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Simon Bartels

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3 papers

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NeurIPS Conference 2024 Conference Paper

A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences

Miguel González-Duque
Richard Michael
Simon Bartels
Yevgen Zainchkovskyy
Søren Hauberg
Wouter Boomsma

Optimizing discrete black-box functions is key in several domains, e. g. protein engineering and drug design. Due to the lack of gradient information and the need for sample efficiency, Bayesian optimization is an ideal candidate for these tasks. Several methods for high-dimensional continuous and categorical Bayesian optimization have been proposed recently. However, our survey of the field reveals highly heterogeneous experimental set-ups across methods and technical barriers for the replicability and application of published algorithms to real-world tasks. To address these issues, we develop a unified framework to test a vast array of high-dimensional Bayesian optimization methods and a collection of standardized black-box functions representing real-world application domains in chemistry and biology. These two components of the benchmark are each supported by flexible, scalable, and easily extendable software libraries (poli and poli-baselines), allowing practitioners to readily incorporate new optimization objectives or discrete optimizers. Project website: https: //machinelearninglifescience. github. io/hdbo_benchmark.

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JMLR Journal 2023 Journal Article

Kernel-Matrix Determinant Estimates from stopped Cholesky Decomposition

Simon Bartels
Wouter Boomsma
Jes Frellsen
Damien Garreau

Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in the size of the matrix. We show that, under mild assumptions, it is possible to estimate the determinant from only a sub-matrix, with probabilistic guarantee on the relative error. We present an augmentation of the Cholesky decomposition that stops under certain conditions before processing the whole matrix. Experiments demonstrate that this can save a considerable amount of time while rarely exceeding an overhead of more than 5% when not stopping early. More generally, we present a probabilistic stopping strategy for the approximation of a sum of known length where addends are revealed sequentially. We do not assume independence between addends, only that they are bounded from below and decrease in conditional expectation. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

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JMLR Journal 2020 Journal Article

Conjugate Gradients for Kernel Machines

Simon Bartels
Philipp Hennig

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large datasets require to resort to approximations. In this work, the computation of the least-squares prediction is itself treated as a probabilistic inference problem. We propose a structured Gaussian regression model on the kernel function that uses projections of the kernel matrix to obtain a low-rank approximation of the kernel and the matrix. A central result is an enhanced way to use the method of conjugate gradients for the specific setting of least-squares regression as encountered in machine learning. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

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