  We propose a method for embedding two-dimensional locations in a continuous
vector space using a neural network-based model incorporating mixtures of
Gaussian distributions, presenting two model variants for text-based
geolocation and lexical dialectology. Evaluated over Twitter data, the proposed
model outperforms conventional regression-based geolocation and provides a
better estimate of uncertainty. We also show the effectiveness of the
representation for predicting words from location in lexical dialectology, and
evaluate it using the DARE dataset.
