Data Selection: A General Principle for Building Small Interpretable Models

TL;DR

The paper addresses how to build small, interpretable models without sacrificing accuracy by learning the training distribution and sampling data accordingly (COAS). It demonstrates COAS across three tasks—explainable clustering, prototype-based classification, and Random Forests—showing that compact models can reach competitive performance with statistically significant improvements over traditional baselines. The main contribution is a broad empirical validation that COAS is a general, model-agnostic strategy for improving small models in diverse settings, including edge devices. The work highlights practical gains, outlines measurement methodologies, and discusses future directions for theory and optimization of training-distribution-based sampling.

Abstract

We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to learn the training distribution and sample accordingly from the provided training data. The distribution learning algorithm is not a contribution of this work; our contribution is a rigorous demonstration of the broad utility of this strategy in various practical settings. We apply it to the tasks of (1) building cluster explanation trees, (2) prototype-based classification, and (3) classification using Random Forests, and show that it improves the accuracy of decades-old weak traditional baselines to be competitive with specialized modern techniques. This strategy is also versatile wrt the notion of model size. In the first two tasks, model size is considered to be number of leaves in the tree and the number of prototypes respectively. In the final task involving Random Forests, the strategy is shown to be effective even when model size comprises of more than one factor: number of trees and their maximum depth. Positive results using multiple datasets are presented that are shown to be statistically significant.

Figures (4)

• Figure 2: Comparisons over explainable clustering algorithms are shown. (a) shows the comparison for a specific dataset mice-protein. (b), (c), (d) and (e) show comparisons over other datasets - miniaturized to fit the page. (f) shows mean ranks of these techniques over five datasets across model sizes; the Friedman test is conducted over the top three techniques only, with $p = 6.688 \times {10}^{-6}$.
• Figure 3: Various prototype-based classifiers are compared. (a) shows comparison for the dataset adult. Number of prototypes are shown as percentage of the training data on the x-axis, and is referred to as "compression". (b), (c), (d) and (e) shows plots for other datasets - these are miniaturized to fit the page. (f) shows the mean ranks of techniques based on five datasets; the Friedman test is conducted over the top four techniques only, with $p=3.5025\times 10^{-8}$.
• Figure 4: (a) shows results for the dataset=covtype. (b), (c), (d) and (e) show plots for other datasets - miniaturized to fit the page. (f) provides mean ranks, but since there are only two models being compared, the Friedman test cannot be performed.
• Figure 5: The cost ratio increases and then decreases with increasing $k$. Shown for the mice-protein dataset.