Metric learning for kernel ridge regression: assessment of molecular similarity

Sep 17, 2026

Supervised and unsupervised kernel-based methods in the physical sciences rely on similarity measures, but fixed distance metrics (e.g., Euclidean or Manhattan) become unreliable when high-dimensional feature vectors fail to reflect differences in the target property. The work introduces an algorithm, metric learning for kernel ridge regression (MLKRR), designed for KRR and built on the Metric Learning for Kernel Regression framework using the Nadaraya-Watson estimator. MLKRR delivers stronger prediction on atomisation energies for QM9 molecules and produces more interpretable low-dimensional projections of the transformed feature space.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

AccessFree to download

Abstract

Introduction

Similarity and kernel-based regression methods

Challenges of fixed distance metrics in high-dimensional spaces

Chemistry representations and their limits

Paper metadata

PAPER • OPEN ACCESS Metric learning for kernel ridge regression: assessment of molecular similarity To cite this article: Raimon Fabregat et al 2022 Mach. Learn.: Sci. Technol. 3 035015 View the article online for updates and enhancements. You may also like -Revving up 13C NMR shielding predictions across chemical space: benchmarks for atoms-in-molecules kernel machine learning with new data for 134 kilo molecules Amit Gupta, Sabyasachi Chakraborty and Raghunathan Ramakrishnan -Speeding up quantum dissipative dynamics of open systems with kernel methods Arif Ullah and Pavlo O. Dral -Improving sample and feature selection with principal covariates regression Rose K Cersonsky, Benjamin A Helfrecht, Edgar A Engel et al. This content was downloaded from IP address [128.179.254.107](128.179.254.107) on 13/10/2022 at 10:55 Mach. Learn.: Sci. Technol. 3 (2022) 035015 [https://doi.org/10.1088/2632-2153/ac8e4f](https://doi.org/10.1088/2632-2153/ac8e4f) OPEN ACCESS RECEIVED 20 June 2022 REVISED 18 August 2022 ACCEPTED FOR PUBLICATION 31 August 2022 PUBLISHED 22 September 2022 Original Content from this work may be used under the terms of the Creative Commons Attribution 4 .0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. PAPER Metric learning for kernel ridge regression: assessment of molecular similarity Raimon Fabregat1,4􀁂, Puck van Gerwen1,2,4􀁂, Matthieu Haeberle1,3,4, Friedrich Eisenbrand3 and Clémence Corminboeuf1,2, ∗􀁂 1 2 3 4 ∗ Laboratory for Computational Molecular Design, Institute of Chemical Sciences and Engineering, ´Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland National Center for Competence in Research-Catalysis (NCCR-Catalysis), Zurich, Switzerland Chair of Discrete Optimisation, ´Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland These authors contributed equally to this work. Author to whom any correspondence should be addressed. [E-mail:](E-mail: clemence.corminboeuf@epfl.ch)[ clemence.corminboeuf@epfl.ch](E-mail: clemence.corminboeuf@epfl.ch) Keywords: metric learning, kernel-ridge regression, molecular similarity, physics-based machine learning Supplementary material for this article is available online Abstract Supervised and unsupervised kernel-based algorithms widely used in the physical sciences depend upon the notion of similarity. Their reliance on pre-defined distance metrics—e.g. the Euclidean or Manhattan distance—are problematic especially when used in combination with high-dimensional feature vectors for which the similarity measure does not well-reflect the differences in the target property. Metric learning is an elegant approach to surmount this shortcoming and find a property-informed transformation of the feature space. We propose a new algorithm for metric learning specifically adapted for kernel ridge regression (KRR): metric learning for kernel ridge regression (MLKRR) . It is based on the Metric Learning for Kernel Regression framework using the Nadaraya-Watson estimator, which we show to be inferior to the KRR estimator for typical physics-based machine learning tasks. The MLKRR algorithm allows for superior predictive performance on the benchmark regression task of atomisation energies of QM9 molecules, as well as generating more meaningful low-dimensional projections ofthe modified feature space. 1. Introduction Over the last decade, supervised and unsupervised machine learning methods have established themselves as reliable tools in the physical sciences [1–12]. Supervised models aim to find a mathematical relationship between input data and target properties. Kernel-based regression methods, e.g. kernel ridge regression (KRR) and Gaussian process regression (GPR), are popular in the field [3, 4, 13–15] . While equivariant neural networks have recently also become state-of-the-ar

FAQs

What problem does MLKRR address in kernel ridge regression?

Kernel ridge regression depends on similarity measures, and predefined distance metrics can poorly reflect target-property differences in high-dimensional feature spaces. MLKRR learns a property-informed transformation to improve that similarity.

On what task is the MLKRR approach evaluated?

MLKRR is evaluated on the benchmark regression task of atomisation energies of QM9 molecules, where it achieves superior predictive performance.

What is the core idea behind MLKRR?

MLKRR is based on the Metric Learning for Kernel Regression framework using the Nadaraya-Watson estimator, and it is tailored specifically for kernel ridge regression.

Sep 17, 2026

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