Results 1  10
of
78
Lifted firstorder belief propagation
 In Association for the Advancement of Artificial Intelligence (AAAI
, 2008
"... Unifying firstorder logic and probability is a longstanding goal of AI, and in recent years many representations combining aspects of the two have been proposed. However, inference in them is generally still at the level of propositional logic, creating all ground atoms and formulas and applying s ..."
Abstract

Cited by 75 (9 self)
 Add to MetaCart
Unifying firstorder logic and probability is a longstanding goal of AI, and in recent years many representations combining aspects of the two have been proposed. However, inference in them is generally still at the level of propositional logic, creating all ground atoms and formulas and applying standard probabilistic inference methods to the resulting network. Ideally, inference should be lifted as in firstorder logic, handling whole sets of indistinguishable objects together, in time independent of their cardinality. Poole (2003) and Braz et al. (2005, 2006) developed a lifted version of the variable elimination algorithm, but it is extremely complex, generally does not scale to realistic domains, and has only been applied to very small artificial problems. In this paper we propose the first lifted version of a scalable probabilistic inference algorithm, belief propagation (loopy or not). Our approach is based on first constructing a lifted network, where each node represents a set of ground atoms that all pass the same messages during belief propagation. We then run belief propagation on this network. We prove the correctness and optimality of our algorithm. Experiments show that it can greatly reduce the cost of inference.
Firstorder probabilistic models for coreference resolution
 In HLT/NAACL
, 2007
"... Traditional noun phrase coreference resolution systems represent features only of pairs of noun phrases. In this paper, we propose a machine learning method that enables features over sets of noun phrases, resulting in a firstorder probabilistic model for coreference. We outline a set of approximat ..."
Abstract

Cited by 57 (17 self)
 Add to MetaCart
Traditional noun phrase coreference resolution systems represent features only of pairs of noun phrases. In this paper, we propose a machine learning method that enables features over sets of noun phrases, resulting in a firstorder probabilistic model for coreference. We outline a set of approximations that make this approach practical, and apply our method to the ACE coreference dataset, achieving a 45 % error reduction over a comparable method that only considers features of pairs of noun phrases. This result demonstrates an example of how a firstorder logic representation can be incorporated into a probabilistic model and scaled efficiently. 1
Compiling relational bayesian networks for exact inference
 International Journal of Approximate Reasoning
, 2004
"... We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available Primula tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evalua ..."
Abstract

Cited by 54 (11 self)
 Add to MetaCart
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available Primula tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose Primula–generated propositional instances have thousands of variables, and whose jointrees have clusters with hundreds of variables.
Lifted probabilistic inference with counting formulas
 Proceedings of the TwentyThird AAAI Conference on Artificial Intelligence (AAAI2008
, 2008
"... Lifted inference algorithms exploit repeated structure in probabilistic models to answer queries efficiently. Previous work such as de Salvo Braz et al.’s firstorder variable elimination (FOVE) has focused on the sharing of potentials across interchangeable random variables. In this paper, we also ..."
Abstract

Cited by 51 (12 self)
 Add to MetaCart
Lifted inference algorithms exploit repeated structure in probabilistic models to answer queries efficiently. Previous work such as de Salvo Braz et al.’s firstorder variable elimination (FOVE) has focused on the sharing of potentials across interchangeable random variables. In this paper, we also exploit interchangeability within individual potentials by introducing counting formulas, which indicate how many of the random variables in a set have each possible value. We present a new lifted inference algorithm, CFOVE, that not only handles counting formulas in its input, but also creates counting formulas for use in intermediate potentials. CFOVE can be described succinctly in terms of six operators, along with heuristics for when to apply them. Because counting formulas capture dependencies among large numbers of variables compactly, CFOVE achieves asymptotic speed improvements compared to FOVE.
Memoryefficient inference in relational domains
 In Proceedings of the TwentyFirst National Conference on Artificial Intelligence
, 2006
"... Propositionalization of a firstorder theory followed by satisfiability testing has proved to be a remarkably efficient approach to inference in relational domains such as planning (Kautz & Selman 1996) and verification (Jackson 2000). More recently, weighted satisfiability solvers have been used su ..."
Abstract

Cited by 30 (7 self)
 Add to MetaCart
Propositionalization of a firstorder theory followed by satisfiability testing has proved to be a remarkably efficient approach to inference in relational domains such as planning (Kautz & Selman 1996) and verification (Jackson 2000). More recently, weighted satisfiability solvers have been used successfully for MPE inference in statistical relational learners (Singla & Domingos 2005). However, fully instantiating a finite firstorder theory requires memory on the order of the number of constants raised to the arity of the clauses, which significantly limits the size of domains it can be applied to. In this paper we propose LazySAT, a variation of the WalkSAT solver that avoids this blowup by taking advantage of the extreme sparseness that is typical of relational domains (i.e., only a small fraction of ground atoms are true, and most clauses are trivially satisfied). Experiments on entity resolution and planning problems show that LazySAT reduces memory usage by orders of magnitude compared to WalkSAT, while taking comparable time to run and producing the same solutions.
Exploiting Shared Correlations in Probabilistic Databases
, 2008
"... There has been a recent surge in work in probabilistic databases, propelled in large part by the huge increase in noisy data sources — from sensor data, experimental data, data from uncurated sources, and many others. There is a growing need for database management systems that can efficiently repre ..."
Abstract

Cited by 26 (6 self)
 Add to MetaCart
There has been a recent surge in work in probabilistic databases, propelled in large part by the huge increase in noisy data sources — from sensor data, experimental data, data from uncurated sources, and many others. There is a growing need for database management systems that can efficiently represent and query such data. In this work, we show how data characteristics can be leveraged to make the query evaluation process more efficient. In particular, we exploit what we refer to as shared correlations where the same uncertainties and correlations occur repeatedly in the data. Shared correlations occur mainly due to two reasons: (1) Uncertainty and correlations usually come from general statistics and rarely vary on a tupletotuple basis; (2) The query evaluation procedure itself tends to reintroduce the same correlations. Prior work has shown that the query evaluation problem on probabilistic databases is equivalent to a probabilistic inference problem on an appropriately constructed probabilistic graphical model (PGM). We leverage this by introducing a new data structure, called the random variable elimination graph (rvelim graph) that can be built from the PGM obtained from query evaluation. We develop techniques based on bisimulation that can be used to compress the rvelim graph exploiting the presence of shared correlations in the PGM, the compressed rvelim graph can then be used to run inference. We validate our methods by evaluating them empirically and show that even with a few shared correlations significant speedups are possible.
Probabilistic Theorem Proving
"... Many representation schemes combining firstorder logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logic ..."
Abstract

Cited by 25 (7 self)
 Add to MetaCart
Many representation schemes combining firstorder logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and firstorder theorem proving (in finite domains with Herbrand interpretations). We first define probabilistic theorem proving, their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how this can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate probabilistic theorem proving, and show that it can greatly outperform lifted belief propagation. 1
MPE and partial inversion in lifted probabilistic variable elimination
 IN: PROCEEDINGS OF THE NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE. (2006
, 2006
"... It is often convenient to represent probabilistic models in a firstorder fashion, using logical atoms such as random variables parameterized by logical variables. (de Salvo Braz et al., 2005), following (Poole, 2003), give a lifted variable elimination algorithm (FOVE) for computing marginal probab ..."
Abstract

Cited by 24 (3 self)
 Add to MetaCart
It is often convenient to represent probabilistic models in a firstorder fashion, using logical atoms such as random variables parameterized by logical variables. (de Salvo Braz et al., 2005), following (Poole, 2003), give a lifted variable elimination algorithm (FOVE) for computing marginal probabilities from firstorder probabilistic models (belief assessment, or BA). FOVE is lifted because it works directly at the firstorder level, eliminating all the instantiations of a set of atoms in a single step. Previous work could treat only restricted potential functions. There, atoms ’ instantiations cannot constrain each other: predicates can appear at most once, or logical variables must not interact across atoms. In this paper, we present two contributions. The first one is a significantly more general lifted variable elimination algorithm, FOVEP, that covers many cases where atoms share logical variables. The second contribution is to use FOVEP for solving the Most Probable Explanation (MPE) problem, which consists of calculating the most probable assignment of the random variables in a model. We introduce the notion of lifted assignments, a distribution of values to a set of random variables rather than to each individual one. Lifted assignments are cheaper to compute while being as useful as regular assignments over that group. Both contributions advance the theoretical understanding of lifted probabilistic inference.
Unifying logical and statistical AI
 Proceedings of the TwentyFirst National Conference on Artificial Intelligence
, 2006
"... Intelligent agents must be able to handle the complexity and uncertainty of the real world. Logical AI has focused mainly on the former, and statistical AI on the latter. Markov logic combines the two by attaching weights to firstorder formulas and viewing them as templates for features of Markov n ..."
Abstract

Cited by 22 (5 self)
 Add to MetaCart
Intelligent agents must be able to handle the complexity and uncertainty of the real world. Logical AI has focused mainly on the former, and statistical AI on the latter. Markov logic combines the two by attaching weights to firstorder formulas and viewing them as templates for features of Markov networks. Inference algorithms for Markov logic draw on ideas from satisfiability, Markov chain Monte Carlo and knowledgebased model construction. Learning algorithms are based on the voted perceptron, pseudolikelihood and inductive logic programming. Markov logic has been successfully applied to problems in entity resolution, link prediction, information extraction and others, and is the basis of the opensource Alchemy system.
Bisimulationbased approximate lifted inference
"... There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the firstorder model is given as input to the system. Here, we describe lifted inference algorithms that determine symmetries and automatically lift the probabilistic m ..."
Abstract

Cited by 21 (2 self)
 Add to MetaCart
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the firstorder model is given as input to the system. Here, we describe lifted inference algorithms that determine symmetries and automatically lift the probabilistic model to speedup inference. In particular, we describe approximate lifted inference techniques that allow the user to trade off inference accuracy for computational efficiency by using a handful of tunable parameters, while keeping the error bounded. Our algorithms are closely related to the graphtheoretic concept of bisimulation. We report experiments on both synthetic and real data to show that in the presence of symmetries, runtimes for inference can be improved significantly, with approximate lifted inference providing orders of magnitude speedup over ground inference.