论文标题
快速反转“无可能”动态系统的可区分可能性
Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems
论文作者
论文摘要
无似然（又称基于仿真的）推理问题是昂贵或棘手的远期模型的反问题。 ode反问题通常被视为不含似然的，因为它们的正向图必须由ode求解器在数值上近似。但是，这不是一个基本的约束，而只是经典ode求解器中缺乏功能，这不会返回可能性，而是一个点估计。为了解决这一缺点，我们采用高斯ode滤波（ODES的概率数值方法）来构建与可能性的局部高斯近似值。这种近似产生了（log-）可能性的梯度和黑森的可进行估计量。将这些估计器插入现有的基于梯度的优化和采样方法中，这为ODE反向问题提供了新的求解器。我们证明，这些方法在三个基准系统上的表现优于标准可能性的无可能方法。
Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically approximated by an ODE solver. This, however, is not a fundamental constraint but just a lack of functionality in classic ODE solvers, which do not return a likelihood but a point estimate. To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood. This approximation yields tractable estimators for the gradient and Hessian of the (log-)likelihood. Insertion of these estimators into existing gradient-based optimization and sampling methods engenders new solvers for ODE inverse problems. We demonstrate that these methods outperform standard likelihood-free approaches on three benchmark-systems.
