## The Annals of Applied Statistics

### Customized training with an application to mass spectrometric imaging of cancer tissue

#### Abstract

We introduce a simple, interpretable strategy for making predictions on test data when the features of the test data are available at the time of model fitting. Our proposal—customized training—clusters the data to find training points close to each test point and then fits an $\ell_{1}$-regularized model (lasso) separately in each training cluster. This approach combines the local adaptivity of $k$-nearest neighbors with the interpretability of the lasso. Although we use the lasso for the model fitting, any supervised learning method can be applied to the customized training sets. We apply the method to a mass-spectrometric imaging data set from an ongoing collaboration in gastric cancer detection which demonstrates the power and interpretability of the technique. Our idea is simple but potentially useful in situations where the data have some underlying structure.

#### Article information

Source
Ann. Appl. Stat., Volume 9, Number 4 (2015), 1709-1725.

Dates
Revised: July 2015
First available in Project Euclid: 28 January 2016

https://projecteuclid.org/euclid.aoas/1453993091

Digital Object Identifier
doi:10.1214/15-AOAS866

Mathematical Reviews number (MathSciNet)
MR3456351

Zentralblatt MATH identifier
06560807

#### Citation

Powers, Scott; Hastie, Trevor; Tibshirani, Robert. Customized training with an application to mass spectrometric imaging of cancer tissue. Ann. Appl. Stat. 9 (2015), no. 4, 1709--1725. doi:10.1214/15-AOAS866. https://projecteuclid.org/euclid.aoas/1453993091

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