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We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
In this work, we present our various contributions to the objective of building a decision support tool for the diagnosis of rare diseases. Our goal is to achieve a state of knowledge where the uncertainty about the patient's disease is…
We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…
Given data generated by an observable stochastic process, we study how to construct statistically optimal decisions for general stochastic optimization problems. Our setting encompasses non-standard data structures, including data…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
Formulating accurate and robust classification strategies is a key challenge of developing diagnostic and antibody tests. Methods that do not explicitly account for disease prevalence and uncertainty therein can lead to significant…
This paper investigates the adaptive identification and prediction problems for stochastic dynamical systems with saturated observations, which arise from various fields in engineering and social systems, but up to now still lack…
A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study…
In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
This paper studies some asymptotic properties of adaptive algorithms widely used in optimization and machine learning, and among them Adagrad and Rmsprop, which are involved in most of the blackbox deep learning algorithms. Our setup is the…
Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at scheduling time, and (ii) an opportunity to reschedule the remaining tasks each time a task processing is…
This paper presents a new approach, based on polynomial optimization and the method of moments, to the problem of anomaly detection. The proposed technique only requires information about the statistical moments of the normal-state…
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of H\'{a}jek and Le Cam for classical statistical problems. We give complementary optimality results,…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic…
We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
Several studies point out different causes of performance degradation in supervised machine learning. Problems such as class imbalance, overlapping, small-disjuncts, noisy labels, and sparseness limit accuracy in classification algorithms.…