The Power of Log-Sum-Exp: Sequential Density Ratio Matrix Estimation for Speed-Accuracy Optimization

TL;DR

This paper introduces a novel density ratio matrix estimation method using a log-sum-exp loss function, enabling early and accurate multiclass time series classification, and demonstrates its effectiveness over baseline models.

Contribution

The paper proposes a new density ratio matrix estimation approach with a specialized loss function, improving early classification accuracy in sequential data.

Findings

The proposed MSPRT-TANDEM model outperforms baselines on four datasets.

The log-sum-exp loss ensures consistency and discriminative power.

The method is effective even with class imbalance.

Abstract

We propose a model for multiclass classification of time series to make a prediction as early and as accurate as possible. The matrix sequential probability ratio test (MSPRT) is known to be asymptotically optimal for this setting, but contains a critical assumption that hinders broad real-world applications; the MSPRT requires the underlying probability density. To address this problem, we propose to solve density ratio matrix estimation (DRME), a novel type of density ratio estimation that consists of estimating matrices of multiple density ratios with constraints and thus is more challenging than the conventional density ratio estimation. We propose a log-sum-exp-type loss function (LSEL) for solving DRME and prove the following: (i) the LSEL provides the true density ratio matrix as the sample size of the training set increases (consistency); (ii) it assigns larger gradients to harder classes (hard class weighting effect); and (iii) it provides discriminative scores even on class-imbalanced datasets (guess-aversion). Our overall architecture for early classification, MSPRT-TANDEM, statistically significantly outperforms baseline models on four datasets including action recognition, especially in the early stage of sequential observations. Our code and datasets are publicly available at: https://github.com/TaikiMiyagawa/MSPRT-TANDEM.