The Random Forest Kernel and other kernels for big data from random partitions

We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random Forest. To demonstrate the potential of this method, we propose two new kernels, the Random Forest Kernel and the Fast Cluster Kernel, and show that these kernels consistently outperform standard kernels on problems involving real-world datasets. Finally, we show how the form of these kernels lend themselves to a natural approximation that is appropriate for certain big data problems, allowing $O(N)$ inference in methods such as Gaussian Processes, Support Vector Machines and Kernel PCA.

A derivation of the asymptotic random-coding prefactor

This paper studies the subexponential prefactor to the random-coding bound for a given rate. Using a refinement of Gallager's bounding techniques, an alternative proof of a recent result by Altuǧ and Wagner is given, and the result is extended to the setting of mismatched decoding. © 2013 IEEE.

Classification using log Gaussian Cox processes

McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over labels is given by a type of conditional Markov random field. In the supervised case, computation of the predictive probability of a single test point scales linearly with the number of training points and the multiclass generalization is straightforward. We show new links between the supervised method and classical nonparametric methods. We give a detailed analysis of the pairwise graph representable Markov random field, which we use to extend the model to semi-supervised learning problems, and propose an inference method based on graph min-cuts. We give the first experimental analysis on supervised and semi-supervised datasets and show good empirical performance.