New Advances in Logic-Based Probabilistic Modeling by PRISM

Sato, Taisuke; Kameya, Yoshitaka

doi:10.1007/978-3-540-78652-8_5

Cited by 38 publications

(26 citation statements)

References 53 publications

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“…In the context of statistical relational learning, abduction has also been widely studied. One of the prominent formalisms is PRISM (Sato and Kameya 2008), which is a general logic-based probabilistic modeling language. In the past two decades, a number of techniques for efficient inference or learning have been studied extensively (see Sato and Kameya (2008) for overview).…”

Section: Related Workmentioning

confidence: 99%

ILP-based Inference for Cost-based Abduction on First-order Predicate Logic

Inoue

Inui

2013

Journal of Natural Language Processing

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Abduction is desirable for many natural language processing (NLP) tasks. While recent advances in large-scale knowledge acquisition warrant applying abduction with large knowledge bases to real-life NLP problems, as of yet, no existing approach to abduction has achieved the efficiency necessary to be a practical solution for largescale reasoning on real-life problems. In this paper, we propose an efficient solution for large-scale abduction. The contributions of our study are as follows: (i) we propose an efficient method of cost-based abduction in first-order predicate logic that avoids computationally expensive grounding procedures; (ii) we formulate the bestexplanation search problem as an integer linear programming optimization problem, making our approach extensible; (iii) we show how cutting plane inference, which is an iterative optimization strategy developed in operations research, can be applied to make abduction in first-order logic tractable; and (iv) the abductive inference engine presented in this paper is made publicly available.

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Section: Related Workmentioning

confidence: 99%

ILP-based Inference for Cost-based Abduction on First-order Predicate Logic

Inoue

Inui

2013

Journal of Natural Language Processing

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“…While the original distribution semantics is defined for binary probabilistic facts only, it can easily be generalised to random variables with finite ranges, e.g. the implementation of the PRISM language supports such random variables [31]. However, as soon as we deal with infinite ranges the generalisation is semantically far from straightforward, in particular when the ranges are uncountable.…”

Section: A Generalised Distribution Semanticsmentioning

confidence: 98%

A new probabilistic constraint logic programming language based on a generalised distribution semantics

Michels

Hommersom

Lucas

et al. 2015

Artificial Intelligence

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Probabilistic logics combine the expressive power of logic with the ability to reason with uncertainty. Several probabilistic logic languages have been proposed in the past, each of them with their own features. We focus on a class of probabilistic logic based on Sato's distribution semantics, which extends logic programming with probability distributions on binary random variables and guarantees a unique probability distribution. For many applications binary random variables are, however, not sufficient and one requires random variables with arbitrary ranges, e.g. real numbers. We tackle this problem by developing a generalised distribution semantics for a new probabilistic constraint logic programming language. In order to perform exact inference, imprecise probabilities are taken as a starting point, i.e. we deal with sets of probability distributions rather than a single one. It is shown that given any continuous distribution, conditional probabilities of events can be approximated arbitrarily close to the true probability. Furthermore, for this setting an inference algorithm that is a generalisation of weighted model counting is developed, making use of SMT solvers. We show that inference has similar complexity properties as precise probabilistic inference, unlike most imprecise methods for which inference is more complex. We also experimentally confirm that our algorithm is able to exploit local structure, such as determinism, which further reduces the computational complexity.

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“…For example EM in PRISM computes generalized inside probabilities and generalized outside probabilities for defined goals in expl(G) using dynamic programming and calculates expectations of the number of occurrences of msw atoms in an SLD proof for the top-goal to update parameters in each iteration, similarly to the Inside-Outside algorithm for PCFGs (Sato and Kameya 2001). MAP (maximum a posteriori) estimation and VB (variational Bayes) inference are also performed similarly (Sato et al 2009;Sato and Kameya 2008).…”

Section: Tabled Search Dynamic Programming Probability Computation mentioning

confidence: 99%

Viterbi training in PRISM

Sato¹,

Kubota²

2014

Theory and Practice of Logic Programming

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VT (Viterbi training), or hard EM, is an efficient way of parameter learning for probabilistic models with hidden variables. Given an observation $y$, it searches for a state of hidden variables $x$ that maximizes $p(x,y \mid \theta)$ by coordinate ascent on parameters $\theta$ and $x$. In this paper we introduce VT to PRISM, a logic-based probabilistic modeling system for generative models. VT improves PRISM in three ways. First VT in PRISM converges faster than EM in PRISM due to the VT's termination condition. Second, parameters learned by VT often show good prediction performance compared to those learned by EM. We conducted two parsing experiments with probabilistic grammars while learning parameters by a variety of inference methods, i.e.\ VT, EM, MAP and VB. The result is that VT achieved the best parsing accuracy among them in both experiments. Also we conducted a similar experiment for classification tasks where a hidden variable is not a prediction target unlike probabilistic grammars. We found that in such a case VT does not necessarily yield superior performance. Third since VT always deals with a single probability of a single explanation, Viterbi explanation, the exclusiveness condition that is imposed on PRISM programs is no more required if we learn parameters by VT. Last but not least we can say that as VT in PRISM is general and applicable to any PRISM program, it largely reduces the need for the user to develop a specific VT algorithm for a specific model. Furthermore since VT in PRISM can be used just by setting a PRISM flag appropriately, it makes VT easily accessible to (probabilistic) logic programmers. To appear in Theory and Practice of Logic Programming (TPLP).Comment: 23 pages, 1 figur

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New Advances in Logic-Based Probabilistic Modeling by PRISM

Cited by 38 publications

References 53 publications

ILP-based Inference for Cost-based Abduction on First-order Predicate Logic

ILP-based Inference for Cost-based Abduction on First-order Predicate Logic

A new probabilistic constraint logic programming language based on a generalised distribution semantics

Viterbi training in PRISM

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