Oracle Inequalities for High-dimensional Prediction
The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general oracle inequality for prediction in high-dimensional linear regression with such methods. Since the proof relies only on convexity and continuity arguments, the result holds irrespective of the design matrix and applies to a wide range of penalized estimators. Overall, the bound demonstrates that generic estimators can provide consistent prediction with any design matrix. From a practical point of view, the bound can help to identify the potential of specific estimators, and they can help to get a sense of the prediction accuracy in a given application.
Code (0)
등록된 구현이 없습니다.
Tasks
PredictionVocal Bursts Intensity PredictionSimilar Papers 제목 키워드 기반
Asymptotic properties for combined $L_1$ and concave regularization
Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined $L_1$ and concave penalties, and study the sampling properties of the glob…
Variable SelectionOracle Inequalities for High Dimensional Vector Autoregressions
This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of …
Vocal Bursts Intensity PredictionAsymptotic equivalence of regularization methods in thresholded parameter space
High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular classes of convex ones and concave ones. A long debate has been on whether on…
Variable SelectionHigh dimensional thresholded regression and shrinkage effect
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in s…
PredictionregressionVariable SelectionVocal Bursts Intensity PredictionOn the Exponentially Weighted Aggregate with the Laplace Prior
In this paper, we study the statistical behaviour of the Exponentially Weighted Aggregate (EWA) in the problem of high-dimensional regression with fixed design. Under the assumption that the underlying regression vector …
regression