Related papers: Shrinkage for Categorical Regressors
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
A novel approach to improve prediction and inference in M-estimation by integrating external information from heterogeneous populations is proposed. Our method leverages joint asymptotics to combine estimates from external and internal…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…
We consider recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values. We adopt an asymptotic framework, in which the matrix…
Ridge regression is a popular method for dense least squares regularization. In this work, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed and a…
In a coherent reliability system composed of multiple components configured according to a specific structure function, the distribution of system time to failure, or system lifetime, is often of primary interest. Accurate estimation of…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
This paper is concerned with the computation of the high-dimensional zero-norm penalized quantile regression estimator, defined as a global minimizer of the zero-norm penalized check loss function. To seek a desirable approximation to the…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
We study a set of regularization methods for high-dimensional linear regression models. These penalized estimators have the square root of the residual sum of squared errors as loss function, and any weakly decomposable norm as penalty…
Many applied settings in empirical economics involve simultaneous estimation of a large number of parameters. In particular, applied economists are often interested in estimating the effects of many-valued treatments (like teacher effects…
The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…
In this work, we propose a mean-squared error-based risk that enables the comparison and optimization of estimators of squared calibration errors in practical settings. Improving the calibration of classifiers is crucial for enhancing the…
We consider high-dimensional sparse regression problems in which we observe $y = X \beta + z$, where $X$ is an $n \times p$ design matrix and $z$ is an $n$-dimensional vector of independent Gaussian errors, each with variance $\sigma^2$.…
Penalised estimation methods for point processes usually rely on a large amount of independent repetitions for cross-validation purposes. However, in the case of a single realisation of the process, existing cross-validation methods may be…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero…
Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high-dimensional covariates primarily…