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Why So Down? The Role of Negative (and Positive) Pointwise Mutual Information in Distributional Semantics

19 Aug 2019arXiv:1908.06941archive 2025-07-28

Alexandre Salle, Aline Villavicencio

In distributional semantics, the pointwise mutual information (𝑃𝑀𝐼) weighting of the cooccurrence matrix performs far better than raw counts. There is, however, an issue with unobserved pair cooccurrences as 𝑃𝑀𝐼 goes to negative infinity. This problem is aggravated by unreliable statistics from finite corpora which lead to a large number of such pairs. A common practice is to clip negative 𝑃𝑀𝐼 (- 𝑃𝑀𝐼) at $0$, also known as Positive 𝑃𝑀𝐼 (𝑃𝑃𝑀𝐼). In this paper, we investigate alternative ways of dealing with - 𝑃𝑀𝐼 and, more importantly, study the role that negative information plays in the performance of a low-rank, weighted factorization of different 𝑃𝑀𝐼 matrices. Using various semantic and syntactic tasks as probes into models which use either negative or positive 𝑃𝑀𝐼 (or both), we find that most of the encoded semantics and syntax come from positive 𝑃𝑀𝐼, in contrast to - 𝑃𝑀𝐼 which contributes almost exclusively syntactic information. Our findings deepen our understanding of distributional semantics, while also introducing novel PMI variants and grounding the popular PPMI measure.

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