  Latent Dirichlet Allocation models discrete data as a mixture of discrete
distributions, using Dirichlet beliefs over the mixture weights. We study a
variation of this concept, in which the documents' mixture weight beliefs are
replaced with squashed Gaussian distributions. This allows documents to be
associated with elements of a Hilbert space, admitting kernel topic models
(KTM), modelling temporal, spatial, hierarchical, social and other structure
between documents. The main challenge is efficient approximate inference on the
latent Gaussian. We present an approximate algorithm cast around a Laplace
approximation in a transformed basis. The KTM can also be interpreted as a type
of Gaussian process latent variable model, or as a topic model conditional on
document features, uncovering links between earlier work in these areas.
