Tunable GMM Kernels

TL;DR

This paper introduces tunable variants of the GMM kernel, demonstrating significant improvements over the original and competitive performance against advanced models like trees and deep nets across numerous datasets.

Contribution

The paper proposes three tunable GMM kernels and shows they outperform the original GMM, offering a fast, effective alternative to complex models in large-scale classification tasks.

Findings

Tunable GMM kernels improve accuracy over original GMM.

On 60 datasets, tunable GMMs often outperform original GMM.

Comparable performance to tree and deep learning methods.

Abstract

The recently proposed "generalized min-max" (GMM) kernel can be efficiently linearized, with direct applications in large-scale statistical learning and fast near neighbor search. The linearized GMM kernel was extensively compared in with linearized radial basis function (RBF) kernel. On a large number of classification tasks, the tuning-free GMM kernel performs (surprisingly) well compared to the best-tuned RBF kernel. Nevertheless, one would naturally expect that the GMM kernel ought to be further improved if we introduce tuning parameters. In this paper, we study three simple constructions of tunable GMM kernels: (i) the exponentiated-GMM (or eGMM) kernel, (ii) the powered-GMM (or pGMM) kernel, and (iii) the exponentiated-powered-GMM (epGMM) kernel. The pGMM kernel can still be efficiently linearized by modifying the original hashing procedure for the GMM kernel. On about 60 publicly available classification datasets, we verify that the proposed tunable GMM kernels typically improve over the original GMM kernel. On some datasets, the improvements can be astonishingly significant. For example, on 11 popular datasets which were used for testing deep learning algorithms and tree methods, our experiments show that the proposed tunable GMM kernels are strong competitors to trees and deep nets. The previous studies developed tree methods including "abc-robust-logitboost" and demonstrated the excellent performance on those 11 datasets (and other datasets), by establishing the second-order tree-split formula and new derivatives for multi-class logistic loss. Compared to tree methods like "abc-robust-logitboost" (which are slow and need substantial model sizes), the tunable GMM kernels produce largely comparable results.