565 citations · 2.9k across the 63 of their papers we have counts for
25 papers · 1 filter
Conformal Prediction Through the Lens of Hypothesis Testing: Universality, Impossibility, and Optimality
Ryan J. Tibshirani, Rina Foygel Barber, Aaditya Ramdas
The connections between conformal prediction and permutation tests are already widely-known in the literature. Some authors motivate conformal prediction by saying that it computes…
Unifying Different Theories of Conformal Prediction
Rina Foygel Barber, Ryan J. Tibshirani
This paper presents a unified framework for understanding the methodology and theory behind several different methods in the conformal prediction literature, which includes standar…
Optimal Ridge Regularization for Out-of-Distribution Prediction
Pratik Patil, Jin-Hong Du, Ryan J. Tibshirani
We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train dis…
Failures and Successes of Cross-Validation for Early-Stopped Gradient Descent
Pratik Patil, Yuchen Wu, Ryan J. Tibshirani
We analyze the statistical properties of generalized cross-validation (GCV) and leave-one-out cross-validation (LOOCV) applied to early-stopped gradient descent (GD) in high-dimens…
De Finetti's theorem and related results for infinite weighted exchangeable sequences
Rina Foygel Barber, Emmanuel J. Candes, Aaditya Ramdas +1
De Finetti's theorem, also called the de Finetti-Hewitt-Savage theorem, is a foundational result in probability and statistics. Roughly, it says that an infinite sequence of exchan…
Minimax Optimal Regression over Sobolev Spaces via Laplacian Eigenmaps on Neighborhood Graphs
Alden Green, Sivaraman Balakrishnan, Ryan J. Tibshirani
In this paper we study the statistical properties of Principal Components Regression with Laplacian Eigenmaps (PCR-LE), a method for nonparametric regression based on Laplacian Eig…
Unbiased Risk Estimation in the Normal Means Problem via Coupled Bootstrap Techniques
Natalia L. Oliveira, Jing Lei, Ryan J. Tibshirani
We develop a new approach for estimating the risk of an arbitrary estimator of the mean vector in the classical normal means problem. The key idea is to generate two auxiliary data…
Minimax Optimal Regression over Sobolev Spaces via Laplacian Regularization on Neighborhood Graphs
Alden Green, Sivaraman Balakrishnan, Ryan J. Tibshirani
In this paper we study the statistical properties of Laplacian smoothing, a graph-based approach to nonparametric regression. Under standard regularity conditions, we establish upp…
Divided Differences, Falling Factorials, and Discrete Splines: Another Look at Trend Filtering and Related Problems
Ryan J. Tibshirani
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, b…
Statistical Guarantees for Local Spectral Clustering on Random Neighborhood Graphs
Alden Green, Sivaraman Balakrishnan, Ryan J. Tibshirani
We study the Personalized PageRank (PPR) algorithm, a local spectral method for clustering, which extracts clusters using locally-biased random walks around a given seed node. In c…
Surprises in High-Dimensional Ridgeless Least Squares Interpolation
Trevor Hastie, Andrea Montanari, Saharon Rosset +1
Interpolators -- estimators that achieve zero training error -- have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be m…
The limits of distribution-free conditional predictive inference
Rina Foygel Barber, Emmanuel J. Candès, Aaditya Ramdas +1
We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existin…
The Generalized Lasso Problem and Uniqueness
Alnur Ali, Ryan J. Tibshirani
We study uniqueness in the generalized lasso problem, where the penalty is the norm of a matrix times the coefficient vector. We derive a broad result on uniqueness th…
Excess Optimism: How Biased is the Apparent Error of an Estimator Tuned by SURE?
Ryan J. Tibshirani, Saharon Rosset
Nearly all estimators in statistical prediction come with an associated tuning parameter, in one way or another. Common practice, given data, is to choose the tuning parameter valu…
The DFS Fused Lasso: Linear-Time Denoising over General Graphs
Oscar Hernan Madrid Padilla, James G. Scott, James Sharpnack +1
The fused lasso, also known as (anisotropic) total variation denoising, is widely used for piecewise constant signal estimation with respect to a given undirected graph. The fused…
Total Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers
Veeranjaneyulu Sadhanala, Yu-Xiang Wang, Ryan Tibshirani
We consider the problem of estimating a function defined over locations on a -dimensional grid (having all side lengths equal to ). When the function is constrained…
Uniform Asymptotic Inference and the Bootstrap After Model Selection
Ryan J. Tibshirani, Alessandro Rinaldo, Robert Tibshirani +1
Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed er…
Rejoinder: "A significance test for the lasso"
Richard Lockhart, Jonathan Taylor, Ryan J. Tibshirani +1
Rejoinder of "A significance test for the lasso" by Richard Lockhart, Jonathan Taylor, Ryan J. Tibshirani, Robert Tibshirani [arXiv:1301.7161].
Degrees of Freedom and Model Search
Ryan J. Tibshirani
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…
Adaptive piecewise polynomial estimation via trend filtering
Ryan J. Tibshirani
We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimize…
A significance test for the lasso
Richard Lockhart, Jonathan Taylor, Ryan J. Tibshirani +1
In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along…
The Lasso Problem and Uniqueness
Ryan J. Tibshirani
The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p>n, the lasso c…
Degrees of freedom in lasso problems
Ryan J. Tibshirani, Jonathan Taylor
We derive the degrees of freedom of the lasso fit, placing no assumptions on the predictor matrix . Like the well-known result of Zou, Hastie and Tibshirani [Ann. Statist. 35 (2…
Strong rules for discarding predictors in lasso-type problems
Robert Tibshirani, Jacob Bien, Jerome Friedman +4
We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui et al (2010) propose "SAFE" rules that guarantee that…