This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as A lges . We compare A lges with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. In addition, A lges overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.

Distant supervision algorithms learn information extraction models given only large readily available databases and text collections. Most previous work has used heuristics for generating labeled data, for example assuming that facts not contained in the database are not mentioned in the text, and facts in the database must be mentioned at least once. In this paper, we propose a new latent-variable approach that models missing data. This provides a natural way to incorporate side information, for instance modeling the intuition that text will often mention rare entities which are likely to be missing in the database. Despite the added complexity introduced by reasoning about missing data, we demonstrate that a carefully designed local search approach to inference is very accurate and scales to large datasets. Experiments demonstrate improved performance for binary and unary relation extraction when compared to learning with heuristic labels, including on average a 27% increase in area under the precision recall curve in the binary case.