[论文解读] Gaussian process emulation for discontinuous response surfaces with applications for cardiac electrophysiology models

Sanmitra Ghosh, David J. Gavaghan+1 more|arXiv (Cornell University)|May 25, 2018

Fault Detection and Control Systems参考文献 35被引用 8

一句话总结

该论文提出了一种两步高斯过程（GP）模拟器，用于处理心脏电生理模型中因分岔导致动作电位时程（APD）发生突变的不连续响应面。该方法利用GP分类器检测不连续性边界，并在这些区域内约束GP回归，实现了仅需全仿真10%计算成本、且在100,000个测试点上推理时间不足一分钟的高精度不确定性量化。

ABSTRACT

Mathematical models of biological systems are beginning to be used for safety-critical applications, where large numbers of repeated model evaluations are required to perform uncertainty quantification and sensitivity analysis. Most of these models are nonlinear both in variables and parameters/inputs which has two consequences. First, analytic solutions are rarely available so repeated evaluation of these models by numerically solving differential equations incurs a significant computational burden. Second, many models undergo bifurcations in behaviour as parameters are varied. As a result, simulation outputs often contain discontinuities as we change parameter values and move through parameter/input space. Statistical emulators such as Gaussian processes are frequently used to reduce the computational cost of uncertainty quantification, but discontinuities render a standard Gaussian process emulation approach unsuitable as these emulators assume a smooth and continuous response to changes in parameter values. In this article, we propose a novel two-step method for building a Gaussian Process emulator for models with discontinuous response surfaces. We first use a Gaussian Process classifier to detect boundaries of discontinuities and then constrain the Gaussian Process emulation of the response surface within these boundaries. We introduce a novel `certainty metric' to guide active learning for a multi-class probabilistic classifier. We apply the new classifier to simulations of drug action on a cardiac electrophysiology model, to propagate our uncertainty in a drug's action through to predictions of changes to the cardiac action potential. The proposed two-step active learning method significantly reduces the computational cost of emulating models that undergo multiple bifurcations.

研究动机与目标

• 为解决由于动力学中分岔导致响应面不连续的心脏电生理模型模拟挑战。
• 降低在安全关键型生物模型中不确定性量化与敏感性分析的计算负担。
• 开发一种即使在参数空间中输出（如APD）发生突变时仍保持高精度的统计模拟器。
• 提出一种基于置信度度量的新颖主动学习方案，以高效检测边界。
• 实现从实验药物筛选数据到全细胞电生理预测的可扩展不确定性传播。

提出的方法

• 两步框架：首先，使用新颖的置信度度量进行主动学习，多分类GP分类器在参数空间中检测不连续性边界。
• 置信度度量量化分类器的置信程度，指导下一步采样位置，以最小化仿真次数提升边界检测效率。
• 在每个识别出的区域内，使用稀疏GP回归模型（采用FITC近似）模拟APD响应面。
• 主动学习优先在不确定性边界附近采样，显著减少所需模拟器评估次数。
• 该方法结合了概率分类与GP回归，两阶段均利用不确定性量化。
• 模拟器在少量模拟器运行结果上进行训练，并可高效预测大规模参数空间中的APD。

实验结果

研究问题

• RQ1 统计模拟器能否在分岔导致动作电位时程发生突变的心脏电生理模型中，准确建模不连续响应面？
• RQ2 基于置信度度量的主动学习如何提升高维参数空间中边界检测的效率？
• RQ3 与全仿真相比，两步GP模拟器在不确定性量化中的计算成本与预测精度如何？
• RQ4 所提方法能否推广至其他具有类似分岔行为的生物标志物或生物物理模型？
• RQ5 使用概率GP分类器如何提升在分岔点附近对数值误差的鲁棒性？

主要发现

• 两步GP模拟器在100,000个测试点的测试集中实现了高预测精度，计算成本仅为全仿真约10%。
• 使用稀疏GP近似（FITC）进行整个测试集的预测推理时间不足一分钟。
• 基于置信度度量的主动学习方案显著减少了所需模拟器评估次数。
• 尽管计算成本更高，使用EP推理的GP分类器在准确性上优于拉普拉斯近似等替代方法。
• 该方法成功捕捉了O’Hara模型中不同药物阻断参数下APD 90响应面的不连续性。
• 该方法可推广至其他表现出分岔与不连续响应的生物标志物及生物物理模型。