Stabilizing black-box model selection with the inflated argmax

• URL: http://arxiv.org/abs/2410.18268v2
• Date: Fri, 31 Jan 2025 21:15:00 GMT
• Title: Stabilizing black-box model selection with the inflated argmax
• Authors: Melissa Adrian, Jake A. Soloff, Rebecca Willett,
• Abstract summary: We present a new approach to stabilizing model selection with theoretical stability guarantees. 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 overlap with the original collection.
• Score: 8.52745154080651
• License:
• Abstract: 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, and (c) a graph subset selection problem using cell-signaling data from proteomics. In these settings, the proposed method yields stable, compact, and accurate collections of selected models, outperforming a variety of benchmarks.

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