Conditional mean embeddings as regressors

Mathematics and Statistics

Associated organisational units

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Published

Standard

Conditional mean embeddings as regressors. / Grunewalder, S.; Lever, G.; Gretton, A. et al.
Proceedings of the 29th International Conference on Machine Learning, Edinburgh, Scotland, 2012. 2012. 898.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Harvard

Grunewalder, S, Lever, G, Gretton, A, Baldassarre, L, Patterson, S & Pontil, M 2012, Conditional mean embeddings as regressors. in Proceedings of the 29th International Conference on Machine Learning, Edinburgh, Scotland, 2012., 898. <http://icml.cc/2012/papers/898.pdf>

APA

Grunewalder, S., Lever, G., Gretton, A., Baldassarre, L., Patterson, S., & Pontil, M. (2012). Conditional mean embeddings as regressors. In Proceedings of the 29th International Conference on Machine Learning, Edinburgh, Scotland, 2012 Article 898 http://icml.cc/2012/papers/898.pdf

Vancouver

Grunewalder S, Lever G, Gretton A, Baldassarre L, Patterson S, Pontil M. Conditional mean embeddings as regressors. In Proceedings of the 29th International Conference on Machine Learning, Edinburgh, Scotland, 2012. 2012. 898

Author

Grunewalder, S. ; Lever, G. ; Gretton, A. et al. / Conditional mean embeddings as regressors. Proceedings of the 29th International Conference on Machine Learning, Edinburgh, Scotland, 2012. 2012.

Bibtex

@inproceedings{64c20018a13e479998e9d77dedd3c87c,

title = "Conditional mean embeddings as regressors",

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 applyingconvergence 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 moreintuitive 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 reinforcementlearning task where the algorithm shows significant improvement in sparsity over an incomplete Cholesky decomposition.",

author = "S. Grunewalder and G. Lever and A. Gretton and L. Baldassarre and S. Patterson and M. Pontil",

year = "2012",

language = "English",

booktitle = "Proceedings of the 29th International Conference on Machine Learning, Edinburgh, Scotland, 2012",

}

RIS

TY - GEN

T1 - Conditional mean embeddings as regressors

AU - Grunewalder, S.

AU - Lever, G.

AU - Gretton, A.

AU - Baldassarre, L.

AU - Patterson, S.

AU - Pontil, M.

PY - 2012

Y1 - 2012

N2 - 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 applyingconvergence 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 moreintuitive 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 reinforcementlearning task where the algorithm shows significant improvement in sparsity over an incomplete Cholesky decomposition.

AB - 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 applyingconvergence 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 moreintuitive 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 reinforcementlearning task where the algorithm shows significant improvement in sparsity over an incomplete Cholesky decomposition.

M3 - Conference contribution/Paper

BT - Proceedings of the 29th International Conference on Machine Learning, Edinburgh, Scotland, 2012

ER -

Research

Associated organisational units

Links