  We propose probabilistic task modelling -- a generative probabilistic model
for collections of tasks used in meta-learning. The proposed model combines
variational auto-encoding and latent Dirichlet allocation to model each task as
a mixture of Gaussian distribution in an embedding space. Such modelling
provides an explicit representation of a task through its task-theme mixture.
We present an efficient approximation inference technique based on variational
inference method for empirical Bayes parameter estimation. We perform empirical
evaluations to validate the task uncertainty and task distance produced by the
proposed method through correlation diagrams of the prediction accuracy on
testing tasks. We also carry out experiments of task selection in meta-learning
to demonstrate how the task relatedness inferred from the proposed model help
to facilitate meta-learning algorithms.
