arXiv subjects

Ryan J. Tibshirani

Publications and source records attributed to Ryan J. Tibshirani.

76 records · Page 5Linked to original sources

arXiv2012

Degrees of freedom in lasso problems

We derive the degrees of freedom of the lasso fit, placing no assumptions on the predictor matrix $X$. Like the well-known result of Zou, Hastie and Tibshirani [Ann. Statist. 35 (2007) 2173-2192], which gives the degrees of freedom of the lasso fit when $X$ has full column rank, we express our result in terms of the active set of a lasso solution. We extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitrary predictor matrix $X$ (and an arbitrary penalty matrix $D$). Though our focus is degrees of freedom, we establish some intermediate results on the lasso and generalized lasso that may be interesting on their own.

math.ST↗

arXiv2010

Strong rules for discarding predictors in lasso-type problems

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 a coefficient will be zero in the solution, based on the inner products of each predictor with the outcome. In this paper we propose strong rules that are not foolproof but rarely fail in practice. These can be complemented with simple checks of the Karush- Kuhn-Tucker (KKT) conditions to provide safe rules that offer substantial speed and space savings in a variety of statistical convex optimization problems.

math.ST↗

arXiv2009

A bias correction for the minimum error rate in cross-validation

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. We propose a simple method for the estimation of this bias that uses information from the cross-validation process. As a result, it requires essentially no additional computation. We apply our bias estimate to a number of popular classifiers in various settings, and examine its performance.

stat.AP↗

arXiv2009

Fast computation of the median by successive binning

This paper describes a new median algorithm and a median approximation algorithm. The former has O(n) average running time and the latter has O(n) worst-case running time. These algorithms are highly competitive with the standard algorithm when computing the median of a single data set, but are significantly faster in updating the median when more data is added.

stat.CO↗