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Model selection via marginal likelihood estimation by combining thermodynamic integration and gradient matching

机译：通过结合热力学集成和梯度匹配来通过边缘似然估计进行模型选择

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摘要

Conducting statistical inference on systems described by ordinary differential equations (ODEs) is a challenging problem. Repeatedly numerically solving the system of equations incurs a high computational cost, making many methods based on explicitly solving the ODEs unsuitable in practice. Gradient matching methods were introduced in order to deal with the computational burden. These methods involve minimising the discrepancy between predicted gradients from the ODEs and those from a smooth interpolant. Work until now on gradient matching methods has focused on parameter inference. This paper considers the problem of model selection. We combine the method of thermodynamic integration to compute the log marginal likelihood with adaptive gradient matching using Gaussian processes, demonstrating that the method is robust and able to outperform BIC and WAIC.
机译：对常微分方程（ODES）描述的系统进行统计推断是一个具有挑战性的问题。在数值上求解方程系统遭受高计算成本，基于在实践中明确解决了不适合的杂散的许多方法。介绍了梯度匹配方法，以处理计算负担。这些方法涉及将预测梯度之间的差异最小化了来自杂散的预测梯度和来自平滑插值的差异。直到现在渐变匹配方法的工作集中在参数推断上。本文考虑了模型选择的问题。我们将热力学集成方法结合起来计算利用高斯过程的自适应梯度匹配来计算日志边缘似然，展示该方法是坚固的并且能够优于BIC和瓦。

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