相关论文: Assessing prediction error of nonparametric regres…

It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…

Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it…

This paper develops a class of Bayesian non- and semiparametric methods for estimating regression curves and surfaces. The main idea is to model the regression as locally linear, and then place suitable local priors on the local parameters.…

The Maximum Likelihood (ML) and Cross Validation (CV) methods for estimating covariance hyper-parameters are compared, in the context of Kriging with a misspecified covariance structure. A two-step approach is used. First, the case of the…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not…

We develop a direct debiased machine learning framework comprising Neyman targeted estimation and generalized Riesz regression. Our framework unifies Riesz regression for automatic debiased machine learning, covariate balancing, targeted…

This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and…

We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…

In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…

Semi-supervised learning by self-training heavily relies on pseudo-label selection (PLS). The selection often depends on the initial model fit on labeled data. Early overfitting might thus be propagated to the final model by selecting…

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…

We propose an estimator of prediction error using an approximate message passing (AMP) algorithm that can be applied to a broad range of sparse penalties. Following Stein's lemma, the estimator of the generalized degrees of freedom, which…

This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…

We introduce a novel \textit{k}-nearest neighbor (\textit{k}-NN) regression method for joint estimation of the conditional mean and variance. The proposed algorithm preserves the computational efficiency and manifold-learning capabilities…

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…

Tuning parameters in supervised learning problems are often estimated by cross-validation. The minimum value of the cross-validation error can be biased downward as an estimate of the test error at that same value of the tuning parameter.…

Penalized logistic regression methods are frequently used to investigate the relationship between a binary outcome and a set of explanatory variables. The model performance can be assessed by measures such as the concordance statistic…

The accuracy of machine learning systems is a widely studied research topic. Established techniques such as cross-validation predict the accuracy on unseen data of the classifier produced by applying a given learning method to a given…

Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…