Minimum Error Rate Training and the Convex Hull Semiring

TL;DR

This paper introduces a novel geometric semiring framework for analyzing the line search in minimum error rate training, providing clarity on complexity and implementation for dynamic programming algorithms.

Contribution

It presents a new geometric semiring perspective for MERT's line search, enhancing understanding and practical implementation of related algorithms.

Findings

Provides a complexity analysis of MERT algorithms

Introduces a semiring framework based on computational geometry

Suggests practical implementation approaches

Abstract

We describe the line search used in the minimum error rate training algorithm MERT as the "inside score" of a weighted proof forest under a semiring defined in terms of well-understood operations from computational geometry. This conception leads to a straightforward complexity analysis of the dynamic programming MERT algorithms of Macherey et al. (2008) and Kumar et al. (2009) and practical approaches to implementation.