摊销重参数化：针对潜在SDE的高效可扩展变分推断
Amortized Reparametrization: Efficient and Scalable Variational Inference for Latent SDEs
AI总结：
针对潜在SDE推断时间复杂度受方程刚度制约的问题，提出结合摊销策略与线性SDE期望重参数化的方法，无需求解微分方程即可近似梯度，训练评估次数降一个数量级以上且性能相当。
摘要：
我们研究潜在随机微分方程（SDEs）的推断问题，目标是让时间和内存成本的变化与数据量、时间序列总长度以及近似微分方程的刚度无关。这与典型的潜在微分方程推断方法形成鲜明对比——后者尽管内存成本恒定，但时间复杂度严重依赖于近似微分方程的刚度。我们通过一种新颖的摊销策略，结合近期推导的线性SDE下期望的重参数化方法，在近似梯度时无需求解微分方程，从而实现了这一计算突破。实验表明，在实际应用中，该方法能达到与基于伴随灵敏度的方法相近的性能，且训练过程中的模型评估次数减少了一个数量级以上。
英文摘要：
We consider the problem of inferring latent stochastic differential equations (SDEs) with a time and memory cost that scales independently with the amount of data, the total length of the time series, and the stiffness of the approximate differential equations. This is in stark contrast to typical methods for inferring latent differential equations which, despite their constant memory cost, have a time complexity that is heavily dependent on the stiffness of the approximate differential equation. We achieve this computational advancement by removing the need to solve differential equations when approximating gradients using a novel amortization strategy coupled with a recently derived reparametrization of expectations under linear SDEs. We show that, in practice, this allows us to achieve similar performance to methods based on adjoint sensitivities with more than an order of magnitude fewer evaluations of the model in training.
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