Randomly shifted grids give binary features whose collision probability, and hence expected inner product, equals an eligible kernel. For separable multivariate kernels, independent one-dimensional grids multiply the collision probabilities across dimensions; averaging P independent partitions lowers variance. The appendix derives the pitch density p(delta)=delta k''(delta) for kernels expressible as convex mixtures of hat kernels.

Randomly shifted grids give binary features whose collision probability, and hence expected inner product, equals an eligible kernel. For separable multivariate kernels, independent one-dimensional grids multiply the collision probabilities across dimensions; averaging P independent partitions lowers variance. The appendix derives the pitch density p(delta)=delta k''(delta) for kernels expressible as convex mixtures of hat kernels. · CiteArk

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