1,230 research outputs found
Lower Complexity Bounds for Lifted Inference
One of the big challenges in the development of probabilistic relational (or
probabilistic logical) modeling and learning frameworks is the design of
inference techniques that operate on the level of the abstract model
representation language, rather than on the level of ground, propositional
instances of the model. Numerous approaches for such "lifted inference"
techniques have been proposed. While it has been demonstrated that these
techniques will lead to significantly more efficient inference on some specific
models, there are only very recent and still quite restricted results that show
the feasibility of lifted inference on certain syntactically defined classes of
models. Lower complexity bounds that imply some limitations for the feasibility
of lifted inference on more expressive model classes were established early on
in (Jaeger 2000). However, it is not immediate that these results also apply to
the type of modeling languages that currently receive the most attention, i.e.,
weighted, quantifier-free formulas. In this paper we extend these earlier
results, and show that under the assumption that NETIME =/= ETIME, there is no
polynomial lifted inference algorithm for knowledge bases of weighted,
quantifier- and function-free formulas. Further strengthening earlier results,
this is also shown to hold for approximate inference, and for knowledge bases
not containing the equality predicate.Comment: To appear in Theory and Practice of Logic Programming (TPLP
Lifted Variable Elimination for Probabilistic Logic Programming
Lifted inference has been proposed for various probabilistic logical
frameworks in order to compute the probability of queries in a time that
depends on the size of the domains of the random variables rather than the
number of instances. Even if various authors have underlined its importance for
probabilistic logic programming (PLP), lifted inference has been applied up to
now only to relational languages outside of logic programming. In this paper we
adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the
problem of computing the probability of queries to probabilistic logic programs
under the distribution semantics. In particular, we extend the Prolog Factor
Language (PFL) to include two new types of factors that are needed for
representing ProbLog programs. These factors take into account the existing
causal independence relationships among random variables and are managed by the
extension to variable elimination proposed by Zhang and Poole for dealing with
convergent variables and heterogeneous factors. Two new operators are added to
GC-FOVE for treating heterogeneous factors. The resulting algorithm, called
LP for Lifted Probabilistic Logic Programming, has been implemented by
modifying the PFL implementation of GC-FOVE and tested on three benchmarks for
lifted inference. A comparison with PITA and ProbLog2 shows the potential of
the approach.Comment: To appear in Theory and Practice of Logic Programming (TPLP). arXiv
admin note: text overlap with arXiv:1402.0565 by other author
Lifted Relax, Compensate and then Recover: From Approximate to Exact Lifted Probabilistic Inference
We propose an approach to lifted approximate inference for first-order
probabilistic models, such as Markov logic networks. It is based on performing
exact lifted inference in a simplified first-order model, which is found by
relaxing first-order constraints, and then compensating for the relaxation.
These simplified models can be incrementally improved by carefully recovering
constraints that have been relaxed, also at the first-order level. This leads
to a spectrum of approximations, with lifted belief propagation on one end, and
exact lifted inference on the other. We discuss how relaxation, compensation,
and recovery can be performed, all at the firstorder level, and show
empirically that our approach substantially improves on the approximations of
both propositional solvers and lifted belief propagation.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
Probabilistic Inference Modulo Theories
We present SGDPLL(T), an algorithm that solves (among many other problems)
probabilistic inference modulo theories, that is, inference problems over
probabilistic models defined via a logic theory provided as a parameter
(currently, propositional, equalities on discrete sorts, and inequalities, more
specifically difference arithmetic, on bounded integers). While many solutions
to probabilistic inference over logic representations have been proposed,
SGDPLL(T) is simultaneously (1) lifted, (2) exact and (3) modulo theories, that
is, parameterized by a background logic theory. This offers a foundation for
extending it to rich logic languages such as data structures and relational
data. By lifted, we mean algorithms with constant complexity in the domain size
(the number of values that variables can take). We also detail a solver for
summations with difference arithmetic and show experimental results from a
scenario in which SGDPLL(T) is much faster than a state-of-the-art
probabilistic solver.Comment: Submitted to StarAI-16 workshop as closely revised version of
IJCAI-16 pape
Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting
In this paper we study lifted inference for the Weighted First-Order Model
Counting problem (WFOMC), which counts the assignments that satisfy a given
sentence in first-order logic (FOL); it has applications in Statistical
Relational Learning (SRL) and Probabilistic Databases (PDB). We present several
results. First, we describe a lifted inference algorithm that generalizes prior
approaches in SRL and PDB. Second, we provide a novel dichotomy result for a
non-trivial fragment of FO CNF sentences, showing that for each sentence the
WFOMC problem is either in PTIME or #P-hard in the size of the input domain; we
prove that, in the first case our algorithm solves the WFOMC problem in PTIME,
and in the second case it fails. Third, we present several properties of the
algorithm. Finally, we discuss limitations of lifted inference for symmetric
probabilistic databases (where the weights of ground literals depend only on
the relation name, and not on the constants of the domain), and prove the
impossibility of a dichotomy result for the complexity of probabilistic
inference for the entire language FOL
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