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We formalize an interpretational error that is common in statistical causal inference, termed identity slippage. This formalism is used to describe historically-recognized fallacies, and analyse a fast-growing literature in statistics and…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…

No man is an island, as individuals interact and influence one another daily in our society. When social influence takes place in experiments on a population of interconnected individuals, the treatment on a unit may affect the outcomes of…

Modelling uncertainty in Machine Learning models is essential for achieving safe and reliable predictions. Most research on uncertainty focuses on output uncertainty (predictions), but minimal attention is paid to uncertainty at inputs. We…

The linear model, in which a set of observations is assumed to be given by a linear combination of columns of a matrix, has long been the mainstay of the statistics and signal processing literature. One particular challenge for inference…

We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…

In the past two decades, psychological science has experienced an unprecedented replicability crisis which uncovered several issues. Among others, statistical inference is too often viewed as an isolated procedure limited to the analysis of…

When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…

We provide a perturbative expansion for the empirical spectral distribution of a Hermitian matrix with large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent…

In both finance and economics, quantitative models are usually studied as isolated mathematical objects --- most often defined by very strong simplifying assumptions concerning rationality, efficiency and the existence of disequilibrium…

The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the…

This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…

Linear mixed effects are considered excellent predictors of cluster-level parameters in various domains. However, previous work has shown that their performance can be seriously affected by departures from modelling assumptions. Since the…

Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…

In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-algebra and extends the group of unitary elements of this…

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…

Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…

We study partially linear models when the outcome of interest and some of the covariates are observed in two different datasets that cannot be linked. This type of data combination problem arises very frequently in empirical microeconomics.…