A Simple Explanation of A Spectral Algorithm for Learning Hidden Markov Models

TL;DR

This paper provides a straightforward linear algebraic explanation of a spectral algorithm for learning Hidden Markov Models, clarifying the original method with simplified claims.

Contribution

It offers a simple, precise linear algebraic interpretation of the spectral algorithm for HMMs, making the method more accessible and understandable.

Findings

Clarifies the spectral algorithm with a linear algebraic perspective

Simplifies the understanding of the original spectral learning method

Provides precise claims that make the algorithm more accessible

Abstract

A simple linear algebraic explanation of the algorithm in "A Spectral Algorithm for Learning Hidden Markov Models" (COLT 2009). Most of the content is in Figure 2; the text just makes everything precise in four nearly-trivial claims.