Related papers: Optimal Linear Discriminators For The Discrete Cho…
In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
In order to identify important variables that are involved in making optimal treatment decision, Lu et al. (2013) proposed a penalized least squared regression framework for a fixed number of predictors, which is robust against the…
We investigate the high-dimensional regression problem using adjacency matrices of unbalanced expander graphs. In this frame, we prove that the $\ell_{2}$-prediction error and the $\ell_{1}$-risk of the lasso and the Dantzig selector are…
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…
Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…
Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
We study the problem of dynamic batch learning in high-dimensional sparse linear contextual bandits, where a decision maker, under a given maximum-number-of-batch constraint and only able to observe rewards at the end of each batch, can…
Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art…
When model predictions inform downstream decision making, a natural question is under what conditions can the decision-makers simply respond to the predictions as if they were the true outcomes. Calibration suffices to guarantee that simple…
I consider a class of statistical decision problems in which the policymaker must decide between two policies to maximize social welfare (e.g., the population mean of an outcome) based on a finite sample. The framework introduced in this…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We investigate high-dimensional nonconvex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property…
We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…
The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the $T_p$-optimality criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289-303]. The…