Related papers: Dense Signals, Linear Estimators, and Out-of-Sampl…
This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…
We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
We study the problem of estimating vector-valued variables from noisy "relative" measurements. This problem arises in several sensor network applications. The measurement model can be expressed in terms of a graph, whose nodes correspond to…
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline…
In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…
Out-of-distribution (OOD) detection is an important task in machine learning systems for ensuring their reliability and safety. Deep probabilistic generative models facilitate OOD detection by estimating the likelihood of a data sample.…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
In this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L1 penalized least absolute deviation method. Different…
Motivated by the many real-world applications of reinforcement learning (RL) that require safe-policy iterations, we consider the problem of off-policy evaluation (OPE) -- the problem of evaluating a new policy using the historical data…
Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against…
Logistic regression is a standard method in multivariate analysis for binary outcome data in epidemiological and clinical studies; however, the resultant odds-ratio estimates fail to provide directly interpretable effect measures. The…
We reassess the use of linear models to approximate response probabilities of binary outcomes, focusing on average partial effects (APE). We confirm that linear projection parameters coincide with APEs in certain scenarios. Through…
Decision trees and their ensembles are endowed with a rich set of diagnostic tools for ranking and screening variables in a predictive model. Despite the widespread use of tree based variable importance measures, pinning down their…
Ratings of a user to most items in recommender systems are usually missing not at random (MNAR), largely because users are free to choose which items to rate. To achieve unbiased learning of the prediction model under MNAR data, three…
Designing deep neural network classifiers that perform robustly on distributions differing from the available training data is an active area of machine learning research. However, out-of-distribution generalization for regression-the…
This paper considers a multiple regression model and compares, under full model hypothesis, analytically as well as by simulation, the performance characteristics of some popular penalty estimators such as ridge regression, LASSO, adaptive…
In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…
Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…
The subspace identification method (SIM) has become a widely adopted approach for the identification of discrete-time linear time-invariant (LTI) systems. In this paper, we derive finite sample high-probability error bounds for the system…