Risk bounds for regularized least-squares algorithm with operator-valued kernels
نویسندگان
چکیده
We show that recent results in [3] on risk bounds for regularized least-squares on reproducing kernel Hilbert spaces can be straightforwardly extended to the vectorvalued regression setting. We first briefly introduce central concepts on operatorvalued kernels, then we show how risk bounds can be expressed in terms of a generalization of effective dimension. This report describes research done at the Center for Biological & Computational Learning, which is in the McGovern Institute for Brain Research at MIT, as well as in the Dept. of Brain & Cognitive Sciences, and which is affiliated with the Computer Sciences & Artificial Intelligence Laboratory (CSAIL). This research was sponsored by grants from: Office of Naval Research (DARPA) Contract No. MDA972-04-1-0037, Office of Naval Research (DARPA) Contract No. N00014-02-1-0915, National Science Foundation (ITR/SYS) Contract No. IIS0112991, National Science Foundation (ITR) Contract No. IIS-0209289, National Science Foundation-NIH (CRCNS) Contract No. EIA-0218693, National Science Foundation-NIH (CRCNS) Contract No. EIA-0218506, and National Institutes of Health (Conte) Contract No. 1 P20 MH66239-01A1. Additional support was provided by: Central Research Institute of Electric Power Industry (CRIEPI), Daimler-Chrysler AG, Compaq/Digital Equipment Corporation, Eastman Kodak Company, Honda R&D Co., Ltd., Industrial Technology Research Institute (ITRI), Komatsu Ltd., Eugene McDermott Foundation, Merrill-Lynch, NEC Fund, Oxygen, Siemens Corporate Research, Inc., Sony, Sumitomo Metal Industries, and Toyota Motor Corporation.
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