  We consider a class of queries called durability prediction queries that
arise commonly in predictive analytics, where we use a given predictive model
to answer questions about possible futures to inform our decisions. Examples of
durability prediction queries include "what is the probability that this
financial product will keep losing money over the next 12 quarters before
turning in any profit?" and "what is the chance for our proposed server cluster
to fail the required service-level agreement before its term ends?" We devise a
general method called Multi-Level Splitting Sampling (MLSS) that can
efficiently handle complex queries and complex models -- including those
involving black-box functions -- as long as the models allow us to simulate
possible futures step by step. Our method addresses the inefficiency of
standard Monte Carlo (MC) methods by applying the idea of importance splitting
to let one "promising" sample path prefix generate multiple "offspring" paths,
thereby directing simulation efforts toward more promising paths. We propose
practical techniques for designing splitting strategies, freeing users from
manual tuning. Experiments show that our approach is able to achieve unbiased
estimates and the same error guarantees as standard MC while offering an
order-of-magnitude cost reduction.
