Quickest Inference of Network Cascades With Noisy Information

We study the problem of estimating source a network cascade given time series noisy information about spread. Initially, there is single vertex affected by (the source) and spreads in discrete steps across network. Although evolution hidden, one observes measurement at each step. Given this information, we aim to reliably estimate as fast possible. investigate Bayesian minimax formulations estimation problem, derive near-optimal estimators for simple dynamics topologies. In setting, samples are taken until error Bayes-optimal estimator falls below threshold. For design novel multi-hypothesis sequential probability ratio test. These optimal require $\log \log n / (k - 1)$ observations notation="LaTeX">$k$ -regular tree network, notation="LaTeX">$(\log n)^{\frac {1}{\ell + 1}}$ notation="LaTeX">$\ell $ -dimensional lattice. then discuss conjectures on general Finally, provide simulations which validate our theoretical results trees lattices, illustrate effectiveness methods sources cascades Erdős-Rényi graphs.