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Introduction

## Publications

Publications (105)

We suggest Darwinian Networks (DNs) as a simplification of working with Bayesian networks (BNs). DNs adapt a handful of well-known concepts in biology into a single framework that is surprisingly simple yet remarkably robust. With respect to modeling, on one hand, DNs not only represent BNs but also faithfully represent the testing of independencie...

Testing independencies is a fundamental task in reasoning with Bayesian networks (BNs). In practice, d-separation is often utilized for this task, since it has linear-time complexity. However, many have had difficulties in understanding d-separation in BNs. An equivalent method that is easier to understand, called m-separation, transforms the probl...

Simple Propagation (SP) is a new junction tree-based algorithm for probabilistic inference in discrete Bayesian networks. It is similar to Lazy Propagation, but uses a simpler approach to exploit the factorization during message computation. The message construction is based on a one-in, one-out-principle meaning a potential has at least one non-ev...

This paper considers the problem of ordering arc-reversal operations and breaking ties in cost measures when eliminating variables in Lazy AR Propagation (LPAR). In particular, the paper presents the BreakTies algorithm for breaking ties in cost measures when selecting the next arc to reverse in a variable elimination operation. BreakTies is based...

This paper discusses a method for implementing a probabilistic inference
system based on an extended relational data model. This model provides a
unified approach for a variety of applications such as dynamic programming,
solving sparse linear equations, and constraint propagation. In this framework,
the probability model is represented as a genera...

It is well-known that the notion of (strong) conditional independence (CI) is
too restrictive to capture independencies that only hold in certain contexts.
This kind of contextual independency, called context-strong independence (CSI),
can be used to facilitate the acquisition, representation, and inference of
probabilistic knowledge. In this paper...

There is mounting evidence in clinical trials that therapist-assisted Internet cognitive behavior therapy (TAICBT) is efficacious in the treatment of depression and anxiety. Nevertheless, many clinical service providers (both individuals and organizations) question whether offering this form of treatment in clinical practice is feasible. As such, h...

Historically, it has been claimed that one inference algorithm or technique, say A, is better than another, say B, based on the running times on a test set of Bayesian networks. Recent studies have instead focusing on identifying situations where A is better than B, and vice versa. We review two cases where competing inference algorithms (technique...

Support vector regression provides an alternative to the neural networks in modeling non-linear real-world patterns. Rough values, with a lower and upper bound, are needed whenever the variables under consideration cannot be represented by a single value. This paper describes two approaches for the modeling of rough values with support vector regre...

Four cost measures s
1, s
2, s
3, s
4 were recently studied for sorting the operations in Lazy propagation with arc reversal (LPAR), a join tree propagation approach
to Bayesian network inference. It has been suggested to use s
1 with LPAR, since there is an effectiveness ranking, say s
1, s
2, s
3, s
4, when applied in isolation. In this paper, we...

In this paper, we put forth the first join tree propagation algorithm that selectively applies either arc reversal (AR) or variable elimination (VE) to build the propagated messages. Our approach utilizes a recent method for identifying the propagated join tree messagesàmessages`messagesà pri-ori. When it is determined that precisely one message is...

This paper describes the relationship between support vector regression (SVR) and rough (or interval) patterns. SVR is the prediction component of the support vector techniques. Rough patterns are based on the notion of rough values, which consist of upper and lower bounds, and are used to effectively represent a range of variable values. Predictio...

Variable elimination (VE), a central component of Bayesian network inference, starts and ends with clear structure and semantics, yet all intermediate distributions, whether normalized or unnormalized, are denoted as potentials. In this paper, a condition is given stating when intermediate distributions are defined with respect to the joint distrib...

We propose the first join tree (JT) propagation architecture that labels the probability information passed between JT nodes in terms of conditional probability tables (CPTs) rather than potentials. By modeling the task of inference involving evidence, we can generate three work schedules
that are more time-efficient for LAZY propagation. Our exper...

We present a simple graphical method for understanding exact probabilistic inference in discrete Bayesian networks (BNs). A conditional probability table (conditional) is depicted as a directed acyclic graph involving one or more black vertices and zero or more white vertices. The probability information propagated in a network can then be graphica...

Current join tree propagation algorithms treat all propagated messages as being of equal importance. On the contrary, it is often the case in real-world Bayesian networks that only some of the messages propagated from one join tree node to another are relevant to subsequent message construction at the receiving node. In this article, we propose the...

We present a comparative study of two approaches to Bayesian network inference, called variable elimination VE and arc reversal AR. It is established that VE never requires more space than AR, and never requires more computation multiplications and additions than AR. These two characteristics are supported by experimental results on six large BNs,...

We compare two approaches to Bayesian network in- ference, called variable elimination (VE) and arc rever- sal (AR). It is established that VE never requires more space than AR, and never requires more computation (multiplications and additions) than AR.

In this paper, we put forth the first join tree propagation algorithm that selectively applies either arc reversal (AR) or variable elimination (VE) to build the propagated messages. Our approach utilizes a recent method for identifying the propagated join tree messages à priori. When it is determined that a join tree node will construct a single d...

The rapid development of the World Wide Web offers an opportunity to apply a large variety of artificial intelligence technologies
in various practical applications. In this chapter, we provide a review of our recent work on developing a Web-based intelligent
tutoring system for computer programming. The decision making process conducted in our int...

Bayesian networks have been applied for several uncertainty management problems in the artificial intelligence and Web intelligence communities. However, one may require the use of Bayesian networks, yet lack the background knowledge to build them. Moreover, it is widely acknowledged in the Bayesian network community that understanding Bayesian net...

The maximal prime decomposition (MPD) of a Bayesian network is a hierarchical structure, which repre-sents conditional independency information. The MPD rep-resentation has shown to facilitate probabilistic inference in uncertainty management. One method for building the MPD involves applying the moralization and triangulation procedures to the giv...

— Rough support vector machines (RSVMs) supplement conventional support vector machines (SVMs) by providing a better representation of the boundary region. Increasing interest has been paid to the theoretical development of RSVMs, which has already lead to a modification of existing SVM implementations as RSVMs. This paper shows how to extend the u...

Support vector machines (SVMs) are essentially binary classifiers. To improve their applicability, several methods have been suggested for extending SVMs for multi-classification, including one-versus-one (1-v-1), one-versus-rest (1-v-r) and DAGSVM. In this paper, we first describe how binary classification with SVMs can be interpreted using rough...

Bayesian networks serve as the basis for developing probabilistic expert systems and have been applied widely in artificial intelligence. In this paper, we examine various algorithms for Bayesian network inference. After comparing and contrasting some of these techniques, possible directions of future research are given.

Complexity of rules created by support vector machine (SVM) based multiclassifiers is an important issue in adopting these classifiers. Recently, we have shown how traditional SVMs can be represented using interval or rough sets. We have also extended the rough SVMs to multiclassification using both the 1-v-r and 1-v-1 approaches. In this paper, we...

We propose LAZY arc-reversal with variable elimination (LAZY-ARVE) as a new approach to probabilistic inference in Bayesian networks (BNs). LAZY-ARVE is an improvement upon LAZY arc- reversal (LAZY-AR), which was very recently proposed and empirically shown to be the state-of-the-art method for exact inference in discrete BNs. The primary advantage...

In this paper, we present a Web-based intelligent tutor-ing system, called BITS. The decision making process con-ducted in our intelligent system is guided by a Bayesian network approach to support students in learning computer programming. Our system takes full advantage of Bayesian networks, which are a formal framework for uncertainty management...

Pawlak recently introduced rough set flow graphs (RSFGs) as a graphical framework for reasoning from data. No study, however, has yet investigated the complexity of the accompanying inference algorithm, nor the complexity of inference in RSFGs. In this paper, we show that the traditional RSFG inference algorithm has exponential time complexity. We...

Multiagent Bayesian networks (MABNs) are a powerful new framework for uncertainty management in a distributed environment. In a MABN, a collective joint probability distribution is defined by the conditional probability tables (CPTs) supplied by the individual agents. It is assumed, however, that CPTs supplied by individual agents agree on the vari...

Pawlak recently introduced rough set flow graphs (RSFGs) as a graphical framework for reasoning from data. Each rule is associated with three coefficients, which have been shown to satisfy Bayes’ theorem. Thereby, RSFGs provide a new perspective on Bayesian inference methodology.
In this paper, we show that inference in RSFGs takes polynomial time...

The methods for extending binary support vectors machines (SVMs) can be broadly divided into two categories, namely, 1-v-r (one versus rest) and 1-v-1 (one versus one). The 1-v-r approach tends to have higher training time, while 1-v-1 approaches tend to create a large number of binary classifiers that need to be analyzed and stored during the oper...

In this paper, we revisit the consensus of computational com- plexity on exact inference in Bayesian networks. We point out that even in singly connected Bayesian networks, which conventionally are believed to have e-cient inference algorithms, the computational complexity is still NP-hard.

Support vector machines (SVMs) are designed for linearly separating binary classes. Researchers have suggested various approaches, such as the one-versus-rest (1-v-r), one-versus-one (1-v-1) and DAGSVM, for applying SVMs to multi-classification problems. The 1-v-r approach tends to have a large training time, while the 1-v-1 and DAGSVM approaches o...

In this paper, we propose that the select operator in relational data- bases be adopted for incorporating evidence in Bayesian networks. This ap- proach does not involve the construction of new evidence potentials, nor the as- sociated computational costs of multiplying the evidence potentials into the knowledge base. The select operator also provi...

Indexes are crucial for the efficient implementation of probabilistic expert systems. However, the indexes previously proposed, and the methods for applying them, are somewhat elementary. Moreover, recent experiments involving large Bayesian networks have resulted in the computer running out of memory. This further emphasizes the importance of inde...

Bayesian networks serve as the basis for developing proba- bilistic expert systems and have been applied widely in artificial intel- ligence. Previous research has argued that Bayesian networks and re- lational databases are different by showing that the logical implication of conditional independence (CI) and embedded multivalued dependency (EMVD)...

Many algorithms have been proposed for learning a causal network from data. It has been shown, however, that learning all
the conditional independencies in a probability distribution is a NP-hard problem. In this chapter, we present an alternative
method for learning a causal network from data. Our approach is novel in that it learns functional dep...

As the amount of available data continues to increase, more and more effective means for discovering important patterns and relationships within that data are required. Although the power of automated tools continues to increase, we contend that greater gains can be achieved by coordinating results from a variety of tools and by enhancing the user'...

Jointree computation continues to be central to the theory and practice of probabilistic expert systems. Recent research has incorporated granular structures to facilitate propagation in the jointree. In this paper, we propose a method for granular jointree probability propagation. Our method extends the previous works by allowing the granular leve...

Previous work seemed to suggest that the logical implication of non-numeric constraints in database systems exactly coincides with that of numeric constraints in probabilistic expert systems, provided that restrictions are imposed on the given set of constraints. In this paper, we dispel this suggestion by showing that the logical implication diffe...

Support vector machines and rough set theory are two classification techniques. Support vector machines can use continuous input variables and transform them to higher dimensions, so that classes can be linear separable. A support vector machine attempts to find the hyperplane that maximizes the margin between classes. This paper shows how the clas...

In this paper, we suggest a novel approach to jointree computation. Unlike all previous jointree methods, we propose that
jointree computation should use conditional probability distributions rather than potentials. One salient feature of this
approach is that the exact form of the messages to be transmitted throughout the network can be identified...

Most approaches to mining association rules implicitly con- sider the utilities of the itemsets to be equal. We assume that the utilities of itemsets may differ, and identify the high utility itemsets based on information in the transac- tion database and external information about utilities. Our theoretical analysis of the resulting problem lays t...

The WIC Canada Research Centre, is one of the cen-tres under the Web Intelligence Consortium,. Dr. Yiyu Yao, serves as the Director and Dr. JingTao Yao, serves as the Co-ordinator of WIC Canada. Currently, there two affili-ated centres, the WIC Regina Center, under the director-ship of Dr. Cory Butz, and the WIC Halifax Centre, under the co-directo...

Web Intelligence is a direction for scientific research that explores practical applications of Artificial Intelligence to the next generation of Web-empowered systems. In this paper, we present a Web-based intelligent tutoring system for computer programming. The decision making process conducted in our intelligent system is guided by Bayesian net...

Hierarchical Markov networks (HMNs) were recently proposed as a faithful representation of Bayesian networks. We propose a query processing algorithm for HMNs. This method takes one query processing algorithm for a traditional Markov network and extends it to a hierarchy of Markov networks. Experimental results explicitly demonstrate the effectiven...

In this paper, we present a hypergraph-based inference method for conditional independence. Our method allows us to obtain several interesting results on graph combination. In particular, our hypergraph approach allows us to strengthen one result obtained in a conventional graph-based approach. We also introduce a new inference axiom, called combin...

Multiply sectioned Bayesian networks (MSBNs) were originally proposed as a modular representation of uncertain knowledge by sectioning a large Bayesian network (BN) into smaller units. More recently, hierarchical Markov networks (HMNs) were developed in part as an hierarchical representation of the flat BN.

Multiply sectioned Bayesian networks (MSBNs) were originally proposed as a modular representation of uncertain knowledge by sectioning a large Bayesian network (BN) into smaller units. More recently, hierarchical Markov networks (HMNs) were developed in part as an hierarchical representation of the flat BN.
In this paper, we compare the MSBN and H...

In this paper, we present a general method for coarsening a set of variables in a probabilistic network. The work here is an extension of our earlier works, which always placed restrictions on the sets to be coarsened. The soundness of our method is also shown.

We present a critical analysis of the maximal prime decomposition of Bayesian networks (BNs). Our analysis suggests that it may be more useful to transform a BN into a hierarchical Markov network.

In our earlier works, we coined the phrase granular probabilistic reasoning and showed a local coarsening result. In this paper, we present a non-local method for coarsening variables (i.e., the variables are spread throughout the network) and establish its correctness.

Probabilistic reasoning in Bayesian networks is normally conducted on a junction tree by repeatedly applying the local propagation whenever new evidence is observed. In this paper, we suggest to treat probabilistic reasoning as database queries. We adapt a method for answering queries in database theory to the setting of probabilistic reasoning in...

In this paper, we present a hypergraph-based inference method for conditional independence. Our method allows us to obtain
several interesting results on graph combination. In particular, our hypergraph approach allows us to strengthen one result
obtained in a conventional graph-based approach. We also introduce a new inference axiom, called combin...

In our earlier works, we coined the phrase granular proba- bilistic reasoning and showed a local coarsening result. In this paper, we present a non-local method for coarsening variables (i.e., the variables are spread throughout the network) and establish its correctness.

We present a critical analysis of the maximal prime decom- position of Bayesian networks (BNs). Our analysis suggests that it may be more useful to transform a BN into a hierarchical Markov network.

Context-specific independence is useful as it can lead to improved inference in Bayesian networks. In this paper, we present a method for detecting this kind of independence from data and emphasize why such an algorithm is needed.

Although contextual weak independence (CWI) has shown promise in leading to more e#cient probabilistic inference, no investigation has examined how CWIs can be obtained. In this paper, we suggest and analyze two methods for obtaining this kind of independence.

In this paper, we study the problem of triangulation of Bayesian networks from a relational database perspective. We show that the problem of triangulating a Bayesian network is equivalent to the problem of identifying a maximal subset of conflict free conditional independencies.

Object-oriented Bayesian networks (OOBNs) facilitate the design of large Bayesian networks by allowing Bayesian networks to be nested inside of one another. Weak conditional independence has been shown to be a necessary and su#cient condition for ensuring consistency in OOBNs. Since weak conditional independence plays such an important role in OOBN...

Although contextual weak independence (CWI) has shown promise in leading to more efficient probabilistic inference, no investiga- tion has examined how CWIs can be obtained. In this paper, we suggest and analyze two methods for obtaining this kind of independence.

Object-oriented Bayesian networks (OOBNs) facilitate the design of large Bayesian networks by allowing Bayesian networks to be nested inside of one another. Weak conditional independence has been shown to be a necessary and sufficient condition for ensuring consistency in OOBNs. Since weak conditional independence plays such an impor- tant role in...

Context-specific independence is useful as it can lead to improved inference in Bayesian networks. In this paper, we present a method for detecting this kind of independence from data and empha- size why such an algorithm is needed.

In this paper, we study the problem of triangulation of Bayesian networks from a relational database perspective. We show that the prob- lem of triangulating a Bayesian network is equivalent to the problem of identifying a maximal subset of conflict free conditional independencies. Several interesting theoretical results regarding triangulating Bay...

Probabilistic reasoning has become an accepted formulism for managing uncertainty in Artificial Intelligence. The usual input to a probabilistic model is a Bayesian network containing both embedded and nonembedded conditional independence information. A Bayesian network comprises a qualitative and a quantitative component, namely a directed acyclic...

It has been suggested that Bayesian networks and relational databases are different because the implication problems for probabilistic conditional independence and embedded multivalued dependency do not always coincide. The present study indicates that the implication problems coincide on solvable classes of dependencies and differ on unsolvable cl...

Empirical studies clearly demonstrate the effectiveness of the nested jointree (NJT) representation in probabilistic inference. A NJT is a traditional Markov network (MN) together with a possible local MN nested in each clique. These nested MNs can themselves contain other nested MNs in a recursive manner. However, the NJT representation is not nec...

This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model.

Numerous probability models have been suggested for information retrieval (IR) over the years. These models have been applied to try to manage the inherent uncertainty in IR, for instance, document and query representation, relevance feedback, and evaluating the effectiveness of IR system. On the other hand, Bayesian networks have become an establi...

Several researchers have suggested that Bayesian networks be used in web search and user profiling. One advantage of this approach is that Bayesian networks are more general than the probabilistic models previously used in information retrieval. In practice, experimental results demonstrate the e#ectiveness the modern Bayesian network approach. On...

In this paper, we suggest the use of probabilistic networks in inductive learning as a plausible alternative to deriving explicit decision rules. Whereas a decision rule can only be applied if its antecedent is given, a probabilistic request can be issued involving any set of attributes and attribute values in the sample observations. We will also...

The implication problem is to test whether a given set of independencies logically implies another independency. This problem is crucial in the design of a probabilistic reasoning system. We advocate that Bayesian networks are a generalization of standard relational databases. On the contrary, it has been suggested that Bayesian networks are differ...

Previous experimental results have clearly demonstrated the effectiveness of utilizing context-specific independence (CSI) in proba- bilistic inference. However, CSI is a special case of a more general inde- pendence called contextual weak independence (CWI). In this paper, we show how CWI can be utilized for more efficient probabilistic i nference...

Previous experimental results have clearly demonstrated the e#ectiveness of utilizing context-specific independence (CSI) in probabilistic inference. However, CSI is a special case of a more general independence called contextual weak independence (CWI). In this paper, we show how CWI can be utilized for more e#cient probabilistic inference.

Several researchers have suggested that Bayesian networks be used
in web search and user profiling. One advantage of this approach is that
Bayesian networks are more general than the probabilistic models
previously used in information retrieval. In practice, experimental
results demonstrate the effectiveness the modern Bayesian network
approach. On...

The discovery of FDs from databases has recently become a significant research problem. In this paper, we propose a new algorithm, called FD-Mine. FD-Mine takes advantage of the rich theory of FDs to reduce both the size of the dataset and the number of FDs to be checked by using discovered equivalences. We show that the pruning does not lead to lo...

Designing a large Bayesian network (BN) has been regarded as a difficult process.It has been suggested that BN librariescan be used to facilitate the construction of alarge BN. That is, a large BN can be definedin terms of smaller BNs stored in a library. Inthis paper, we point out that it may be possibleto combine the conditional independenciesdef...

This volume contains the papers selected for presentation at the Third International Conference on Rough Sets and Current Trends in Computing (RSCTC 2002) held at Penn State Great Valley, Malvern, Pennsylvania, U.S.A., 14-16 October 2002.

Based on the elegant theory of relational databases, the present investigation establishes a unified model for both relational databases and Bayesian networks. This is in contradiction to the argument that relational databases and Bayesian networks are different, where it was shown that the implication problem does not coincide for embedded multiva...

A probabilistic network consists of a dependency structure and
corresponding probability tables. The dependency structure is a
graphical representation of the conditional independencies that are
known to hold in the problem domain. We propose an automated process for
constructing the combined dependency structure of a multiagent
probabilistic netwo...

Numerous probabilitymodelshave been suggested for information retrieval (IR) over the years. These models have been applied to try to manage the inherent uncertaintyin IR, for instance, document and query representation, relevance feedback, and evaluating the effectiveness of IR system. On the other hand, Bayesian networks have become an establishe...

Several researchers have suggested that Bayesian networks (BNs) should be used to manage the inherent uncertainty in information retrieval. However, it has been argued that manually constructing a large BN is a difficult process. In this paper, we obtain the only minimal complete subset of the semi-graphoid axiomatization governing the independency...

Several researchers have suggestedthat Bayesian networks (BNs) shouldb e usedto manage the inherent uncertainty in information retrieval. However, it has been arguedthat manually
constructing a large BN is a difficult process. In this paper, we obtain the only minimal complete subset of the semi-graphoidaxiomatization governing the independency inf...

The implication problem is to test whether a given set of
independencies logically implies another independency. This problem is
crucial in the design of a probabilistic reasoning system. We advocate
that Bayesian networks are a generalization of standard relational
databases. On the contrary, it has been suggested that Bayesian networks
are differ...

Rough sets have traditionally been applied to decision (classification) problems. We suggest that rough sets are even better suited for reasoning. It has already been shown that rough sets can be applied for reasoning about knowledge. In this preliminary paper, we show how rough sets provide a convenient framework for uncertainty reasoning. This di...

An attribute is deemed important in data mining if it partitions the database such that previously unknown regularities are observable. Many information-theoretic measures have been applied to quantify the importance of an attribute. In this paper, we summarize and critically analyze these measures. 1

In our earlier paper, we introduced the notion of granular probabilistic networks. We use the term granular to mean the ability to coarsen and refine parts of a joint probability distribution. In practice, however, the joint distribution is usually represented as a product of marginal distributions. In this paper, we show that the coarsening operat...

There is current interest in generalizing Bayesian networks by using dependencies which are more general than probabilistic con- ditional independence (CI). Contextual dependencies, such as context- specific independence (CSI), are used to decompose a subset of the joint distribution. We have introduced a more general contextual dependency than CSI...

Based on the elegant theory of relational databases, the present investigation establishes a unified model for both relational databases and Bayesian networks. This is in contradiction to the argument that relational databases and Bayesian networks are different, where it was shown that the implication problem does not coincide for embedded multiva...

Introduces a probabilistic relational data model as the basis for
developing multi-agent probabilistic reasoning systems. Since our model
subsumes the traditional relational data model, it immediately follows
that we can take full advantage of the existing distributed and
concurrency control techniques to address the undesirable
characteristics exh...

An attribute is deemed important in data mining if it parti- tions the database such that previously unknown regularities are observ- able. Many information-theoretic measures have been applied to quantify the importance of an attribute. In this paper, we summarize and criti- cally analyze these measures. Watanabe (21) suggested that pattern recogn...

Data dependencies have been extensively studied in relational
databases as they play a key role in the normalization process. On the
other hand, probabilistic reasoning systems would not be practical
without the notion of probabilistic conditional independence. In this
paper, we present a detailed comparison of these two types of
(in)dependencies....

In this paper, a model is proposed for multi-agent probabilistic
reasoning in a distributed environment. Unlike other methods, this model
is capable of processing input in a truly asynchronous fashion.
Asynchronous control protocols and a method for processing evidence are
developed to ensure global consistency at all times. The proposed system
the...

Data dependencies are used in database schema design to enforce the correctness of a database as well as to reduce redundant data. These dependencies are usually determined from the semantics of the attributes and are then enforced upon the relations. This paper describes a bottom-up procedure for discovering multivalued dependencies (MVDs) in obse...