Related papers: Dimension reduction and variable selection in case…

Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…

This paper studies an integrated learning and optimization problem in which a prediction model estimates the right-hand-side parameters of a linear program (LP) using a contextual vector. Considering that such a prediction alters the…

To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for…

We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…

Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson…

Pairwise likelihood is a useful approximation to the full likelihood function for covariance estimation in high-dimensional context. It simplifies high-dimensional dependencies by combining marginal bivariate likelihood objects, thus making…

We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…

We investigate two perturbation approaches to overcome conservatism that optimism based algorithms chronically suffer from in practice. The first approach replaces optimism with a simple randomization when using confidence sets. The second…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy…

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…

The root-cause diagnostics of product quality defects in multistage manufacturing processes often requires a joint identification of crucial stages and process variables. To meet this requirement, this paper proposes a novel penalized…

We describe here a framework for a certain class of multiscale likelihood factorizations wherein, in analogy to a wavelet decomposition of an L^2 function, a given likelihood function has an alternative representation as a product of…

The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…

We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify the uncertainty in the minimizer due to…

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product…

We present a new family of model selection algorithms based on the resampling heuristics. It can be used in several frameworks, do not require any knowledge about the unknown law of the data, and may be seen as a generalization of local…

In the regression setting, given a set of hyper-parameters, a model-estimation procedure constructs a model from training data. The optimal hyper-parameters that minimize generalization error of the model are usually unknown. In practice…

This article considers a linear model in a high dimensional data scenario. We propose a process which uses multiple loss functions both to select relevant predictors and to estimate parameters, and study its asymptotic properties. Variable…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…