Szabo, Z; Gretton, A; Póczos, B; Sriperumbudur, B; (2014) Learning on Distributions. Presented at: Kernel methods for big data workshop, Lille, France.

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Abstract

Problems formulated in terms of distributions have recently gained widespread attention. An important task that belongs to this family is distribution regression: regressing to a real-valued response from a probability distribution. One particularly challenging difficulty of the task is its two-stage sampled nature: in practise we only have samples from sampled distributions. In my presentation I am going to talk about two (intimately related) directions to tackle this difficulty. Firstly, I am going to present a recently released information theoretical estimators open source toolkit capable of estimating numerous dependency, similarity measures on distributions in a nonparametric way. Next, I will propose an algorithmically very simple approach to tackle the distribution regression: embed the distributions to a reproducing kernel Hilbert space, and learn a ridge regressor from the embeddings to the outputs. I will show that (i) this technique is consistent in the two-stage sampled setting under fairly mild conditions, and (ii) it gives state-of-the-art results on supervised entropy learning and the prediction problem of aerosol optical depth based on satellite images. preprint: http://arxiv.org/pdf/1402.1754 ITE toolbox: https://bitbucket.org/szzoli/ite/

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