  In reasoning about sequential events it is natural to pose probabilistic
queries such as "when will event A occur next" or "what is the probability of A
occurring before B", with applications in areas such as user modeling,
medicine, and finance. However, with machine learning shifting towards neural
autoregressive models such as RNNs and transformers, probabilistic querying has
been largely restricted to simple cases such as next-event prediction. This is
in part due to the fact that future querying involves marginalization over
large path spaces, which is not straightforward to do efficiently in such
models. In this paper we introduce a general typology for predictive queries in
neural autoregressive sequence models and show that such queries can be
systematically represented by sets of elementary building blocks. We leverage
this typology to develop new query estimation methods based on beam search,
importance sampling, and hybrids. Across four large-scale sequence datasets
from different application domains, as well as for the GPT-2 language model, we
demonstrate the ability to make query answering tractable for arbitrary queries
in exponentially-large predictive path-spaces, and find clear differences in
cost-accuracy tradeoffs between search and sampling methods.
