  In the principles-and-parameters framework, the structural features of
languages depend on parameters that may be toggled on or off, with a single
parameter often dictating the status of multiple features. The implied
covariance between features inspires our probabilisation of this line of
linguistic inquiry---we develop a generative model of language based on
exponential-family matrix factorisation. By modelling all languages and
features within the same architecture, we show how structural similarities
between languages can be exploited to predict typological features with
near-perfect accuracy, outperforming several baselines on the task of
predicting held-out features. Furthermore, we show that language embeddings
pre-trained on monolingual text allow for generalisation to unobserved
languages. This finding has clear practical and also theoretical implications:
the results confirm what linguists have hypothesised, i.e.~that there are
significant correlations between typological features and languages.
