Aligning ligand binding cavities by optimizing superposed volume

Chen, Ruobing; Scheinberg, Katya; Chen, Brian Y.

doi:10.1109/bibm.2012.6392629

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…In these approaches, we use the measures of convergence (e.g., trust-region radius, model gradient) to determine a suitable level of accuracy with which to evaluate the objective; we start with low-accuracy requirements, and increase the required accuracy as we converge to a solution. In a DFO context, this framework is the basis of [19], and a similar approach was considered in [15] in the context of analyzing protein structures. This framework has also been recently extended in a derivative-based context to higherorder regularization methods [7,26].…”

Section: Derivative-free Optimizationmentioning

confidence: 99%

“…We will need to be able to solve the lower-level problem to sufficient accuracy that we can guarantee x k −x * 2 ≤ , for a suitable accuracy > 0. We can guarantee this accuracy by ensuring we terminate with k sufficiently large, given an estimate x 0 − x * 2 , using the a priori bounds (15)…”

Section: Ensuring Accuracy Requirementsmentioning

confidence: 99%

“…In Fig. 3, we compare the true error x k − x * 2 against the a priori linear convergence bounds (15) or (19) with the true value of x 0 − x * 2 , and the a posteriori gradient bound (20). In both cases, the gradient-based bound (20) provides a much tighter estimate of the error, particularly for highaccuracy requirements.…”

Section: Ensuring Accuracy Requirementsmentioning

confidence: 99%

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Inexact Derivative-Free Optimization for Bilevel Learning

Ehrhardt

Roberts

2021

J Math Imaging Vis

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Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by-now common strategy to resolve this issue is to learn these parameters from data. While mathematically appealing, this strategy leads to a nested optimization problem (known as bilevel optimization) which is computationally very difficult to handle. It is common when solving the upper-level problem to assume access to exact solutions of the lower-level problem, which is practically infeasible. In this work we propose to solve these problems using inexact derivative-free optimization algorithms which never require exact lower-level problem solutions, but instead assume access to approximate solutions with controllable accuracy, which is achievable in practice. We prove global convergence and a worst-case complexity bound for our approach. We test our proposed framework on ROF denoising and learning MRI sampling patterns. Dynamically adjusting the lower-level accuracy yields learned parameters with similar reconstruction quality as high-accuracy evaluations but with dramatic reductions in computational work (up to 100 times faster in some cases).

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Section: Derivative-free Optimizationmentioning

confidence: 99%

Section: Ensuring Accuracy Requirementsmentioning

confidence: 99%

Section: Ensuring Accuracy Requirementsmentioning

confidence: 99%

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Inexact Derivative-Free Optimization for Bilevel Learning

Ehrhardt

Roberts

2021

J Math Imaging Vis

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“…trust-region radius, model gradient) to determine a suitable level of accuracy with which to evaluate the objective; we start with low accuracy requirements, and increase the required accuracy as we converge to a solution. In a DFO context, this framework is the basis of [25], and a similar approach was considered in [27] in the context of analyzing protein structures. This framework has also been recently extended in a derivative-based context to higher-order regularization methods [28,29].…”

mentioning

confidence: 99%

Inexact Derivative-Free Optimization for Bilevel Learning

Ehrhardt¹,

Roberts²

2020

Preprint

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Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to resolve this issue is to learn these parameters from data. While mathematically appealing this strategy leads to a nested optimization problem (known as bilevel optimization) which is computationally very difficult to handle. A key ingredient in solving the upper-level problem is the exact solution of the lower-level problem which is practically infeasible. In this work we propose to solve these problems using inexact derivative-free optimization algorithms which never require to solve the lower-level problem exactly. We provide global convergence and worst-case complexity analysis of our approach, and test our proposed framework on ROF-denoising and learning MRI sampling patterns. Dynamically adjusting the lower-level accuracy yields learned parameters with similar reconstruction quality as high-accuracy evaluations but with dramatic reductions in computational work (up to 100 times faster in some cases).

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Explaining Small Molecule Binding Specificity with Volumetric Representations of Protein Binding Sites

Guo

Chen²

2022

Computational Biology

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Aligning ligand binding cavities by optimizing superposed volume

Cited by 4 publications

References 27 publications

Inexact Derivative-Free Optimization for Bilevel Learning

Inexact Derivative-Free Optimization for Bilevel Learning

Inexact Derivative-Free Optimization for Bilevel Learning

Explaining Small Molecule Binding Specificity with Volumetric Representations of Protein Binding Sites

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