Computing observables from conditioned dynamics is typically computationally hard, because, although obtaining independent samples efficiently from the unconditioned dynamics is usually feasible, generally most of the samples must be discarded (in a form of importance sampling) because they do not satisfy the imposed conditions. Sampling directly from the conditioned distribution is non-trivial, as conditioning breaks the causal properties of the dynamics which ultimately renders the sampling procedure efficient. One standard way of achieving it is through a Metropolis Monte-Carlo procedure, but this procedure is normally slow and a very large number of Monte-Carlo steps is needed to obtain a small number of statistically independent samples. In this work, we propose an alternative method to produce independent samples from a conditioned distribution. The method learns the parameters of a generalized dynamical model that optimally describe the conditioned distribution in a variational sense. The outcome is an effective, unconditioned, dynamical model, from which one can trivially obtain independent samples, effectively restoring causality of the conditioned distribution. The consequences are twofold: on the one hand, it allows us to efficiently compute observables from the conditioned dynamics by simply averaging over independent samples. On the other hand, the method gives an effective unconditioned distribution which is easier to interpret. The method is flexible and can be applied virtually to any dynamics. We discuss an important application of the method, namely the problem of epidemic risk assessment from (imperfect) clinical tests, for a large family of time-continuous epidemic models endowed with a Gillespie-like sampler. We show that the method compares favorably against the state of the art, including the soft-margin approach and mean-field methods.

翻译：从条件动力学中计算可观测量通常具有较高的计算复杂度，这是因为尽管从无条件动力学中高效获取独立样本通常是可行的，但大多数样本由于不满足施加的条件而必须被舍弃（以重要性采样的形式）。直接对条件分布进行采样并非易事，因为条件作用破坏了动力学的因果特性，而正是这种因果特性从根本上保证了采样过程的高效性。实现这一目标的常规方法是通过Metropolis蒙特卡洛过程，但该过程通常速度较慢，且需要极大量的蒙特卡洛步数才能获得少量统计独立的样本。在本研究中，我们提出了一种从条件分布中生成独立样本的替代方法。该方法通过变分原理学习一个广义动力学模型的参数，该模型能以最优方式描述条件分布。其结果是得到一个有效的无条件动力学模型，从中可以轻易地获得独立样本，从而有效恢复了条件分布的因果性。这带来双重意义：一方面，它使我们能够通过简单地对独立样本取平均来高效计算条件动力学中的可观测量；另一方面，该方法产生了一个更易于解释的有效无条件分布。该方法具有灵活性，几乎可应用于任何动力学过程。我们讨论了该方法的一个重要应用，即针对一大类具备Gillespie类采样器的连续时间流行病模型，基于（不完美的）临床检测进行流行病风险评估的问题。我们证明，相较于包括软边界方法和平均场方法在内的现有先进技术，本方法具有明显优势。