Second, we…
In this paper, we present a generalized estimating equations based estimation approach and a variable selection procedure for single-index models when the observed data are clustered. Unlike the case of independent observations,…
We study a coarsening model describing the dynamics of interfaces in the one-dimensional Allen-Cahn equation. Given a partition of the real line into intervals of length greater than one, the model consists in constantly eliminating the…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…
In a broad and fundamental type of ''inverse problems'' in science, one infers a spatially distributed physical attribute based on observations of processes that are controlled by the spatial attribute in question. The data-generating field…
Generalized linear models are widely used in many areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in generalized linear models using residuals that are approximately standard…
Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure…
Quantile regression is a statistical method which, unlike classical regression, aims to predict the conditional quantiles. Classical quantile regression methods face difficulties, particularly when the quantile under consideration is…