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We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…

We present a general methodology for using unlabeled data to design semi supervised learning (SSL) variants of the Empirical Risk Minimization (ERM) learning process. Focusing on generalized linear regression, we analyze of the…

We consider the problem of state estimation from limited discrete and noisy measurements. In particular, we focus on modal state estimation, which approximates the unknown state of the system within a prescribed basis. We estimate the…

This paper studies binary logistic regression for rare events data, or imbalanced data, where the number of events (observations in one class, often called cases) is significantly smaller than the number of nonevents (observations in the…

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…

The insight that causal parameters are particularly suitable for out-of-sample prediction has sparked a lot development of causal-like predictors. However, the connection with strict causal targets, has limited the development with good…

Minimax $L_2$ risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on $d=O(\log n)$ important predictors among a list of $p$…

Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been…

This article introduces a subbagging (subsample aggregating) approach for variable selection in regression within the context of big data. The proposed subbagging approach not only ensures that variable selection is scalable given the…

In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. In this work, we challenge such a…

VARs are often estimated with Bayesian techniques to cope with model dimensionality. The posterior means define a class of shrinkage estimators, indexed by hyperparameters that determine the relative weight on maximum likelihood estimates…

Subclassification estimators are one of the methods used to estimate causal effects of interest using the propensity score. This method is more stable compared to other weighting methods, such as inverse probability weighting estimators, in…

One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic…

We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…

Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes. Motivated by…

Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the…

Distributionally Robust Optimisation (DRO) protects risk-averse decision-makers by considering the worst-case risk within an ambiguity set of distributions based on the empirical distribution or a model. To further guard against finite,…

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

We revisit the problem of mean estimation in the Gaussian sequence model with $\ell_p$ constraints for $p \in [0, \infty]$. We demonstrate two phenomena for the behavior of the maximum likelihood estimator (MLE), which depend on the noise…

Estimation of small failure probabilities is one of the most important and challenging computational problems in reliability engineering. The failure probability is usually given by an integral over a high-dimensional uncertain parameter…