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As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…

Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

Stochastic gradient descent (SGD) has been widely studied in the literature from different angles, and is commonly employed for solving many big data machine learning problems. However, the averaging technique, which combines all iterative…

In this work we provide a simple estimation procedure for a general frailty model for analysis of prospective correlated failure times. Rigorous large-sample theory for the proposed estimators of both the regression coefficient vector and…

We propose VarFA, a variational inference factor analysis framework that extends existing factor analysis models for educational data mining to efficiently output uncertainty estimation in the model's estimated factors. Such uncertainty…

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased…

In this paper, we propose a method for estimating model parameters using Small-Angle Scattering (SAS) data based on the Bayesian inference. Conventional SAS data analyses involve processes of manual parameter adjustment by analysts or…

Intercurrent events, common in clinical trials and observational studies, affect the existence or interpretation of final outcomes. Principal stratification addresses this challenge by defining local average treatment effect estimands…

We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…

We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility…

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…

We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The…

Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…

Generalized linear mixed models (GLMM) encompass large class of statistical models, with a vast range of applications areas. GLMM extends the linear mixed models allowing for different types of response variable. Three most common data…

We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address…

Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a…

In this paper we consider a network of spatially distributed sensors which collect measurement samples of a spatial field, and aim at estimating in a distributed way (without any central coordinator) the entire field by suitably fusing all…

In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…

Beta-sorted portfolios -- portfolios comprised of assets with similar covariation to selected risk factors -- are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little…