Universal Prediction of Selected Bits

TL;DR

This paper demonstrates that a normalized form of Solomonoff induction can effectively predict recursive patterns within unstructured sequences, extending its applicability to classification tasks and highlighting limitations of the unnormalized version.

Contribution

It introduces the use of normalized Solomonoff induction for sequence prediction in classification, showing it can detect recursive patterns where unnormalized methods fail.

Findings

Normalized Solomonoff induction detects recursive sub-patterns.

Unnormalized version may fail on simple recursive patterns.

Applicable to sequence prediction and classification tasks.

Abstract

Many learning tasks can be viewed as sequence prediction problems. For example, online classification can be converted to sequence prediction with the sequence being pairs of input/target data and where the goal is to correctly predict the target data given input data and previous input/target pairs. Solomonoff induction is known to solve the general sequence prediction problem, but only if the entire sequence is sampled from a computable distribution. In the case of classification and discriminative learning though, only the targets need be structured (given the inputs). We show that the normalised version of Solomonoff induction can still be used in this case, and more generally that it can detect any recursive sub-pattern (regularity) within an otherwise completely unstructured sequence. It is also shown that the unnormalised version can fail to predict very simple recursive sub-patterns.