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ANC/DTC Seminar: Arthur Gretton, Gatsby unit, University College London

Hypothesis Testing and Bayesian Inference: New Applications of Kernel Methods

What
When Nov 22, 2011
from 11:00 AM to 12:00 PM
Where IF 4.31/33
Contact Name Charles Sutton
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In the early days of kernel machines research, the "kernel trick" was considered a useful way of constructing nonlinear learning algorithms from linear ones, by applying the linear algorithms to feature space mappings of the original data. More recently, it has become clear that a potentially more far reaching use of kernels is as a linear way of dealing with higher order statistics, by mapping probabilities to a suitable reproducing kernel Hilbert space (i.e., the feature space is an RKHS).

 

I will describe how probabilities can be mapped to kernel feature spaces, and how to compute distances between these mappings. A measure of strength of dependence between two random variables follows naturally from this distance. Applications that make use of kernel probability embeddings include:

 

  • Nonparametric two-sample testing and independence testing in complex (high dimensional) domains. In the latter case, we test whether text in English is translated from the French, as opposed to being random extracts on the same topic.
  • Inference on graphical models, in cases where the variable interactions are modeled nonparametrically (i.e., when parametric models are impractical or unknown). In experiments, this approach outperforms state-of-the-art nonparametric techniques in 3-D depth reconstruction from 2-D images, and on a protein structure prediction task.