Optimizing Non-decomposable Performance Measures: A Tale of Two Classes

TL;DR

This paper introduces new stochastic optimization methods for non-decomposable performance measures like F-measure, enabling faster and more accurate training for imbalanced classification tasks.

Contribution

It develops adaptive linearization schemes and two novel algorithms, SPADE and STAMP, with convergence guarantees for optimizing concave and pseudo-linear measures.

Findings

Significant speedups over existing methods, often by an order of magnitude.

Achieves similar or improved accuracy on test data.

Provides convergence guarantees for the proposed algorithms.

Abstract

Modern classification problems frequently present mild to severe label imbalance as well as specific requirements on classification characteristics, and require optimizing performance measures that are non-decomposable over the dataset, such as F-measure. Such measures have spurred much interest and pose specific challenges to learning algorithms since their non-additive nature precludes a direct application of well-studied large scale optimization methods such as stochastic gradient descent. In this paper we reveal that for two large families of performance measures that can be expressed as functions of true positive/negative rates, it is indeed possible to implement point stochastic updates. The families we consider are concave and pseudo-linear functions of TPR, TNR which cover several popularly used performance measures such as F-measure, G-mean and H-mean. Our core contribution is an adaptive linearization scheme for these families, using which we develop optimization techniques that enable truly point-based stochastic updates. For concave performance measures we propose SPADE, a stochastic primal dual solver; for pseudo-linear measures we propose STAMP, a stochastic alternate maximization procedure. Both methods have crisp convergence guarantees, demonstrate significant speedups over existing methods - often by an order of magnitude or more, and give similar or more accurate predictions on test data.