Tanimoto Random Features for Scalable Molecular Machine Learning

TL;DR

This paper introduces novel random feature methods to efficiently approximate the Tanimoto kernel, enabling scalable molecular machine learning on large datasets and extending the kernel to real-valued vectors.

Contribution

It proposes the first random feature approximations for the Tanimoto kernel, including an extension to real-valued vectors, with theoretical analysis and practical validation.

Findings

Effective approximation of Tanimoto coefficient on real datasets

Improved scalability for molecular property prediction

Theoretical error bounds on Gram matrix spectral norm

Abstract

The Tanimoto coefficient is commonly used to measure the similarity between molecules represented as discrete fingerprints, either as a distance metric or a positive definite kernel. While many kernel methods can be accelerated using random feature approximations, at present there is a lack of such approximations for the Tanimoto kernel. In this paper we propose two kinds of novel random features to allow this kernel to scale to large datasets, and in the process discover a novel extension of the kernel to real-valued vectors. We theoretically characterize these random features, and provide error bounds on the spectral norm of the Gram matrix. Experimentally, we show that these random features are effective at approximating the Tanimoto coefficient of real-world datasets and are useful for molecular property prediction and optimization tasks.