Predicting conditional probability distributions: a connectionist approach

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.