Szabo, Z;
Gretton, A;
Póczos, B;
Sriperumbudur, B;
(2014)
Distribution Regression - the Set Kernel Heuristic is Consistent.
Presented at: CSML Lunch Talk Series, London, UK.
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Abstract
Bag of feature (BoF) representations are omnipresent in machine learning; for example, an image can be described by a bag of visual features, a document might be considered as a bag of words, or a molecule can be handled as a bag of its different configurations. Set kernels (also called multi-instance or ensemble kernels; Gaertner 2002) defining the similarity of two bags as the average pairwise point similarities between the sets, are among the most widely applied tools to handle problems based on such BoF representations. Despite the wide applicability of set kernels, even the most fundamental theoretical questions such as their consistency in specific learning tasks is unknown. In my talk, I am going to focus on the distribution regression problem: regressing from a probability distribution to a real-valued response. By considering the mean embeddings of the distributions, this is a natural generalization of set kernels to the infinite sample limit: the bags can be seen as i.i.d. (independent identically distributed) samples from a distribution. We will propose an algorithmically simple ridge regression based solution for distribution regression and prove its consistency under fairly mild conditions (for probability distributions defined on locally compact Polish spaces). As a special case, we give positive answer to a 12-year-old open question, the consistency of set kernels in regression. We demonstrate the efficiency of the studied ridge regression technique on (i) supervised entropy learning, and (ii) aerosol prediction based on satellite images.
| Type: | Conference item (Presentation) |
|---|---|
| Title: | Distribution Regression - the Set Kernel Heuristic is Consistent |
| Event: | CSML Lunch Talk Series |
| Location: | London, UK |
| Dates: | 2014-05-02 - 2014-05-02 |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://www.csml.ucl.ac.uk/events/164 |
| Language: | English |
| Additional information: | http://arxiv.org/abs/1402.1754 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1433098 |
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