264,910 research outputs found
Around -independence
In this article we study various forms of -independence (including the
case ) for the cohomology and fundamental groups of varieties over
finite fields and equicharacteristic local fields. Our first result is a strong
form of -independence for the unipotent fundamental group of smooth and
projective varieties over finite fields, by then proving a certain `spreading
out' result we are able to deduce a much weaker form of -independence for
unipotent fundamental groups over equicharacteristic local fields, at least in
the semistable case. In a similar vein, we can also use this to deduce
-independence results for the cohomology of semistable varieties from the
well-known results on -independence for smooth and proper varieties over
finite fields. As another consequence of this `spreading out' result we are
able to deduce the existence of a Clemens--Schmid exact sequence for formal
semistable families. Finally, by deforming to characteristic we show a
similar weak version of -independence for the unipotent fundamental group
of a semistable curve in mixed characteristic.Comment: 23 pages, comments welcom
Symbolic Exact Inference for Discrete Probabilistic Programs
The computational burden of probabilistic inference remains a hurdle for
applying probabilistic programming languages to practical problems of interest.
In this work, we provide a semantic and algorithmic foundation for efficient
exact inference on discrete-valued finite-domain imperative probabilistic
programs. We leverage and generalize efficient inference procedures for
Bayesian networks, which exploit the structure of the network to decompose the
inference task, thereby avoiding full path enumeration. To do this, we first
compile probabilistic programs to a symbolic representation. Then we adapt
techniques from the probabilistic logic programming and artificial intelligence
communities in order to perform inference on the symbolic representation. We
formalize our approach, prove it sound, and experimentally validate it against
existing exact and approximate inference techniques. We show that our inference
approach is competitive with inference procedures specialized for Bayesian
networks, thereby expanding the class of probabilistic programs that can be
practically analyzed
Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference
Exchangeability is a central notion in statistics and probability theory. The
assumption that an infinite sequence of data points is exchangeable is at the
core of Bayesian statistics. However, finite exchangeability as a statistical
property that renders probabilistic inference tractable is less
well-understood. We develop a theory of finite exchangeability and its relation
to tractable probabilistic inference. The theory is complementary to that of
independence and conditional independence. We show that tractable inference in
probabilistic models with high treewidth and millions of variables can be
understood using the notion of finite (partial) exchangeability. We also show
that existing lifted inference algorithms implicitly utilize a combination of
conditional independence and partial exchangeability.Comment: In Proceedings of the 28th AAAI Conference on Artificial Intelligenc
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