Context mixing

Context mixing is a type of data compression algorithm in which the next-symbol predictions of two or more statistical models are combined to yield a prediction that is often more accurate than any of the individual predictions. For example, one simple method (not necessarily the best) is to average the probabilities assigned by each model. The random forest is another method: it outputs the prediction that is the mode of the predictions output by individual models. Combining models is an active area of research in machine learning.

The PAQ series of data compression programs use context mixing to assign probabilities to individual bits of the input.

Application to Data Compression

Suppose that we are given two conditional probabilities, P(X|A) and P(X|B), and we wish to estimate P(X|A,B), the probability of event X given both conditions A and B. There is insufficient information for probability theory to give a result. In fact, it is possible to construct scenarios in which the result could be anything at all. But intuitively, we would expect the result to be some kind of average of the two.