696 research outputs found
Oblivious Bounds on the Probability of Boolean Functions
This paper develops upper and lower bounds for the probability of Boolean
functions by treating multiple occurrences of variables as independent and
assigning them new individual probabilities. We call this approach dissociation
and give an exact characterization of optimal oblivious bounds, i.e. when the
new probabilities are chosen independent of the probabilities of all other
variables. Our motivation comes from the weighted model counting problem (or,
equivalently, the problem of computing the probability of a Boolean function),
which is #P-hard in general. By performing several dissociations, one can
transform a Boolean formula whose probability is difficult to compute, into one
whose probability is easy to compute, and which is guaranteed to provide an
upper or lower bound on the probability of the original formula by choosing
appropriate probabilities for the dissociated variables. Our new bounds shed
light on the connection between previous relaxation-based and model-based
approximations and unify them as concrete choices in a larger design space. We
also show how our theory allows a standard relational database management
system (DBMS) to both upper and lower bound hard probabilistic queries in
guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281
A General Framework for Anytime Approximation in Probabilistic Databases
Anytime approximation algorithms that compute the probabilities of queries
over probabilistic databases can be of great use to statistical learning tasks.
Those approaches have been based so far on either (i) sampling or (ii)
branch-and-bound with model-based bounds. We present here a more general
branch-and-bound framework that extends the possible bounds by using
'dissociation', which yields tighter bounds.Comment: 3 pages, 2 figures, submitted to StarAI 2018 Worksho
Approximate Lifted Inference with Probabilistic Databases
This paper proposes a new approach for approximate evaluation of #P-hard
queries with probabilistic databases. In our approach, every query is evaluated
entirely in the database engine by evaluating a fixed number of query plans,
each providing an upper bound on the true probability, then taking their
minimum. We provide an algorithm that takes into account important schema
information to enumerate only the minimal necessary plans among all possible
plans. Importantly, this algorithm is a strict generalization of all known
results of PTIME self-join-free conjunctive queries: A query is safe if and
only if our algorithm returns one single plan. We also apply three relational
query optimization techniques to evaluate all minimal safe plans very fast. We
give a detailed experimental evaluation of our approach and, in the process,
provide a new way of thinking about the value of probabilistic methods over
non-probabilistic methods for ranking query answers.Comment: 12 pages, 5 figures, pre-print for a paper appearing in VLDB 2015.
arXiv admin note: text overlap with arXiv:1310.625
Tractability in probabilistic databases
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