Logic Programming: Proceedings of the 1993 International by Dale Miller

By Dale Miller

The previous years have noticeable a great number of potent implementations of common sense courses for quite a few laptop architectures in several program parts. common sense programming maintains to enhance by means of broadening its foundations, exploring new language designs, and setting up extra connections with different parts of machine science.

Topics comprise: Algorithmic research. Constraints. Environmental aid. average Language. Programming Methodologies. man made Intelligence. Concurrency and Parallelism. Logical Extensions. Meta and Higher-Order Programming. Semantic research. Compilation ideas. Deductive Databases. Implementations and Architectures. evidence concept. Programming Language layout.

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22) uk = −yj if k = j, ⎪ ⎪ ⎩ 0 otherwise. 18) along direction uij (for positive λ) or direction −uij = uji (for negative λ). 22). Since we need a feasible direction, we can further require that i ∈ Iup and j ∈ Idown . 1 Maximal Gain Working Set Selection Let U = { uij | i ∈ Iup , j ∈ Idown } be the set of the potential search directions. 23) yj αj − λ ≥ Aj . Unfortunately the search of the best direction uij requires iterating over the n(n−1) possible pairs of indices. The maximization of λ then amounts to performing a direction search.

Here nsv has been computed from LIBSVM (note that the solutions are not exactly the same). For this plot, h = 2−5 . 6 Advantages of Primal Optimization As explained throughout this chapter, primal and dual optimizations are very similar, and it is not surprising that they lead to the same computational complexity, O(nnsv + n3sv ). So is there any reason to use one rather than the other? We believe that primal optimization might have advantages for large-scale optimization. Indeed, when the number of training points is large, the number of support vectors is also typically large and it becomes intractable to compute the exact solution.

82; see appendix) is based on the SMO algorithm, but relies on a more advanced working set selection scheme. After discussing the stopping criteria and the working set selection, we present the shrinking heuristics and their impact on the design of the cache of kernel values. This section discusses the dual maximization problem n n max D(α) = αi − i=1 subject to 1 yi αi yj αj K(xi , xj ) 2 i,j=1 0 ≤ αi ≤ C, ∀i i yi αi = 0 Let g = (g1 . . gn ) be the gradient of the dual objective function, ∂D(α) gi = = 1 − yi ∂αi n yk αk Kik .

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