A Statistical Learning Theory Framework for Supervised Pattern Discovery

TL;DR

This paper introduces a formal statistical framework for supervised pattern discovery, providing uniform risk bounds for different pattern generation models, including a new complexity measure called quasi-Rademacher complexity.

Contribution

It formalizes supervised pattern discovery as a latent variable inference problem and derives uniform risk bounds for two pattern generation scenarios, introducing quasi-Rademacher complexity.

Findings

Established uniform risk bounds for arbitrary pattern collections.

Derived risk bounds using quasi-Rademacher complexity for i.i.d. pattern generation.

Provided theoretical foundations for supervised pattern discovery methods.

Abstract

This paper formalizes a latent variable inference problem we call {\em supervised pattern discovery}, the goal of which is to find sets of observations that belong to a single ``pattern.'' We discuss two versions of the problem and prove uniform risk bounds for both. In the first version, collections of patterns can be generated in an arbitrary manner and the data consist of multiple labeled collections. In the second version, the patterns are assumed to be generated independently by identically distributed processes. These processes are allowed to take an arbitrary form, so observations within a pattern are not in general independent of each other. The bounds for the second version of the problem are stated in terms of a new complexity measure, the quasi-Rademacher complexity.