Distributional models are derived from co-occurrences in a corpus, where only a small proportion of all possible plausible co-occurrences will be observed. This results in a very sparse vector space, requiring a mechanism for inferring missing knowledge. Most methods face this challenge in ways that render the resulting word representations uninterpretable, with the consequence that semantic composition becomes hard to model. In this paper we explore an alternative which involves explicitly inferring unobserved co-occurrences using the distributional neighbourhood. We show that distributional inference improves sparse word representations on several word similarity benchmarks and demonstrate that our model is competitive with the state-of-the-art for adjective-noun, noun-noun and verb-object compositions while being fully interpretable.