Log-Sum-Exp：序贯密度比矩阵估计在速度精度优化中的功效
The Power of Log-Sum-Exp: Sequential Density Ratio Matrix Estimation for Speed-Accuracy Optimization
摘要：
我们提出了一个多类分类的时间序列模型，使预测尽可能早，尽可能准确。矩阵序贯概率比检验（MSPRT）被认为是这种情况下的渐近最优检验，但它包含一个关键假设，这阻碍了广泛的实际应用; MSPRT需要潜在的概率密度。为了解决这个问题，我们提出解决密度比矩阵估计（DRME），一种新型的密度比估计，包括估计矩阵的多个密度比的约束，因此比传统的密度比估计更具挑战性。我们提出了一个对数和指数型损失函数（LSEL）解决DRME，并证明了以下几点：（i）LSEL提供了真实的密度比矩阵作为训练集的样本大小增加（一致性）;（ii）它分配更大的梯度更硬的类（硬类加权效应）;（iii）它甚至提供了分类不平衡的数据集（猜测厌恶）的区别性得分。我们用于早期分类的整体架构MSPRT-TANDEM在统计上显著优于包括动作识别在内的四个数据集的基线模型，特别是在顺序观察的早期阶段。我们的代码和数据集可在https://github.com/TaikiMiyagawa/MSPRT-TANDEM上公开获取。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
