Simplex Clustering via sBeta with Applications to Online Adjustment of Black-Box Predictions

TL;DR

This paper introduces a novel probabilistic clustering method called k-sBetas for softmax predictions of neural networks, improving unsupervised adjustment of black-box model outputs by modeling data with a flexible sBeta density.

Contribution

It proposes a new clustering approach based on sBeta densities that generalizes existing methods and enhances performance in adjusting black-box predictions.

Findings

Competitive performance in adjusting black-box predictions

Flexible modeling of simplex data with sBeta densities

Outperforms existing clustering approaches

Abstract

We explore clustering the softmax predictions of deep neural networks and introduce a novel probabilistic clustering method, referred to as k-sBetas. In the general context of clustering discrete distributions, the existing methods focused on exploring distortion measures tailored to simplex data, such as the KL divergence, as alternatives to the standard Euclidean distance. We provide a general maximum a posteriori (MAP) perspective of clustering distributions, emphasizing that the statistical models underlying the existing distortion-based methods may not be descriptive enough. Instead, we optimize a mixed-variable objective measuring data conformity within each cluster to the introduced sBeta density function, whose parameters are constrained and estimated jointly with binary assignment variables. Our versatile formulation approximates various parametric densities for modeling simplex data and enables the control of the cluster-balance bias. This yields highly competitive performances for the unsupervised adjustment of black-box model predictions in various scenarios. Our code and comparisons with the existing simplex-clustering approaches and our introduced softmax-prediction benchmarks are publicly available: https://github.com/fchiaroni/Clustering_Softmax_Predictions.