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

• URL: http://arxiv.org/abs/2105.13636v2
• Date: Mon, 31 May 2021 01:44:50 GMT
• Title: The Power of Log-Sum-Exp: Sequential Density Ratio Matrix Estimation for Speed-Accuracy Optimization
• Authors: Taiki Miyagawa and Akinori F. Ebihara
• Abstract summary: We propose a model for multiclass classification of time series to make a prediction as early and as accurate as possible. Our overall architecture for early classification, MSPRT-TANDEM, statistically significantly outperforms baseline models on four datasets.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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