Related papers: Leave-one-out prediction intervals in linear regre…
In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of…
We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (2013). In particular the candidate models used can…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable, and predictors are trained in a memoryless fashion. However, these assumptions and constraints are…
We develop methodology for valid inference after variable selection in logistic regression when the responses are partially observed, that is, when one observes a set of error-prone testing outcomes instead of the true values of the…
Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators…
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…
Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations,…
The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as $K$-fold cross validation suffer from large biases. Motivated by the low bias of the leave-one-out cross…
We consider predictive checking for Bayesian model assessment using leave-one-out probability integral transform (LOO-PIT). LOO-PIT values are conditional cumulative predictive probabilities given LOO predictive distributions and…
A generic out-of-sample error estimate is proposed for robust $M$-estimators regularized with a convex penalty in high-dimensional linear regression where $(X,y)$ is observed and $p,n$ are of the same order. If $\psi$ is the derivative of…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…
Residual variance and the signal-to-noise ratio are important quantities in many statistical models and model fitting procedures. They play an important role in regression diagnostics, in determining the performance limits in estimation and…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…
An important issue when using Machine Learning algorithms in recent research is the lack of interpretability. Although these algorithms provide accurate point predictions for various learning problems, uncertainty estimates connected with…
When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the…
Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional…
Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the…