Department of Computer Science

Machine Learning Research Group

University of Texas at Austin Artificial Intelligence Lab

Publications: Uncertain and Probabilistic Reasoning

Uncertain reasoning in AI concerns various forms of "probabilistic" as opposed to logical inference. Our work in the area has focused on theory refinement for knowledge bases using uncertainty such as certainty-factor rule bases and Bayesian networks. Rather than building such knowledge-bases completely manually or learning them form scratch, our work focuses on using data to revise imperfect expert-supplied initial KB's.
  1. University of Texas at Austin KBP 2013 Slot Filling System: Bayesian Logic Programs for Textual Inference
    [Details] [PDF]
    Yinon Bentor and Amelia Harrison and Shruti Bhosale and Raymond Mooney
    In Proceedings of the Sixth Text Analysis Conference (TAC 2013), 2013.
    This document describes the University of Texas at Austin 2013 system for the Knowledge Base Population (KBP) English Slot Filling (SF) task. The UT Austin system builds upon the output of an existing relation extractor by augmenting relations that are explicitly stated in the text with ones that are inferred from the stated relations using probabilistic rules that encode commonsense world knowledge. Such rules are learned from linked open data and are encoded in the form of Bayesian Logic Programs (BLPs), a statistical relational learning framework based on directed graphical models. In this document, we describe our methods for learning these rules, estimating their associated weights, and performing probabilistic and logical inference to infer unseen relations. In the KBP SF task, our system was able to infer several unextracted relations, but its performance was limited by the base level extractor.
    ML ID: 299
  2. Montague Meets Markov: Deep Semantics with Probabilistic Logical Form
    [Details] [PDF] [Slides]
    Islam Beltagy, Cuong Chau, Gemma Boleda, Dan Garrette, Katrin Erk, Raymond Mooney
    In Proceedings of the Second Joint Conference on Lexical and Computational Semantics (*Sem-2013), 11--21, Atlanta, GA, June 2013.
    We combine logical and distributional representations of natural language meaning by transforming distributional similarity judgments into weighted inference rules using Markov Logic Networks (MLNs). We show that this framework supports both judging sentence similarity and recognizing textual entailment by appropriately adapting the MLN implementation of logical connectives. We also show that distributional phrase similarity, used as textual inference rules created on the fly, improves its performance.
    ML ID: 285
  3. Bayesian Logic Programs for Plan Recognition and Machine Reading
    [Details] [PDF] [Slides]
    Sindhu Raghavan
    PhD Thesis, Department of Computer Science, University of Texas at Austin, December 2012. 170.
    Several real world tasks involve data that is uncertain and relational in nature. Traditional approaches like first-order logic and probabilistic models either deal with structured data or uncertainty, but not both. To address these limitations, statistical relational learning (SRL), a new area in machine learning integrating both first-order logic and probabilistic graphical models, has emerged in the recent past. The advantage of SRL models is that they can handle both uncertainty and structured/relational data. As a result, they are widely used in domains like social network analysis, biological data analysis, and natural language processing. Bayesian Logic Programs (BLPs), which integrate both first-order logic and Bayesian networks are a powerful SRL formalism developed in the recent past. In this dissertation, we develop approaches using BLPs to solve two real world tasks -- plan recognition and machine reading.

    Plan recognition is the task of predicting an agent's top-level plans based on its observed actions. It is an abductive reasoning task that involves inferring cause from effect. In the first part of the dissertation, we develop an approach to abductive plan recognition using BLPs. Since BLPs employ logical deduction to construct the networks, they cannot be used effectively for abductive plan recognition as is. Therefore, we extend BLPs to use logical abduction to construct Bayesian networks and call the resulting model Bayesian Abductive Logic Programs (BALPs).

    In the second part of the dissertation, we apply BLPs to the task of machine reading, which involves automatic extraction of knowledge from natural language text. Most information extraction (IE) systems identify facts that are explicitly stated in text. However, much of the information conveyed in text must be inferred from what is explicitly stated since easily inferable facts are rarely mentioned. Human readers naturally use common sense knowledge and "read between the lines" to infer such implicit information from the explicitly stated facts. Since IE systems do not have access to common sense knowledge, they cannot perform deeper reasoning to infer implicitly stated facts. Here, we first develop an approach using BLPs to infer implicitly stated facts from natural language text. It involves learning uncertain common sense knowledge in the form of probabilistic first-order rules by mining a large corpus of automatically extracted facts using an existing rule learner. These rules are then used to derive additional facts from extracted information using BLP inference. We then develop an online rule learner that handles the concise, incomplete nature of natural-language text and learns first-order rules from noisy IE extractions. Finally, we develop a novel approach to calculate the weights of the rules using a curated lexical ontology like WordNet.

    Both tasks described above involve inference and learning from partially observed or incomplete data. In plan recognition, the underlying cause or the top-level plan that resulted in the observed actions is not known or observed. Further, only a subset of the executed actions can be observed by the plan recognition system resulting in partially observed data. Similarly, in machine reading, since some information is implicitly stated, they are rarely observed in the data. In this dissertation, we demonstrate the efficacy of BLPs for inference and learning from incomplete data. Experimental comparison on various benchmark data sets on both tasks demonstrate the superior performance of BLPs over state-of-the-art methods.

    ML ID: 280
  4. Learning to "Read Between the Lines" using Bayesian Logic Programs
    [Details] [PDF] [Slides]
    Sindhu Raghavan and Raymond J. Mooney and Hyeonseo Ku
    In Proceedings of the 50th Annual Meeting of the Association for Computational Linguistics (ACL-2012), 349--358, July 2012.
    Most information extraction (IE) systems identify facts that are explicitly stated in text. However, in natural language, some facts are implicit, and identifying them requires "reading between the lines". Human readers naturally use common sense knowledge to infer such implicit information from the explicitly stated facts. We propose an approach that uses Bayesian Logic Programs (BLPs), a statistical relational model combining first-order logic and Bayesian networks, to infer additional implicit information from extracted facts. It involves learning uncertain commonsense knowledge (in the form of probabilistic first-order rules) from natural language text by mining a large corpus of automatically extracted facts. These rules are then used to derive additional facts from extracted information using BLP inference. Experimental evaluation on a benchmark data set for machine reading demonstrates the efficacy of our approach.
    ML ID: 270
  5. Extending Bayesian Logic Programs for Plan Recognition and Machine Reading
    [Details] [PDF] [Slides]
    Sindhu V. Raghavan
    Technical Report, PhD proposal, Department of Computer Science, The University of Texas at Austin, May 2011.

    Statistical relational learning (SRL) is the area of machine learning that integrates both first-order logic and probabilistic graphical models. The advantage of these formalisms is that they can handle both uncertainty and structured/relational data. As a result, they are widely used in domains like social network analysis, biological data analysis, and natural language processing. Bayesian Logic Programs (BLPs), which integrate both first-order logic and Bayesian networks are a powerful SRL formalism developed in the recent past. In this proposal, we focus on applying BLPs to two real worlds tasks -- plan recognition and machine reading.

    Plan recognition is the task of predicting an agent's top-level plans based on its observed actions. It is an abductive reasoning task that involves inferring cause from effect. In the first part of the proposal, we develop an approach to abductive plan recognition using BLPs. Since BLPs employ logical deduction to construct the networks, they cannot be used effectively for plan recognition as is. Therefore, we extend BLPs to use logical abduction to construct Bayesian networks and call the resulting model Bayesian Abductive Logic Programs (BALPs). Experimental evaluation on three benchmark data sets demonstrate that BALPs outperform the existing state-of-art methods like Markov Logic Networks (MLNs) for plan recognition.

    For future work, we propose to apply BLPs to the task of machine reading, which involves automatic extraction of knowledge from natural language text. Present day information extraction (IE) systems that are trained for machine reading are limited by their ability to extract only factual information that is stated explicitly in the text. We propose to improve the performance of an off-the-shelf IE system by inducing general knowledge rules about the domain using the facts already extracted by the IE system. We then use these rules to infer additional facts using BLPs, thereby improving the recall of the underlying IE system. Here again, the standard inference used in BLPs cannot be used to construct the networks. So, we extend BLPs to perform forward inference on all facts extracted by the IE system and then construct the ground Bayesian networks. We initially use an existing inductive logic programming (ILP) based rule learner to learn the rules. In the longer term, we would like to develop a rule/structure learner that is capable of learning an even better set of first-order rules for BLPs.

    ML ID: 258
  6. Improving the Accuracy and Scalability of Discriminative Learning Methods for Markov Logic Networks
    [Details] [PDF] [Slides]
    Tuyen N. Huynh
    PhD Thesis, Department of Computer Science, University of Texas at Austin, May 2011.
    159 pages.

    Many real-world problems involve data that both have complex structures and uncertainty. Statistical relational learning (SRL) is an emerging area of research that addresses the problem of learning from these noisy structured/relational data. Markov logic networks (MLNs), sets of weighted first-order logic formulae, are a simple but powerful SRL formalism that generalizes both first-order logic and Markov networks. MLNs have been successfully applied to a variety of real-world problems ranging from extraction knowledge from text to visual event recognition. Most of the existing learning algorithms for MLNs are in the generative setting: they try to learn a model that is equally capable of predicting the values of all variables given an arbitrary set of evidence; and they do not scale to problems with thousands of examples. However, many real-world problems in structured/relational data are discriminative---where the variables are divided into two disjoint sets input and output, and the goal is to correctly predict the values of the output variables given evidence data about the input variables. In addition, these problems usually involve data that have thousands of examples. Thus, it is important to develop new discriminative learning methods for MLNs that are more accurate and more scalable, which are the topics addressed in this thesis.

    First, we present a new method that discriminatively learns both the structure and parameters for a special class of MLNs where all the clauses are non-recursive ones. Non-recursive clauses arise in many learning problems in Inductive Logic Programming. To further improve the predictive accuracy, we propose a max-margin approach to learning weights for MLNs. Then, to address the issue of scalability, we present CDA, an online max-margin weight learning algorithm for MLNs. Ater that, we present OSL, the first algorithm that performs both online structure learning and parameter learning. Finally, we address an issue arising in applying MLNs to many real-world problems: learning in the presence of many hard constraints. Including hard constraints during training greatly increases the computational complexity of the learning problem. Thus, we propose a simple heuristic for selecting which hard constraints to include during training.

    Experimental results on several real-world problems show that the proposed methods are more accurate, more scalable (can handle problems with thousands of examples), or both more accurate and more scalable than existing learning methods for MLNs.

    ML ID: 257
  7. Discriminative Learning with Markov Logic Networks
    [Details] [PDF] [Slides]
    Tuyen N. Huynh
    October 2009. Ph.D. proposal, Department of Computer Sciences, University of Texas at Austin.
    Statistical relational learning (SRL) is an emerging area of research that addresses the problem of learning from noisy structured/relational data. Markov logic networks (MLNs), sets of weighted clauses, are a simple but powerful SRL formalism that combines the expressivity of first-order logic with the flexibility of probabilistic reasoning. Most of the existing learning algorithms for MLNs are in the generative setting: they try to learn a model that maximizes the likelihood of the training data. However, most of the learning problems in relational data are discriminative. So to utilize the power of MLNs, we need discriminative learning methods that well match these discriminative tasks.

    In this proposal, we present two new discriminative learning algorithms for MLNs. The first one is a discriminative structure and weight learner for MLNs with non-recursive clauses. We use a variant of Aleph, an off-the-shelf Inductive Logic Programming (ILP) system, to learn a large set of Horn clauses from the training data, then we apply an L1-regularization weight learner to select a small set of non-zero weight clauses that maximizes the conditional log-likelihood (CLL) of the training data. The experimental results show that our proposed algorithm outperforms existing learning methods for MLNs and traditional ILP systems in term of predictive accuracy, and its performance is comparable to state-of-the-art results on some ILP benchmarks. The second algorithm we present is a max-margin weight learner for MLNs. Instead of maximizing the CLL of the data like all existing discriminative weight learners for MLNs, the new weight learner tries to maximize the ratio between the probability of the correct label (the observable data) and and the closest incorrect label (among all the wrong labels, this one has the highest probability), which can be formulated as an optimization problem called 1-slack structural SVM. This optimization problem can be solved by an efficient algorithm based on the cutting plane method. However, this cutting plane algorithm requires an efficient inference method as a subroutine. Unfortunately, exact inference in MLNs is intractable. So we develop a new approximation inference method for MLNs based on Linear Programming relaxation. Extensive experiments in two real-world MLN applications demonstrate that the proposed max-margin weight learner generally achieves higher F1 scores than the current best discriminative weight learner for MLNs.

    For future work, our short-term goal is to develop a more efficient inference algorithm and test our max-margin weight learner on more complex problems where there are complicated relationships between the input and output variables and among the outputs. In the longer-term, our plan is to develop more efficient learning algorithms through online learning and algorithms that revise both the clauses and their weights to improve predictive performance.

    ML ID: 238
  8. Max-Margin Weight Learning for Markov Logic Networks
    [Details] [PDF] [Slides]
    Tuyen N. Huynh and Raymond J. Mooney
    In Proceedings of the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD), Part 1, 564--579, Bled, Slovenia, September 2009.
    Markov logic networks (MLNs) are an expressive representation for statistical relational learning that generalizes both first-order logic and graphical models. Existing discriminative weight learning methods for MLNs all try to learn weights that optimize the Conditional Log Likelihood (CLL) of the training examples. In this work, we present a new discriminative weight learning method for MLNs based on a max-margin framework. This results in a new model, Max-Margin Markov Logic Networks (M3LNs), that combines the expressiveness of MLNs with the predictive accuracy of structural Support Vector Machines (SVMs). To train the proposed model, we design a new approximation algorithm for loss-augmented inference in MLNs based on Linear Programming (LP). The experimental result shows that the proposed approach generally achieves higher F1 scores than the current best discriminative weight learner for MLNs.
    ML ID: 234
  9. Discriminative Structure and Parameter Learning for Markov Logic Networks
    [Details] [PDF] [Slides]
    Tuyen N. Huynh and Raymond J. Mooney
    In Proceedings of the 25th International Conference on Machine Learning (ICML), Helsinki, Finland, July 2008.
    Markov logic networks (MLNs) are an expressive representation for statistical relational learning that generalizes both first-order logic and graphical models. Existing methods for learning the logical structure of an MLN are not discriminative; however, many relational learning problems involve specific target predicates that must be inferred from given background information. We found that existing MLN methods perform very poorly on several such ILP benchmark problems, and we present improved discriminative methods for learning MLN clauses and weights that outperform existing MLN and traditional ILP methods.
    ML ID: 220
  10. Bottom-Up Learning of Markov Logic Network Structure
    [Details] [PDF]
    Lilyana Mihalkova and Raymond J. Mooney
    In Proceedings of 24th International Conference on Machine Learning (ICML-2007), Corvallis, OR, June 2007.
    Markov logic networks (MLNs) are a statistical relational model that consists of weighted first-order clauses and generalizes first-order logic and Markov networks. The current state-of-the-art algorithm for learning MLN structure follows a top-down paradigm where many potential candidate structures are systematically generated without considering the data and then evaluated using a statistical measure of their fit to the data. Even though this existing algorithm outperforms an impressive array of benchmarks, its greedy search is susceptible to local maxima or plateaus. We present a novel algorithm for learning MLN structure that follows a more bottom-up approach to address this problem. Our algorithm uses a ``propositional'' Markov network learning method to construct ``template'' networks that guide the construction of candidate clauses. Our algorithm significantly improves accuracy and learning time over the existing top-down approach in three real-world domains.
    ML ID: 202
  11. Theory Refinement for Bayesian Networks with Hidden Variables
    [Details] [PDF]
    Sowmya Ramachandran and Raymond J. Mooney
    In Proceedings of the Fifteenth International Conference on Machine Learning (ICML-98), 454--462, Madison, WI, July 1998.
    While there has been a growing interest in the problem of learning Bayesian networks from data, no technique exists for learning or revising Bayesian networks with Hidden variables (i.e. variables not represented in the data), that has been shown to be efficient, effective, and scalable through evaluation on real data. The few techniques that exist for revising such networks perform a blind search through a large spaces of revisons, and are therefore computationally expensive. This paper presents BANNER, a technique for using data to revise a given bayesian network with noisy-or and noisy-and nodes, to improve its classification accuracy. The initial network can be derived directly from a logical theory expresssed as propositional rules. BANNER can revise networks with hidden variables, and add hidden variables when necessary. Unlike previous approaches, BANNER employs mechanisms similar to logical theory refinement techniques for using the data to focus the search for effective modifications. Experiments on real-world problems in the domain of molecular biology demonstrate that BANNER can effectively revise fairly large networks to significantly improve their accuracies.
    ML ID: 87
  12. Theory Refinement of Bayesian Networks with Hidden Variables
    [Details] [PDF]
    Sowmya Ramachandran and Raymond J. Mooney
    PhD Thesis, Department of Computer Sciences, University of Texas at Austin, Austin, TX, May 1998. 139 pages. Also appears as Technical Report AI 98-265, Artificial Intelligence Lab, University of Texas at Austin.
    Research in theory refinement has shown that biasing a learner with initial, approximately correct knowledge produces more accurate results than learning from data alone. While techniques have been developed to revise logical and connectionist representations, little has been done to revise probabilistic representations. Bayesian networks are well-established as a sound formalism for representing and reasoning with probabilistic knowledge, and are widely used. There has been a growing interest in the problem of learning Bayesian networks from data. However, there is no existing technique for learning or revising Bayesian networks with hidden variables (i.e. variables not represented in the data) that has been shown to be efficient, effective, and scalable through evaluation on real data. The few techniques that exist for revising such networks perform a blind search through a large space of revisions, and are therefore computationally expensive. This dissertation presents Banner, a technique for using data to revise a giv en Bayesian network with Noisy-Or and Noisy-And nodes, to improve its classification accuracy. Additionally, the initial netwrk can be derived directly from a logical theory expressed as propositional Horn-clause rules. Banner can revise networks with hidden variables, and add hidden variables when necessary. Unlike previous approaches to this problem, Banner employs mechanisms similar to those used in logical theory refinement techniques for using the data to focus the search for effective modifications to the network. It can also be used to learn networks with hidden variables from data alone. We also introduce Banner-Pr, a technique for revising the parameters of a Bayesian network with Noisy-Or/And nodes, that directly exploits the computational efficiency afforded by these models. Experiments on several real-world learning problems in domains such as molecular biology and intelligent tutoring systems demonstrate that Banner can effectively and efficiently revise networks to significantly improve their accuracies, and thus learn highly accurate classifiers. Comparisons with the Naive Bayes algorithm show that using the theory refinement approach gives Banner a substantial edge over learning from data alone. We also show that Banner-Pr converges faster and produces more accurate classifiers than an existing algorithm for learning the parameters of a network.
    ML ID: 84
  13. Combining Symbolic and Connectionist Learning Methods to Refine Certainty-Factor Rule-Bases
    [Details] [PDF]
    J. Jeffrey Mahoney
    PhD Thesis, Department of Computer Sciences, University of Texas at Austin, May 1996. 113 pages.
    This research describes the system RAPTURE, which is designed to revise rule bases expressed in certainty-factor format. Recent studies have shown that learning is facilitated when biased with domain-specific expertise, and have also shown that many real-world domains require some form of probabilistic or uncertain reasoning in order to successfully represent target concepts. RAPTURE was designed to take advantage of both of these results.

    Beginning with a set of certainty-factor rules, along with accurately-labelled training examples, RAPTURE makes use of both symbolic and connectionist learning techniques for revising the rules, in order that they correctly classify all of the training examples. A modified version of backpropagation is used to adjust the certainty factors of the rules, ID3's information-gain heuristic is used to add new rules, and the Upstart algorithm is used to create new hidden terms in the rule base.

    Results on refining four real-world rule bases are presented that demonstrate the effectiveness of this combined approach. Two of these rule bases were designed to identify particular areas in strands of DNA, one is for identifying infectious diseases, and the fourth attempts to diagnose soybean diseases. The results of RAPTURE are compared with those of backpropagation, C4.5, KBANN, and other learning systems. RAPTURE generally produces sets of rules that are more accurate that these other systems, often creating smaller sets of rules and using less training time.

    ML ID: 61
  14. Revising Bayesian Network Parameters Using Backpropagation
    [Details] [PDF]
    Sowmya Ramachandran and Raymond J. Mooney
    In Proceedings of the International Conference on Neural Networks (ICNN-96), Special Session on Knowledge-Based Artificial Neural Networks, 82--87, Washington DC, June 1996.
    The problem of learning Bayesian networks with hidden variables is known to be a hard problem. Even the simpler task of learning just the conditional probabilities on a Bayesian network with hidden variables is hard. In this paper, we present an approach that learns the conditional probabilities on a Bayesian network with hidden variables by transforming it into a multi-layer feedforward neural network (ANN). The conditional probabilities are mapped onto weights in the ANN, which are then learned using standard backpropagation techniques. To avoid the problem of exponentially large ANNs, we focus on Bayesian networks with noisy-or and noisy-and nodes. Experiments on real world classification problems demonstrate the effectiveness of our technique.
    ML ID: 58
  15. Refinement of Bayesian Networks by Combining Connectionist and Symbolic Techniques
    [Details] [PDF]
    Sowmya Ramachandran
    , 1995. Unpublished Ph.D. Thesis Proposal.
    Bayesian networks provide a mathematically sound formalism for representing and reasoning with uncertain knowledge and are as such widely used. However, acquiring and capturing knowledge in this framework is difficult. There is a growing interest in formulating techniques for learning Bayesian networks inductively. While the problem of learning a Bayesian network, given complete data, has been explored in some depth, the problem of learning networks with unobserved causes is still open. In this proposal, we view this problem from the perspective of theory revision and present a novel approach which adapts techniques developed for revising theories in symbolic and connectionist representations. Thus, we assume that the learner is given an initial approximate network (usually obtained from a expert). Our technique inductively revises the network to fit the data better. Our proposed system has two components: one component revises the parameters of a Bayesian network of known structure, and the other component revises the structure of the network. The component for parameter revision maps the given Bayesian network into a multi-layer feedforward neural network, with the parameters mapped to weights in the neural network, and uses standard backpropagation techniques to learn the weights. The structure revision component uses qualitative analysis to suggest revisions to the network when it fails to predict the data accurately. The first component has been implemented and we will present results from experiments on real world classification problems which show our technique to be effective. We will also discuss our proposed structure revision algorithm, our plans for experiments to evaluate the system, as well as some extensions to the system.
    ML ID: 51
  16. Comparing Methods For Refining Certainty Factor Rule-Bases
    [Details] [PDF]
    J. Jeffrey Mahoney and Raymond J. Mooney
    In Proceedings of the Eleventh International Workshop on Machine Learning (ML-94), 173--180, Rutgers, NJ, July 1994.
    This paper compares two methods for refining uncertain knowledge bases using propositional certainty-factor rules. The first method, implemented in the RAPTURE system, employs neural-network training to refine the certainties of existing rules but uses a symbolic technique to add new rules. The second method, based on the one used in the KBANN system, initially adds a complete set of potential new rules with very low certainty and allows neural-network training to filter and adjust these rules. Experimental results indicate that the former method results in significantly faster training and produces much simpler refined rule bases with slightly greater accuracy.
    ML ID: 37
  17. Modifying Network Architectures For Certainty-Factor Rule-Base Revision
    [Details] [PDF]
    J. Jeffrey Mahoney and Raymond J. Mooney
    In Proceedings of the International Symposium on Integrating Knowledge and Neural Heuristics (ISIKNH-94), 75--85, Pensacola, FL, May 1994.
    This paper describes RAPTURE --- a system for revising probabilistic rule bases that converts symbolic rules into a connectionist network, which is then trained via connectionist techniques. It uses a modified version of backpropagation to refine the certainty factors of the rule base, and uses ID3's information-gain heuristic (Quinlan) to add new rules. Work is currently under way for finding improved techniques for modifying network architectures that include adding hidden units using the UPSTART algorithm (Frean). A case is made via comparison with fully connected connectionist techniques for keeping the rule base as close to the original as possible, adding new input units only as needed.
    ML ID: 33
  18. Combining Connectionist and Symbolic Learning to Refine Certainty-Factor Rule-Bases
    [Details] [PDF]
    J. Jeffrey Mahoney and Raymond J. Mooney
    Connection Science:339-364, 1993.
    This paper describes Rapture --- a system for revising probabilistic knowledge bases that combines connectionist and symbolic learning methods. Rapture uses a modified version of backpropagation to refine the certainty factors of a Mycin-style rule base and it uses ID3's information gain heuristic to add new rules. Results on refining three actual expert knowledge bases demonstrate that this combined approach generally performs better than previous methods.
    ML ID: 23
  19. Combining Symbolic and Neural Learning to Revise Probabilistic Theories
    [Details] [PDF]
    J. Jeffrey Mahoney and Raymond J. Mooney
    In Proceedings of the ML92 Workshop on Integrated Learning in Real Domains, Aberdeen, Scotland, July 1992.
    This paper describes RAPTURE --- a system for revising probabilistic theories that combines symbolic and neural-network learning methods. RAPTURE uses a modified version of backpropagation to refine the certainty factors of a Mycin-style rule-base and it uses ID3's information gain heuristic to add new rules. Results on two real-world domains demonstrate that this combined approach performs as well or better than previous methods.
    ML ID: 14