In this paper we propose a novel problem called the ForeClassing problem where the loss of a classification decision is only observed at a future time point after the classification decision has to be made. To solve this problem, we propose an approximately Bayesian deep neural network architecture called ForeClassNet for time series forecasting and classification. This network architecture forces the network to consider possible future realizations of the time series, by forecasting future time points and their likelihood of occurring, before making its final classification decision. To facilitate this, we introduce two novel neural network layers, Welford mean-variance layers and Boltzmann convolutional layers. Welford mean-variance layers allow networks to iteratively update their estimates of the mean and variance for the forecasted time points for each inputted time series to the network through successive forward passes, which the model can then consider in combination with a learned representation of the observed realizations of the time series for its classification decision. Boltzmann convolutional layers are linear combinations of approximately Bayesian convolutional layers with different filter lengths, allowing the model to learn multitemporal resolution representations of the input time series, and which resolutions to focus on within a given Boltzmann convolutional layer through a Boltzmann distribution. Through several simulation scenarios and two real world applications we demonstrate ForeClassNet achieves superior performance compared with current state of the art methods including a near 30% improvement in test set accuracy in our financial example compared to the second best performing model.

翻译：本文提出了一种称为"预测分类"的新问题，其分类决策的损失仅在决策完成后于未来时间点才能观测到。为解决该问题，我们提出了一种近似贝叶斯深度神经网络架构ForeClassNet，用于时间序列预测与分类。该网络架构通过预测未来时间点及其发生概率，迫使网络在做出最终分类决策前考虑时间序列可能的未来实现。为此，我们引入了两种新型神经网络层：Welford均值方差层与玻尔兹曼卷积层。Welford均值方差层允许网络通过连续前向传播，迭代更新每个输入时间序列的预测时间点均值与方差估计，模型可结合时间序列观测实况的学习表征进行综合分类决策。玻尔兹曼卷积层是不同滤波器长度的近似贝叶斯卷积层的线性组合，通过玻尔兹曼分布使模型能够学习输入时间序列的多时间分辨率表征，并确定在给定玻尔兹曼卷积层中应聚焦的分辨率。通过多个仿真场景和两个实际应用案例，我们证明ForeClassNet相比当前最先进方法具有更优性能，其中金融案例的测试集准确率较次优模型提升近30%。