相关论文: Degrees of freedom for nonlinear least squares est…
In this paper we study the effective degrees of freedom of a general class of reduced rank estimators for multivariate regression in the framework of Stein's unbiased risk estimation (SURE). We derive a finite-sample exact unbiased…
We study the effective degrees of freedom of the lasso in the framework of Stein's unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degrees of freedom of the lasso--a…
A representation of the degrees of freedom akin to Stein's lemma is given for a class of estimators of a mean value parameter in $\mathbb{R}^n$. Contrary to previous results our representation holds for a range of discontinues estimators.…
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…
Estimating a low rank matrix from its linear measurements is a problem of central importance in contemporary statistical analysis. The choice of tuning parameters for estimators remains an important challenge from a theoretical and…
Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quantitative description of the amount of fitting performed by a given procedure. But, despite this fundamental role in statistics, its behavior not…
The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this…
In the framework of matrix valued observables with low rank means, Stein's unbiased risk estimate (SURE) can be useful for risk estimation and for tuning the amount of shrinkage towards low rank matrices. This was demonstrated by Cand\`es…
In this work, we construct a risk estimator for hard thresholding which can be used as a basis to solve the difficult task of automatically selecting the threshold. As hard thresholding is not even continuous, Stein's lemma cannot be used…
A central question in modern machine learning and imaging sciences is to quantify the number of effective parameters of vastly over-parameterized models. The degrees of freedom is a mathematically convenient way to define this number of…
Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
Overparametrized interpolating models have drawn increasing attention from machine learning. Some recent studies suggest that regularized interpolating models can generalize well. This phenomenon seemingly contradicts the conventional…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
In this paper, we investigate the degrees of freedom ($\dof$) of penalized $\ell_1$ minimization (also known as the Lasso) for linear regression models. We give a closed-form expression of the $\dof$ of the Lasso response. Namely, we show…
Recent work has focused on the problem of nonparametric estimation of information divergence functionals. Many existing approaches are restrictive in their assumptions on the density support set or require difficult calculations at the…
We identify and correct an error in the paper "Excess Optimism: How Biased is the Apparent Error of an Estimator Tuned by SURE?" This correction allows new guarantees on the excess degrees of freedom--the bias in the error estimate of…
The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…
In this paper, we explore degrees of freedom in deep sigmoidal neural networks. We show that the degrees of freedom in these models is related to the expected optimism, which is the expected difference between test error and training error.…
Unrolled neural networks emerged recently as an effective model for learning inverse maps appearing in image restoration tasks. However, their generalization risk (i.e., test mean-squared-error) and its link to network design and train…