Operator-valued kernels have shown promise in supervised learning problems with functional inputs and functional outputs. The crucial (and possibly restrictive) assumption of positive definiteness of operator-valued kernels has been instrumental in developing efficient algorithms. In this work, we consider operator-valued kernels which might not be necessarily positive definite. To tackle the indefiniteness of operator-valued kernels, we harness the machinery of Reproducing Kernel Krein Spaces (RKKS) of function-valued functions. A representer theorem is illustrated which yields a suitable loss stabilization problem for supervised learning with function-valued inputs and outputs. Analysis of generalization properties of the proposed framework is given. An iterative Operator based Minimum Residual (OpMINRES) algorithm is proposed for solving the loss stabilization problem. Experiments with indefinite operator-valued kernels on synthetic and real data sets demonstrate the utility of the proposed approach.
Akash Saha (Indian Institute of Technology Bombay)
Ph.D. Student at IEOR Department, IIT Bombay
Balamurugan Palaniappan (Indian Institute of Technology Bombay)
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2020 Poster: Learning with Operator-valued Kernels in Reproducing Kernel Krein Spaces »
Wed Dec 9th 05:00 -- 07:00 PM Room Poster Session 3