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

机译：通过热力学积分和梯度匹配相结合的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（ODE）描述的系统进行统计推断是一个具有挑战性的问题。反复地对方程组进行数值求解会导致较高的计算成本，使得基于显式求解ODE的许多方法在实践中不适用。为了解决计算量的不足，引入了梯度匹配方法。这些方法包括最小化ODE的预测梯度与平滑插值的预测梯度之间的差异。到目前为止，梯度匹配方法的工作主要集中在参数推断上。本文考虑了模型选择的问题。我们将热力学积分方法与使用高斯过程的自适应梯度匹配相结合来计算对数边际似然率，证明该方法是鲁棒的并且能够胜过BIC和WAIC。

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