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Consider a regression problem where the learner is given a large collection of $d$-dimensional data points, but can only query a small subset of the real-valued labels. How many queries are needed to obtain a $1+\epsilon$ relative error…
We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified regression plane in a linear regression setting, when the observed samples are potentially contaminated with adversarially corrupted outliers. Our…
We consider the random design regression model with square loss. We propose a method that aggregates empirical minimizers (ERM) over appropriately chosen random subsets and reduces to ERM in the extreme case, and we establish sharp oracle…
Robust regression models in the presence of outliers have significant practical relevance in areas such as signal processing, financial econometrics, and energy management. Many existing robust regression methods, either grounded in…
In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…
In this paper we consider an optimal investment and reinsurance problem with partially unknown model parameters which are allowed to be learned. The model includes multiple business lines and dependence between them. The aim is to maximize…
We study the problem of training an accurate linear regression model by procuring labels from multiple noisy crowd annotators, under a budget constraint. We propose a Bayesian model for linear regression in crowdsourcing and use variational…
The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the…
We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample…
We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed…
The paper is about developing a solver for maximizing a real-valued function of binary variables. The solver relies on an algorithm that estimates the optimal objective-function value of instances from the underlying distribution of…
Given a data matrix $X \in R^{n\times d}$ and a response vector $y \in R^{n}$, suppose $n>d$, it costs $O(n d^2)$ time and $O(n d)$ space to solve the least squares regression (LSR) problem. When $n$ and $d$ are both large, exactly solving…
Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios,…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
In this paper, we consider a multi-attribute decision making problem where the decision maker's (DM's) objective is to maximize the expected utility of outcomes but the true utility function which captures the DM's risk preference is…
We consider the estimation of a bounded regression function with nonparametric heteroscedastic noise and random design. We study the true and empirical excess risks of the least-squares estimator on finite-dimensional vector spaces. We give…
In this paper we consider the problem of Learning from Satisfying Assignments introduced by \cite{1} of finding a distribution that is a close approximation to the uniform distribution over the satisfying assignments of a low complexity…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…
We consider the problem of estimating the expected value of information (the knowledge gradient) for Bayesian learning problems where the belief model is nonlinear in the parameters. Our goal is to maximize some metric, while simultaneously…