The Mondrian Kernel

TL;DR

The paper presents the Mondrian kernel, a fast and adaptable random feature approximation for the Laplace kernel that enables efficient online and batch learning, with a novel connection to Mondrian forests.

Contribution

It introduces the Mondrian kernel, linking kernel methods and random forests through a new efficient random feature approximation based on the Mondrian process.

Findings

Efficient kernel-width selection via re-usable features

Connection established between kernel methods and Mondrian forests

Suitable for both online and batch learning scenarios

Abstract

We introduce the Mondrian kernel, a fast random feature approximation to the Laplace kernel. It is suitable for both batch and online learning, and admits a fast kernel-width-selection procedure as the random features can be re-used efficiently for all kernel widths. The features are constructed by sampling trees via a Mondrian process [Roy and Teh, 2009], and we highlight the connection to Mondrian forests [Lakshminarayanan et al., 2014], where trees are also sampled via a Mondrian process, but fit independently. This link provides a new insight into the relationship between kernel methods and random forests.