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Wikipedia / 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

. 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.

are the probability estimates by two independent models. The compression ratio in each context, but the two contexts either have not occurred together frequently, or there are insufficient computing resources (time and memory) to collect statistics for the combined case.

). How should these predictions be combined?

is based on a greater number of tests. Older versions of PAQ uses this approach. Newer versions use logistic (or neural network) mixing by first transforming the predictions into the logistic domain, log(p/(1-p)) before averaging.. In both cases, additional weights may be given to each of the input models and adapted to favor the models that have given the most accurate predictions in the past. All but the oldest versions of PAQ use adaptive weighting.

Most context mixing compressors predict one bit of input at a time. The output probability is simply the probability that the next bit will be a 1.

Linear Mixing

'th model. The probabilities are computed by weighted addition of the 0 and 1 counts:

(0 or 1). Then the weight adjustment is:.

Logistic Mixing

is calculated:

'th model, and

After each prediction, the model is updated by adjusting the weights to minimize coding cost.

) is the prediction error.

List of Context Mixing Compressors

All versions below use logistic mixing unless otherwise indicated.

References