Weigend A S, Srivastava A N
Int J Neural Syst. 1995 Jun;6(2):109-18. doi: 10.1142/s0129065795000093.
Most traditional prediction techniques deliver a single point, usually the mean of a probability distribution. For multimodal processes, instead of predicting the mean, it is important to predict the full distribution. This article presents a new connectionist method to predict the conditional probability distribution in response to an input. The main idea is to transform the problem from a regression problem to a classification problem. The conditional probability distribution network can perform both direct predictions and iterated predictions, the latter task being specific for time series problems. We compare this new method to fuzzy logic and discuss important differences, and also demonstrate the architecture on two time series. The first is the benchmark laser series used in the Santa Fe competition, a deterministic chaotic system. The second is a time series from a Markov process which exhibits structure on two time scales. The network produces multimodal predictions for this series. We compare the predictions of the network with a nearest-neighbor predictor and find that the conditional probability network is more than twice as likely a model.
大多数传统预测技术给出的是单个点，通常是概率分布的均值。对于多模态过程，重要的不是预测均值，而是预测完整的分布。本文提出了一种新的连接主义方法来预测响应输入的条件概率分布。主要思想是将问题从回归问题转换为分类问题。条件概率分布网络既可以进行直接预测，也可以进行迭代预测，后一项任务是时间序列问题所特有的。我们将这种新方法与模糊逻辑进行比较并讨论重要差异，还在两个时间序列上展示了该架构。第一个是圣达菲竞赛中使用的基准激光序列，一个确定性混沌系统。第二个是来自马尔可夫过程的时间序列，它在两个时间尺度上表现出结构。该网络对这个序列产生多模态预测。我们将网络的预测与最近邻预测器进行比较，发现条件概率网络成为模型的可能性是其两倍多。
