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Publication Detail
Conditional mean embeddings as regressors
  • Publication Type:
    Journal article
  • Publication Sub Type:
    Conference Proceeding
  • Authors:
    Grünewälder S, Lever G, Baldassarre L, Patterson S, Gretton A, Pontil M
  • Publication date:
    10/10/2012
  • Pagination:
    1823, 1830
  • Journal:
    Proceedings of the 29th International Conference on Machine Learning, ICML 2012
  • Volume:
    2
  • Status:
    Published
Abstract
We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings minimise, providing an intuitive understanding of the embeddings and a justification for their use. Furthermore, the equivalence allows the application of vector-valued regression methods and results to the problem of learning conditional distributions. Using this link we derive a sparse version of the embedding by considering alternative formulations. Further, by applying convergence results for vector-valued regression to the embedding problem we derive minimax convergence rates which are O(log(n)/n) - compared to current state of the art rates of O(n -1/4 ) - and are valid under milder and more intuitive assumptions. These minimax upper rates coincide with lower rates up to a logarithmic factor, showing that the embedding method achieves nearly optimal rates. We study our sparse embedding algorithm in a reinforcement learning task where the algorithm shows significant improvement in sparsity over an incomplete Cholesky decomposition. Copyright 2012 by the author(s)/owner(s).
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