Minimax Optimization for Ambiguity Resolution in Multilingual Text Analysis

Abstract

Multilingual text analysis needs a procedure capable of differentiating between interpretations based on their dependency on context, language, and presence of lexical information. Selecting the interpretation with maximal probability can result in a decision error under circumstances of uncertain probabilities. In this paper we propose a minimax decision procedure for solving the problem of lexical ambiguity resolution. The contextual module generates interpretations and associated nominal probabilities; an uncertainty set is defined for a set of alternative probability distributions. In the decision module the interpretation with the minimum worst-case expected loss is chosen or a decision of deferment is made if the cost of a decision error outweighs the cost of deferral. For binary ambiguities, our approach boils down to a clear-cut criterion using the extremes of the interval probability distribution. We present a numerical example with six cases in English, Spanish, and Romanized Hindi, comparing the forced prediction, threshold-based selection, and minimax selection approaches. Based on our assumptions regarding probabilities and losses, minimax selection resolves three out of six cases and cuts the average worst case expected decision loss from 0.4383 to 0.2250. Its nominal expected loss rises to 0.1867, starting from 0.1717 due to the deferral penalty for the unassigned items. The above examples show the tradeoff between robustness and coverage that cannot be described by a language benchmark. The method disentangles the uncertainty over probabilities from the uncertainty in the text and allows for inspectable decision-making. The future assessment needs to derive the uncertainty sets based on multilingual validation corpora.