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Learning and compression are driven by the common aim of identifying andexploiting statistical regularities in data, which opens the door for fertilecollaboration between these areas. A promising group of compression techniquesfor learning scenarios is normalised maximum likelihood (NML) coding, whichprovides strong guarantees for compression of small datasets - in contrast withmore popular estimators whose guarantees hold only in the asymptotic limit.Here we consider a NML-based decision strategy for supervised classificationproblems, and show that it attains heuristic PAC learning when applied to awide variety of models. Furthermore, we show that the misclassification rate ofour method is upper bounded by the maximal leakage, a recently proposed metricto quantify the potential of data leakage in privacy-sensitive scenarios.

Learning, compression, and leakage: Minimising classification error via meta-universal compression principles