We consider a problem of inferring contact network from nodal states observed during an epidemiological process. In a black-box Bayesian optimisation framework this problem reduces to a discrete likelihood optimisation over the set of possible networks. The high dimensionality of this set, which grows quadratically with the number of network nodes, makes this optimisation computationally challenging. Moreover, the computation of the likelihood of a network requires estimating probabilities of the observed data to realise during the evolution of the epidemiological process on this network. A stochastic simulation algorithm struggles to estimate rare events of observing the data (corresponding to the ground truth network) during the evolution with a significantly different network, and hence prevents optimisation of the likelihood. We replace the stochastic simulation with solving the chemical master equation for the probabilities of all network states. This equation also suffers from the curse of dimensionality due to the exponentially large number of network states. We overcome this by approximating the probability of states in the tensor-train decomposition. This enables fast and accurate computation of small probabilities and likelihoods. Numerical simulations demonstrate efficient black-box Bayesian inference of the network.

翻译：我们考虑从流行病过程中观测到的节点状态推断接触网络的问题。在黑箱贝叶斯优化框架下，该问题简化为对可能网络集合的离散似然优化。该集合的高维特性——其维度随网络节点数呈二次增长——使得优化面临计算挑战。此外，计算特定网络的似然性需要估计在该网络上流行病演化过程中观测数据（即真实网络对应的数据）发生的概率。当使用显著不同的网络进行演化时，随机模拟算法难以估计观测数据（对应真实网络）这一稀有事件，从而阻碍似然优化。我们采用化学主方程替代随机模拟，以计算所有网络状态的概率。该方程同样因网络状态数量呈指数级增长而面临维数诅咒。我们通过张量列分解近似状态概率来克服这一难题，从而实现对极小概率和似然值的快速精确计算。数值模拟验证了该黑箱贝叶斯网络推断方法的高效性。