Related papers: Empirical risk minimization is consistent with the…

Empirical risk minimization (ERM) is a fundamental learning rule for statistical learning problems where the data is generated according to some unknown distribution $\mathsf{P}$ and returns a hypothesis $f$ chosen from a fixed class…

While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper,…

Missing data is a common problem in clinical data collection, which causes difficulty in the statistical analysis of such data. To overcome problems caused by incomplete data, we propose a new imputation method called projective resampling…

Explicit modelling of between-study heterogeneity is essential in network meta-analysis (NMA) to ensure valid inference and avoid overstating precision. While the additive random-effects (RE) model is the conventional approach, the…

In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…

Radio maps provide metrics such as the received signal strength at every location in a geographical region of interest. Extensive research has been carried out in this context, but it relies almost exclusively on synthetic-data experiments.…

Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…

In this paper, we show that, in vector-to-vector regression utilizing deep neural networks (DNNs), a generalized loss of mean absolute error (MAE) between the predicted and expected feature vectors is upper bounded by the sum of an…

Evaluating the effects of time-varying exposures is essential for longitudinal studies. The effect estimation becomes increasingly challenging when dealing with hundreds of time-dependent confounders. We propose a Marginal Structure…

In order to circumvent statistical and computational hardness results in sequential decision-making, recent work has considered smoothed online learning, where the distribution of data at each time is assumed to have bounded likeliehood…

Empirical risk minimization (ERM) can be computationally expensive, with standard solvers scaling poorly even in the convex setting. We propose a novel lossless compression framework for convex ERM based on color refinement, extending prior…

Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…

Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…

A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…

Quantifying the data uncertainty in learning tasks is often done by learning a prediction interval or prediction set of the label given the input. Two commonly desired properties for learned prediction sets are \emph{valid coverage} and…

Representative risk estimation is fundamental to clinical decision-making. However, risks are often estimated from non-representative epidemiologic studies, which usually underrepresent minorities. "Model-based" methods use population…

We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a…

Analysis of repair systems usually uses an As Good As New or As Bad As Old repair assumptions. In practice, repair actions do not result in such extreme situations, but rather in a complex transitional one, that is imperfect maintenance,…

In this article asymptotic expressions for the final prediction error (FPE) and the accumulated prediction error (APE) of the least squares predictor are obtained in regression models with nonstationary regressors. It is shown that the term…