On multiple spline approximations for Bayesian computations

Abstract

Probabilistic reasoning typically suffers from the explosive amount of information it must maintain. There are a variety of methods available for curbing this explosion. However, in doing so, it is important to avoid oversimplifying the given domain through injudicious use of assumptions such as independence. Multiple splining is an approach for compressing and approximating the probabilistic information. Instead of positing additional independence conditions, it attempts to identify patterns in the information. While the data explosion is multiplicative in nature, O(n ₁ n ₂⋯n _k), multiple splines reduces it to an additive one, O(n ₁ + n ₂ + ⋯n _k). We consider how these splines can be found and used. Since splines exploit patterns in the data, we can also use them to help in filling in missing data. As it turns out, our splining method is quite general and may be applied to other domains besides probabilistic reasoning which can benefit from data compression.