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Out-of-sample risk estimation in no time flat

Abstract Number:

2344 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Paper 

Participants:

Daniel LeJeune (1), Parth Nobel (1), Emmanuel Candes (1)

Institutions:

(1) Stanford University, N/A

Co-Author(s):

Parth Nobel  
Stanford University
Emmanuel Candes  
Stanford University

First Author:

Daniel LeJeune  
Stanford University

Presenting Author:

Daniel LeJeune  
N/A

Abstract Text:

Hyperparameter tuning is an essential part of statistical machine learning pipelines, and becomes more computationally challenging as datasets become large. Furthermore, the standard method of k-fold cross-validation is known to be inconsistent for high-dimensional problems. We propose instead an efficient implementation of approximate leave-one-out (ALO) risk estimation, providing consistent risk estimation in high-dimensions at a fraction of the cost of k-fold cross-validation. We leverage randomized numerical linear algebra and reduce the computational task to a handful of quasisemidefinite linear systems, equivalent to equality-constrained quadratic programs, for any convex non-smooth loss and linear-separable regularizer.

Keywords:

Risk estimation|Cross-validation|High dimensions|Convex optimization|Randomized methods|

Sponsors:

Section on Statistical Learning and Data Science

Tracks:

Machine Learning

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