Abstract: In distributional semantics, the pointwise mutual information ($\mathit{PMI}$) weighting of the cooccurrence matrix performs far better than raw counts. There is, however, an issue with unobserved pair cooccurrences as $\mathit{PMI}$ 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 $\mathit{PMI}$ ($\mathit{\texttt{-} PMI}$) at $0$, also known as Positive $\mathit{PMI}$ ($\mathit{PPMI}$). In this paper, we investigate alternative ways of dealing with $\mathit{\texttt{-} PMI}$ and, more importantly, study the role that negative information plays in the performance of a low-rank, weighted factorization of different $\mathit{PMI}$ matrices. Using various semantic and syntactic tasks as probes into models which use either negative or positive $\mathit{PMI}$ (or both), we find that most of the encoded semantics and syntax come from positive $\mathit{PMI}$, in contrast to $\mathit{\texttt{-} PMI}$ 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.

Introduction: Dense word vectors (or embeddings) are a key component in modern NLP architectures for tasks such as sentiment analysis, parsing, and machine translation. These vectors can be learned by exploiting the distributional hypothesis BIBREF0, paraphrased by BIBREF1 as “a word is characterized by the company that it keeps”, usually by constructing a cooccurrence matrix over a training corpus, re-weighting it using Pointwise Mutual Information ($\mathit {PMI}$) BIBREF2, and performing a low-rank factorization to obtain dense vectors. Unfortunately, $\mathit {PMI}(w,c)$ goes to negative infinity when the word-context pair $(w,c)$ does not appear in the training corpus. Due to unreliable statistics, this happens very frequently in finite corpora. Many models work around this issue by clipping negative $\mathit {PMI}$ values at 0, a measure known as Positive $\mathit {PMI}$ ($\mathit {PPMI}$), which works very well in practice. An unanswered question is: “What is lost/gained by collapsing the negative $\mathit {PMI}$ spectrum to 0?”. Understanding which type of information is captured by $\mathit {\texttt {-}PMI}$ can help in tailoring models for optimal performance. In this work, we attempt to answer this question by studying the kind of information contained in the negative and positive spectrums of $\mathit {PMI}$ ($\mathit {\texttt {-}PMI}$ and $\mathit {\texttt {+}PMI}$). We evaluate weighted factorization of different matrices which use either $\mathit {\texttt {-}PMI}$, $\mathit {\texttt {+}PMI}$, or both on various semantic and syntactic tasks. Results show that $\mathit {\texttt {+}PMI}$ alone performs quite well on most tasks, capturing both semantics and syntax, in contrast to $\mathit {\texttt {-}PMI}$, which performs poorly on nearly all tasks, except those that test for syntax. Our main contribution is deepening our understanding of distributional semantics by extending BIBREF1's paraphrase of the distributional hypothesis to “a word is not only characterized by the company that it keeps, but also by the company it rejects”. Our secondary contributions are the proposal of two $PMI$ variants that account for the spectrum of $\mathit {\texttt {-}PMI}$, and the justification of the popular $PPMI$ measure. In this paper, we first look at related work ($§$SECREF2), then study $\mathit {\texttt {-}PMI}$ and ways of accounting for it ($§$SECREF3), describe experiments ($§$SECREF4), analyze results ($§$SECREF5), and close with ideas for future work ($§$SECREF6).

Question: Why are statistics from finite corpora unreliable?
Answer: A finite corpora may entirely omit rare word combinations