Josiah Couch

Josiah Couch, Rima Arnaout, Ramy Arnaout

In deep learning, achieving high performance on image classification tasks requires diverse training sets. However, the current best practice$\unicode{x2013}$maximizing dataset size and class balance$\unicode{x2013}$does not guarantee dataset diversity. We hypothesized that, for a given model architecture, model performance can be improved by maximizing diversity more directly. To test this hypothesis, we introduce a comprehensive framework of diversity measures from ecology that generalizes familiar quantities like Shannon entropy by accounting for similarities among images. (Size and class balance emerge as special cases.) Analyzing thousands of subsets from seven medical datasets showed that the best correlates of performance were not size or class balance but $A$$\unicode{x2013}$"big alpha"$\unicode{x2013}$a set of generalized entropy measures interpreted as the effective number of image-class pairs in the dataset, after accounting for image similarities. One of these, $A_0$, explained 67% of the variance in balanced accuracy, vs. 54% for class balance and just 39% for size. The best pair of measures was size-plus-$A_1$ (79%), which outperformed size-plus-class-balance (74%). Subsets with the largest $A_0$ performed up to 16% better than those with the largest size (median improvement, 8%). We propose maximizing $A$ as a way to improve deep learning performance in medical imaging.

Phuc Nguyen, Josiah Couch, Rahul Bansal et al.

A canonical step in quantifying a system is to measure its entropy. Shannon entropy and other traditional entropy measures capture only the information encoded in the frequencies of a system's elements. Recently, Leinster, Cobbold, and Reeve (LCR) introduced a method that also captures the rich information encoded in the similarities and differences among elements, yielding similarity-sensitive entropy. More recently, the Vendi score (VS) was introduced as an alternative, raising the question of how LCR and VS compare, and which is preferable. Here we address these questions conceptually, analytically, and experimentally, using 53 machine-learning datasets. We show that LCR and VS can differ by orders of magnitude and can capture complementary information about a system, except in limiting cases. We demonstrate that both LCR and VS depend on how similarities are scaled and introduce the concept of ``half distance'' to parameterize this dependence. We prove that VS provides an upper bound on LCR for several values of the Rényi-Hill order parameter and conjecture that this bound holds for all values. We conclude that VS is preferable only when interpreting elements as linear combinations of a more fundamental set of ``ur-elements'' or when the system or dataset possesses a quantum-mechanical character. In the broader circumstance where one seeks simply to capture the rich information encoded by similarity, LCR is favored; nevertheless, for certain half-distances the two methods can complement each other.