Related papers: Shrinking characteristics of precision matrix esti…
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 consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…
This paper proposes a penalized composite likelihood method for model selection in colored graphical Gaussian models. The method provides a sparse and symmetry-constrained estimator of the precision matrix, and thus conducts model selection…
We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…
Precision medicine is accelerating rapidly in the field of health research. This includes fitting predictive models for individual patients based on patient similarity in an attempt to improve model performance. We propose an algorithm…
Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…
Approximate computing is being considered as a promising design paradigm to overcome the energy and performance challenges in computationally demanding applications. If the case where the accuracy can be configured, the quality level versus…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…
Given a binary prediction problem, which performance metric should the classifier optimize? We address this question by formalizing the problem of Metric Elicitation. The goal of metric elicitation is to discover the performance metric of a…
Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…
We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
This article explores the estimation of precision matrices in high-dimensional Gaussian graphical models. We address the challenge of improving the accuracy of maximum likelihood-based precision estimation through penalization.…
We propose a new simulation-based estimation method, adversarial estimation, for structural models. The estimator is formulated as the solution to a minimax problem between a generator (which generates simulated observations using the…
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…
We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…
We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…