Stabilizing black-box model selection with the inflated argmax

Fuente: arXiv
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Main Authors: Adrian, Melissa, Soloff, Jake A., Willett, Rebecca
Format: Preprint
Published: 2024
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author Adrian, Melissa
Soloff, Jake A.
Willett, Rebecca
author_facet Adrian, Melissa
Soloff, Jake A.
Willett, Rebecca
contents Model selection is the process of choosing from a class of candidate models given data. For instance, methods such as the LASSO and sparse identification of nonlinear dynamics (SINDy) formulate model selection as finding a sparse solution to a linear system of equations determined by training data. However, absent strong assumptions, such methods are highly unstable: if a single data point is removed from the training set, a different model may be selected. In this paper, we present a new approach to stabilizing model selection with theoretical stability guarantees that leverages a combination of bagging and an ''inflated'' argmax operation. Our method selects a small collection of models that all fit the data, and it is stable in that, with high probability, the removal of any training point will result in a collection of selected models that overlaps with the original collection. We illustrate this method in (a) a simulation in which strongly correlated covariates make standard LASSO model selection highly unstable, (b) a Lotka-Volterra model selection problem focused on identifying how competition in an ecosystem influences species' abundances, (c) a graph subset selection problem using cell-signaling data from proteomics, and (d) unsupervised $κ$-means clustering. In these settings, the proposed method yields stable, compact, and accurate collections of selected models, outperforming a variety of benchmarks.
format Preprint
id arxiv_https___arxiv_org_abs_2410_18268
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Stabilizing black-box model selection with the inflated argmax
Adrian, Melissa
Soloff, Jake A.
Willett, Rebecca
Machine Learning
Methodology
Model selection is the process of choosing from a class of candidate models given data. For instance, methods such as the LASSO and sparse identification of nonlinear dynamics (SINDy) formulate model selection as finding a sparse solution to a linear system of equations determined by training data. However, absent strong assumptions, such methods are highly unstable: if a single data point is removed from the training set, a different model may be selected. In this paper, we present a new approach to stabilizing model selection with theoretical stability guarantees that leverages a combination of bagging and an ''inflated'' argmax operation. Our method selects a small collection of models that all fit the data, and it is stable in that, with high probability, the removal of any training point will result in a collection of selected models that overlaps with the original collection. We illustrate this method in (a) a simulation in which strongly correlated covariates make standard LASSO model selection highly unstable, (b) a Lotka-Volterra model selection problem focused on identifying how competition in an ecosystem influences species' abundances, (c) a graph subset selection problem using cell-signaling data from proteomics, and (d) unsupervised $κ$-means clustering. In these settings, the proposed method yields stable, compact, and accurate collections of selected models, outperforming a variety of benchmarks.
title Stabilizing black-box model selection with the inflated argmax
topic Machine Learning
Methodology
url https://arxiv.org/abs/2410.18268