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Learning with infinitely many kernels via semi-infinite programming

Oezoeguer-Akyuez, Suereyya
Weber, Gerhard Wilhelm
In recent years, learning methods are desirable because of their reliability and efficiency in real-world problems. We propose a novel method to find infinitely many kernel combinations for learning problems with the help of infinite and semi-infinite optimization regarding all elements in kernel space. This will provide to study variations of combinations of kernels when considering heterogeneous data in real-world applications. Looking at all infinitesimally fine convex combinations of the kernels from the infinite kernel set, the margin is maximized subject to an infinite number of constraints with a compact index set and an additional (Riemann-Stieltjes) integral constraint due to the combinations. After a parametrisation in the space of probability measures it becomes semi-infinite. We analyze the conditions which satisfy the Reduction Ansatz and discuss the type of distribution functions of the kernel coefficients within the structure of the constraints and our bilevel optimization problem.