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Learning probabilistic models of link structure

Learning probabilistic models of link structure
Learning probabilistic models of link structure

Learning Probabilistic Models of Link Structure

Lise Getoor GETOOR@https://www.wendangku.net/doc/918971742.html, Computer Science Dept.

University of Maryland

College Park,MD20742

Nir Friedman NIR@CS.HUJI.AC.IL School of Computer Sci.&Eng.

Hebrew University

Jerusalem,91904,Israel

Daphne Koller KOLLER@https://www.wendangku.net/doc/918971742.html, Computer Science Dept.

Stanford University

Stanford,CA94305

Ben Taskar BTASKAR@https://www.wendangku.net/doc/918971742.html, Computer Science Dept.

Stanford University

Stanford,CA94305

Abstract

Most real-world data is heterogeneous and richly interconnected.Examples include the Web,hypertext, bibliometric data and social networks.In contrast,most statistical learning methods work with“?at”data representations,forcing us to convert our data into a form that loses much of the link structure.The re-cently introduced framework of probabilistic relational models(PRMs)embraces the object-relational nature of structured data by capturing probabilistic interactions between attributes of related entities.In this paper, we extend this framework by modeling interactions between the attributes and the link structure itself.An advantage of our approach is a uni?ed generative model for both content and relational structure.We propose two mechanisms for representing a probabilistic distribution over link structures:reference uncertainty and existence uncertainty.We describe the appropriate conditions for using each model and present learning algo-rithms for each.We present experimental results showing that the learned models can be used to predict link structure and,moreover,the observed link structure can be used to provide better predictions for the attributes in the model.

1.Introduction

In recent years,we have witnessed an explosion in the amount of information that is available to us in digital form.More and more data is being stored,and more and more data is being made accessible,through traditional interfaces such as corporate databases and,of course,via the Internet and the World Wide Web.There is much to be gained by applying machine learning techniques to these data,in order to extract useful information and patterns.

Most often,the objects in these data do not exist in isolation—there are“links”or relationships that hold between them.For example,there are links from one web page to another,a scienti?c

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paper cites another paper,and an actor is linked to a movie by the appearance relationship.Most work in machine learning,however,has focused on“?at”data,where the instances are independent and identically distributed.The main exception to this rule has been the work on inductive logic programming(Muggleton,1992,Lavra?c and D?z eroski,1994).This work focuses on the problem of inferring link structure from a logical perspective.

More recently,there has been a growing interest in combining the statistical approaches that have been so successful when learning from a collection of homogeneous independent instances(typi-cally represented as a single table in a relational database)with relational learning methods.Slattery and Craven(1998)were the?rst to consider combining a statical approach with a?rst-order rela-tional learner(FOIL)for the task of web page classi?cation.Chakrabarti et al.(1998)explored methods for hypertext classi?cations which used both the content of the current page and informa-tion from related pages.Popescul et al.(2002)use an approach that uses a relational learner to guide in the construction of features to be used by a(statistical)propositional learner.Yang et al.(2002) identify certain categories of relational regularities and explore the conditions under which they can be exploited to improve classi?cation accuracy.

Here,we propose a uni?ed statistical framework for content and links.Our frameworks builds on the recent work on probabilistic relational models(PRMs)(Poole,1993,Ngo and Haddawy,1995, Koller and Pfeffer,1998).PRMs extend the standard attribute-based Bayesian network representa-tion to incorporate a much richer relational structure.These models allow properties of an entity to depend probabilistically on properties of other related entities.The model represents a generic de-pendence for a class of objects,which is then instantiated for particular sets of entities and relations between them.Friedman et al.(1999)adapt the machinery for learning Bayesian networks from a set of unrelated homogeneous instances to the task of learning PRMs from structured relational data.

The original PRM framework focused on modeling the distribution over the attributes of the ob-jects in the model.It took the relational structure itself—the relational links between entities—to be background knowledge,determined outside the probabilistic model.This assumption implies that the model cannot be used to predict the relational structure itself.A more subtle yet very im-portant point is that the relational structure is informative in and of itself.For example,the links from and to a web page are very informative about the type of web page(Craven et al.,1998),and the citation links between papers are very informative about the paper topics(Cohn and Hofmann, 2001).

The PRM framework can be naturally extended to address this limitation.By making links?rst-class citizens in the model,the PRM language easily allows us to place a probabilistic model directly over them.In other words,we can extend our framework to de?ne probability distributions over the presence of relational links between objects in our model.The concept of a probabilistic model over relational structure was introduced by Koller and Pfeffer(1998)under the name structural uncertainty.They de?ned several variants of structural uncertainty,and presented algorithms for doing probabilistic inference in models involving structural uncertainty.

In this paper,we show how a probabilistic model of relational structure can be learned directly from data.Speci?cally,we provide two simple probabilistic models of link structure:The?rst is an extension of the reference uncertainty model of Koller and Pfeffer(1998),which makes it suitable for a learning framework;the second is a new type of structural uncertainty,called existence uncertainty.We present a clear semantics for these extensions,and propose a method for learning

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such models from a relational database.We present empirical results on real-world data,showing that these models can be used to predict the link structure,as well as use the presence of(observed) links in the model to provide better predictions about attribute values.Interestingly,these bene?ts are obtained even with the very simple models of link structure that we use in this paper.Thus,even simplistic models of link uncertainty provide us with increased predictive accuracy.

2.Probabilistic Relational Models

A probabilistic relational model(PRM)speci?es a template for a probability distribution over a database.The template describes the relational schema for the domain,and the probabilistic depen-dencies between attributes in the domain.A PRM,together with a particular database of objects and relations,de?nes a probability distribution over the attributes of the objects and the relations.

2.1Relational Schema

A schema for a relational model describes a set of classes,.Each class is associated with a set of descriptive attributes and a set of reference slots.1The set of descriptive attributes of a class is denoted.Attribute of class is denoted,and its domain of values is denoted.For example,the class might have the descriptive attributes Gender,with domain male,female.For simplicity,we assume in this paper that attribute domains are?nite;this is not a fundamental limitation of our approach.

The set of reference slots of a class is denoted.We use to denote the reference slot of.Each reference slot is typed:the domain type of and the range type ,where is some class in.A slot denotes a function from to

.For example,we might have a class with the reference slots Actor,whose range is the class,and Movie,whose range is the class.We note that the functional nature of slots does not prevent us from having many-to-many relations between classes.We simply use a standard transformation where we introduce a class corresponding to the relationship object. This class will have an object for every pair(or tuple)of related objects,with functional reference slots to the objects it relates.The Role class above is an example of this transformation.

It is useful to distinguish between an entity and a relationship,as in entity-relationship diagrams. In our language,classes are used to represent both entities and relationships.Thus,a relationship such as Role,which relates actors to movies,is also represented as a class,with reference slots to the class Actor and the class Movie.We use to denote the set of classes that represent entities, and to denote those that represent relationships.We use the generic term object to refer both to entities and to relationships.

The semantics of this language is straightforward.An complete instantiation speci?es the set of objects in each class,and the values for each attribute and each reference slot of each object. Thus,a complete instantiation is a set of objects with no missing values and no dangling refer-ences.It describes the set of objects,the relationships that hold between the objects and all the values of the attributes of the objects.For example,Figure1shows an instantiation of our simple movie schema.It speci?es a particular set of actors,movies and roles,along with values for each of their attributes and references.

1.There is a direct mapping between our notion of class and the tables in a relational database:descriptive attributes

correspond to standard table attributes,and reference slots correspond to foreign keys(key attributes of another table).

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ACTOR

name gender fred male ginger female bing male

MOVIE name genre m1drama m2comedy

ROLE

role movie actor role-type

r1m1fred hero

r2m1ginger heroine

r3m1bing villain

r4m2bing hero

r5m2ginger love-interest

Figure1:An instantiation of the relational schema for a simple movie domain.

As discussed in the introduction,our goal in this paper is to construct probabilistic models over instantiations.To do so,we need to provide enough background knowledge to circumscribe the set of possible instantiations.Friedman et al.(1999)assume that the entire relational structure is given as background knowledge.More precisely,they assume that they are given a relational skeleton, ,which speci?es the set of objects in all classes,as well as all the relationships that hold between them;in other words,it speci?es the values for all of the reference slots.In our simple movie example,the relational skeleton would contain all of the information except for the gender of the actors,the genre of the movies,and the nature of the role.

2.2Probabilistic Model for Attributes

A probabilistic relational model speci?es a probability distribution over a set of instantiations of the relational schema.More precisely,given a relational skeleton,it speci?es a distribution over all complete instantiations that extend the skeleton.

A PRM consists of a qualitative dependency structure,,and the parameters associated with it, .The dependency structure is de?ned by associating with each attribute a set of formal parents Pa.These correspond to formal parents;they will be instantiated in different ways for different objects in.Intuitively,the parents are attributes that are“direct in?uences”on. The attribute can depend on another probabilistic attribute of.It can also depend on attributes of related objects.2

The quantitative part of the PRM speci?es the parameterization of the model.Given a set of parents for an attribute,we can de?ne a local probability model by associating with it a conditional probability distribution(CPD).For each attribute we have a CPD that speci?es Pa. Each CPD in our PRM is legal,i.e.,the entries are positive and sum to1.

De?nition1A probabilistic relational model(PRM)for a relational schema de?nes for each class and each descriptive attribute,a set of formal parents Pa,and a conditional probability distribution(CPD)that represents Pa.

2.PRMs allow a much richer dependency model,where objects can depend on each other via longer slot chains.They

also allow dependencies via inverse slots,which generally de?ne one-to-many relations(e.g.,the set of all roles of an actor).There is no dif?culty adding these features to our language,but they complicate the presentation considerably;

we have therefore chosen to omit them for simplicity.

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Given a relational skeleton,a PRM speci?es a distribution over a set of instantiations

consistent with.This speci?cation is done by mapping the dependencies in the class-level PRM

to the actual objects in the domain.For a class,we use to denote the objects,as speci?ed by the relational skeleton.(In general we will use the notation to refer to the

set objects of each class as de?ned by any type of domain skeleton.)Let be an attribute in

the schema,and let be some object in.Recall that the PRM allows two types of formal parents:and.For a formal parent of the form,the corresponding actual parent of is.For a formal parent of the form,the corresponding formal parent of is, where in.Thus,the class-level dependencies in the PRM are instantiated according to the relational skeleton,to de?ne object-level dependencies.The parameters speci?ed by the PRM are used for each object in the skeleton,in the obvious way.

Thus,for a given skeleton,the PRM basically de?nes a ground Bayesian network.The qualitative

structure of the network is de?ned via an instance dependency graph,whose nodes correspond

to descriptive attributes of entities in the skeleton.These are the random variables in our model.

We have a directed edge from to if is an actual parent of,as de?ned above.The

quantitative parameters of the network are de?ned by the CPDs in the PRM,with the same CPD

used multiple times in the network.This ground Bayesian network leads to the following chain rule

which de?nes a distribution over the instantiations compatible with our particular skeleton:

Pa(1)

For this de?nition to specify a coherent probability distribution over instantiations,we must ensure that our probabilistic dependencies are acyclic.In particular,we must verify that each random variable does not depend,directly or indirectly,on its own value.In other words,must be acyclic.We say that a dependency structure is acyclic relative to a relational skeleton if the directed graph is acyclic.

Theorem2(Friedman et al.,1999)Let be a PRM with an acyclic instance dependency graph, and let be a relational skeleton.Then,Eq.(1)de?nes a coherent distributions over instances that extend.

The de?nition of the instance dependency graph is speci?c to the particular skeleton at hand:the existence of an edge from to depends on whether,which in turn depends on the interpretation of the reference slots.Thus,it allows us to determine the coherence of a PRM only relative to a particular relational skeleton.When we are evaluating different possible PRMs as part of our learning algorithm,we want to ensure that the dependency structure we choose results in coherent probability models for any skeleton.

For this purpose,we use a class dependency graph,which describes all possible dependencies among attributes.In this graph,we have an(intra-object)edge if is a parent of .If is a parent of,and,we have an(inter-object)edge.

Theorem3(Friedman et al.,1999)If the class dependency graph of a PRM is acyclic,then the instance dependency graph for any relational skeleton is also acyclic.Hence,de?nes a legal model for any relational skeleton.

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Figure2:Reference uncertainty in a simple citation domain.

In the model described here,all relations between attributes are determined by the relational skele-ton;only the descriptive attributes are uncertain.Thus,Eq.(1)determines the probabilistic model of the attributes of objects,but does not provide a model for the relations between objects.In the subsequent sections,we extend our framework to deal with link uncertainty,by extending our prob-abilistic model to include a distribution over the relational structure itself.

3.Reference Uncertainty

In the previous section,we assumed that the relational structure was not a part of our probabilistic model,that it was given as background knowledge in the relational skeleton.But by incorporating the links into the probabilistic model,we can both predict links and more importantly use the links to help us make predictions about other attributes in the model.

Consider a simple citation domain illustrated in Figure2.Here we have a document collection. Each document has a bibliography that references some of the other documents in the collection. We may know the number of citations made by each document(i.e.,it is outside the probabilistic model).By observing the citations that are made,we can use the links to reach conclusions about other attributes in the model.For example,by observing the number of citations to papers of various topics,we may be able to infer something about the topic of the citing paper.

Figure3(a)shows a simple schema for this domain.We have two classes,Paper and Cites.The Paper class has information about the topic of the paper and the words contained in the paper. For now,we simply have an attribute for each word that is true if the word occurs in the page and false otherwise.The Cites class represents the citation of one paper,the Cited paper,by another paper,the Citing paper.(In the?gure,for readability,we show the Paper class twice.)In this model,we assume that the set of objects is pre-speci?ed,but relations among them,i.e.,reference slots,are subject to probabilistic choices.Thus,rather than being given a full relational skeleton, we assume that we are given an object skeleton.The object skeleton speci?es only the objects in each class,but not the values of the reference slots.In our example,the object skeleton speci?es the objects in class Paper and the objects in class Cites,but the reference slots of the Cites relation,Cites.Cited and Cites.Citing are unspeci?ed.In other words,the probabilistic model does not provide a model of the total number of citation links,but only a distribution over their“endpoints”.Figure3shows an object skeleton for the citation domain.

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(a)(b)

Figure3:(a)A relational schema for the citation domain.(b)An object skeleton for the citation domain.

3.1Probabilistic model

In the case of reference uncertainty,we must specify a probabilistic model for the value of the reference slots.The domain of a reference slot is the set of keys(unique identi?ers)of the objects in the class to which refers.Thus,we need to specify a probability distribution over the set of all objects in.For example for Cited,we must specify a distribution over the objects in class Paper.

A naive approach is to simply have the PRM specify a probability distribution directly over the objects in.For example for Cited,we would have to specify a distribution over the primary keys of Paper.This approach has two major?aws.Most obviously,this distribution would require a parameter for each object in,leading to a very large number of parameters.This is a problem both from a computational perspective—the model becomes very large,and from a statistical perspective—we often would not have enough data to make robust estimates for the parameters.More importantly,we want our dependency model to be general enough to apply over all possible object skeletons;a distribution de?ned in terms of the objects within a speci?c object skeleton would not apply to others.

In order to achieve a general and compact representation,we use the attributes of to de?ne the probability distribution.In this model,we partition the class into subsets labeled ac-cording to the values of some of its attributes,and specify a probability for choosing each partition, i.e.,a distribution over the partitions.We then select an object within that partition uniformly.

For example,consider a description of movie theater showings as in Figure4(a).For the foreign key Shows.Movie,we can partition the class Movie by Genre,indicating that a movie theater?rst selects the genre of movie it wants to show,and then selects uniformly among the movies with the selected genre.For example,a movie theater may be much more likely to show a movie which is a thriller in comparison to a foreign movie.Having selected,for example,to show a thriller,the theater then selects the actual movie to show uniformly from within the set of thrillers.In addition, just as in the case of descriptive attributes,the partition choice can depend on other attributes in our model.Thus,the selector attribute can have parents.As illustrated in the?gure,the choice of movie genre might depend on the type of theater.Consider another example,in our citation domain. As shown in Figure4(b),we can partition the class Paper by Topic,indicating that the topic of a

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(a)(b)

Figure 4:(a)An example of reference uncertainty for a movie theater’s showings.(b)A simple

example of reference uncertainty in the citation domain

citing paper determines the topics of the papers it cites;and then the cited paper is chosen uniformly among the papers with the selected topic.

We make this intuition precise by de?ning,for each slot ,a partition function .We place several restrictions on the partition function which are captured in the following de?nition:

De?nition 4Let

be a reference slot with domain .Let be a function where

is a ?nite set of labels.We say that is a partition function for if there is a subset of the attributes of ,

,such that for any and any ,if the values of the attributes

of and are the same,i.e.,for each ,,then .We refer to as the partition attributes for .

Thus,the values of the partition attributes are all that is required to determine the partition to which an object belongs.

In our ?rst example,Movie Foreign Thriller and the partition attribute is Movie Genre .In the second example,Cited AI Theory and the partition attribute is

Cited Topic .There are a number of natural methods for specifying the partition function.It can be de?ned simply by having one partition for each possible combination of values of the partition attributes,i.e.,one partition for each value in the cross product of the partition attribute values.Our examples above take this approach.In both cases,there is only a single partition attribute,so specifying the partition function in this manner is not too unwieldy,but for larger collections of partition attributes or for partition attributes with large domains,this method for de?ning the partitioning function may be problematic.A more ?exible and scalable approach is to de?ne the partition function using a decision tree built over the partition attributes.In this case,there is one partition for each of the leaves in the decision tree.

Each possible value determines a subset of from which the value of (the referent)will be

selected.For a particular instantiation of the database,we use

to represent the set of objects in

that fall into the partition .8

We now represent a probabilistic model over the values of by specifying a distribution over

possible partitions,which encodes how likely the reference value of is to fall into one partition

versus another.We formalize our intuition above by introducing a selector attribute,whose

domain is.The speci?cation of the probabilistic model for the selector attribute is the same as that of any other attribute:it has a set of parents and a CPD.In our earlier example,the

CPD of Movie might have as a parent Type.For each instantiation of the parents,we

have a distribution over.3The choice of value for determines the partition from which the reference value of is chosen;the choice of reference value for is uniformly distributed within this set.

De?nition5A probabilistic relational model with reference uncertainty has the same compo-nents as in De?nition1.In addition,for each reference slot with,we have:

a partition function with a set of partition attributes;

a new selector attribute within which takes on values in the range of;

a set of parents and a CPD for.

To de?ne the semantics of this extension,we must de?ne the probability of reference slots as well as descriptive attributes:

Pa

Pa

(2)

where refers to—the partition that the partition function assigns.Note that the last term in Eq.(2)depends on in three ways:the interpretation of,the values of the attributes within the object,and the size of.

There is one small problem with this de?nition:the probability is not well-de?ned if there are no objects in a partition,i.e.,.In this case,we will perform a renormalization of the distribution for the selector attribute,removing all probability mass from the empty partition. We then treat this term,Pa,as in the above product.In other words,an instantiation where and is an empty partition necessarily has probability zero.4

3.In the current work,we treat this distribution as a simple multinomial distribution over this value space.In gen-

eral,however,we can represent such a distribution more compactly,e.g.,using a Bayesian network.For example, the genre of movies shown by a movie theater might depend on its type(as above).However,the language of the movie can depend on the location of the theater.Thus,the partition will be de?ned by Movie Genre Language,and its parents would be Type and Location.We can rep-resent this conditional distribution more compactly by introducing a separate variable Genre,with a parent Type,and another Language,with a parent Location.

4.While an important technical detail,in practice,for the majority of our experimental domains,we did not encounter

empty partitions.

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3.2Coherence of the Probabilistic Model

As in the case of PRMs with attribute uncertainty,we must be careful to guarantee that our proba-bility distribution is in fact coherent.In this case,the object skeleton does not specify which objects are related to which,and therefore the mapping of formal to actual parents depends on probabilistic choices made in the model.The associated ground Bayesian network will therefore be cumbersome and not particularly intuitive.We de?ne our coherence constraints using an instance dependency graph,relative to our PRM and object skeleton.

De?nition6The instance dependency graph for a PRM and an object skeleton is a graph with the nodes and edges described below.For each class and each,we have the following nodes:

a node for every descriptive attribute;

a node and a node,for every reference slot

The dependency graph contains?ve types of edges:

Type I edges:Consider any attribute(descriptive or selector)and formal parent.

We de?ne an edge,for every.

Type II edges:Consider any attribute(descriptive or selector)and formal parent

where.We de?ne an edge,for every and.

Type III edges:Consider any attribute and formal parent,where, and.We de?ne an edge,for every.In addition,for ,we add an edge for for every and for every.

Type IV edges:Consider any slot and partition attribute for.

We de?ne an edge,for every and.

Type V edges:Consider any slot.We de?ne an edge,for every.

We say that a dependency structure is acyclic relative to an object skeleton if the directed graph is acyclic.

Intuitively,type I edges correspond to intra-object dependencies and type II edges to inter-object dependencies.These are the same edges that we had in the dependency graph for regular PRMs, except that they also apply to selector attributes.Moreover,there is an important difference in our treatment of type II edges.In this case,the skeleton does not specify the value of,and hence we cannot determine from the skeleton on which object the attribute actually depends.Therefore, our instance dependency graph must include an edge from every attribute.

Type III edges represent the fact that the actual choice of parent for depends on the value of the slots used to de?ne it.When the parent is de?ned via a slot-chain,the actual choice depends on the values of all the slots along the chain.Since we cannot determine the particular object from the skeleton,we must include an edge from every slot potentially included in the chain.

Type V edges represent the dependency of a slot on the attributes de?ning the associated partition. To see why this dependence is required,we observe that our choice of reference value for depends on the values of the partition attributes of all of the different objects in.Thus,

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these attributes must be determined before is determined.Finally,type V edges represent the fact that the actual choice of parent for depends on the value of the selector attributes for the slots used to de?ne it.In our example,as Movie Genre,the genres of all movies must be determined before we can select the value of the reference slot Movie.

Based on this de?nition,we can specify conditions under which Eq.(2)speci?es a coherent prob-ability distribution.

Theorem7Let be a PRM with reference uncertainty whose dependency structure is acyclic relative to an object skeleton.Then and de?ne a coherent probability distribution over instantiations that extend via Eq.(2).

Proof:The probability of an instantiation is the joint distribution over a set of random variables de?ned via the object skeleton.We have two types of variables:

We have one random variable for each and each.Note that this also includes variables of the form that correspond to selector variables.

We have one random variable for each reference slot and.This variable denotes the actual object in that the slot points to.

Let be the entire set of variables de?ned by the object skeleton.Clearly,there is a one-to-one mapping between joint assignments to these variables and instantiations of the PRM that are consistent with.Because the instance dependency graph is acyclic,we can assume without loss of generality that the ordering is a topological sort of the instance dependency graph;thus,if,then all ancestors of in the instance dependency graph appear before it in the ordering.

Our proof will use the following argument.Assume that we can construct a non-negative function which has the form of a conditional distribution,i.e.,for any assignment to,we have that

(3) Then,by the chain rule for probabilities,we can de?ne

If satis?es Eq.(3),then is a well-de?ned joint distribution.

All that remains is to de?ne the function in a way that it satis?es Eq.(3).Speci?cally,the function will be de?ned via Eq.(2).We consider the two types of variables in our distribution. Suppose that is of the form,and consider any parent of.There are two cases: If the parent is of the form,then by the existence of type I edges,we have that

precedes in.Hence,the variable precedes.

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If the parent is of the form,then by the existence of type III edges,for each along precedes in and hence,by the existence of type V edges all of the also precede.Furthermore,by the existence of type II edges,for any,we have that precedes.

In both cases,we can de?ne

Pa

as in Eq.(2).As the right-hand-side is simply a CPD in the PRM,it speci?es a well-de?ned condi-tional distribution,as required.

Now,suppose that is of the form.In this case,the conditional probability depends on, and the value of the partition attributes of all objects in.By the existence of type V edges,precedes.Furthermore,by the existence of type IV edges,we have that for every and.Consequently,the assignment to determines the number of objects in each partition of values of and hence the set for every. Finally,we set

if

otherwise

which is a well de?ned distribution on the objects in.

This theorem is limited in that it is very speci?c to the constraints of a given object skeleton.As in the case of PRMs without relational uncertainty,we want to learn a model in one setting,and be assured that it will be acyclic for any skeleton we might encounter.We accomplish this goal by extending our de?nition of class dependency graph.We do so by extending the class dependency graph to contain edges that correspond to the edges we de?ned in the instance dependency graph. De?nition8The class dependency graph for a PRM with reference uncertainty has a node for each descriptive or selector attribute and each reference slot,and the following edges: Type I edges:For any attribute and formal parent,we have an edge.

Type II edges:For any attribute and formal parent where,we have an edge.

Type III edges:For any attribute and formal parent,where,and ,we de?ne an edge.In addition,each,we add an edge

.

Type IV edges:For any slot and partition attribute for,we have an edge.

Type V edges:For any slot,we have an edge.

Figure5shows the class dependency graph for our extended movie example.

It is now easy to show that if this class dependency graph is acyclic,then the instance dependency graph is acyclic.

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(a)(b)

Figure5:(a)A PRM for the movie theater example.The partition attributes are indicated using dashed lines.(b)The dependency graph for the movie theater example.The different

edge types are labeled.

Lemma9If the class dependency graph is acyclic for a PRM with reference uncertainty,then for any object skeleton,the instance dependency graph is acyclic.

Proof:Assume by contradiction that there is a cycle

Then,because each of these object edges corresponds to an edge in the class dependency graph,we have the following cycle in the class dependency graph:

This contradicts our hypothesis that the class dependency graph is acyclic.

The following corollary follows immediately:

Corollary10Let be a PRM with reference uncertainty whose class dependency structure is acyclic.For for any object skeleton,and de?ne a coherent probability distribution over instantiations that extend via Eq.(2).

4.Existence Uncertainty

The second form of structural uncertainty we introduce is called existence uncertainty.In this case, we make no assumptions about the number of links that exist.The number of links that exist and the identity of the links are all part of the probabilistic model and can be used to make inferences about other attributes in our model.In our citation example above,we might assume that the set of papers is part of our background knowledge,but we want to provide an explicit model for the presence or absence of citations.Unlike the reference uncertainty model of the previous section,we do not assume that the total number of citations is?xed,but rather that each potential citation can be present or absent.

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(a)(b)

Figure6:(a)An entity skeleton for the citation domain.(b)A CPD for the Exists attribute of Cites.

4.1Semantics of relational model

The object skeleton used for reference uncertainty assumes that the number of objects in each rela-tion is known.Thus,if we consider a division of objects into entities and relations,the number of objects in classes of both types are?xed.Existence uncertainty assumes even less background infor-mation than speci?ed by the object skeleton.Speci?cally,we assume that the number of relationship objects is not?xed in advance.

We assume that we are given only an entity skeleton,which speci?es the set of objects in our domain only for the entity classes.Figure6(a)shows an entity skeleton for the citation example.Our basic approach is to allow other objects within the model—those in the relationship classes—to be undetermined,i.e.,their existence can be uncertain.In other words,we introduce into the model all of the objects that can potentially exist in it;with each of them,we associate a special binary variable that tells us whether the object actually exists or not.We call entity classes determined and relationship classes undetermined.

To specify the set of potential objects,we note that relationship classes typically represent many-many relationships;they have at least two reference slots,which refer to determined classes.For example,our Cite class has the two reference slots Citing and Cited.Thus the potential domain of the Cites class in a given instantiation is.Each“potential”object in this class has to form.Each such object is associated with a binary attribute that speci?es whether paper did or did not cite paper.

De?nition11Consider a schema with determined and undetermined classes,and let be an entity skeleton over this schema.We de?ne the induced relational skeleton,,to be the relational skeleton that contains the following objects:

If is a determined class,then.

Let be an undetermined class with reference slots whose range types are

respectively.Then contains an object for all tuples

.

14

The relations in are de?ned in the obvious way:Slots of objects of determined classes are taken from the entity skeleton.Slots of objects of undetermined classes are induced from the object de?nition:is.

To ensure that the semantics of schemas with undetermined classes is well-de?ned,we need a few tools.Speci?cally,we need to ensure that the set of potential objects is well de?ned and?nite.It is clear that if we allow cyclic references(e.g.,an undetermined class with a reference to itself),then the set of potential objects is not?nite.To avoid such situations,we need to put some requirements on the schema.

De?nition12A set of classes is strati?ed if there exists a partial ordering over the classes such that for any reference slot with range type,.

Lemma13If the set of undetermined classes in a schema is strati?ed,then given any entity skeleton the number of potential objects in any undetermined class is?nite.

Proof:We prove this by induction on the strati?cation level of the class.Let be the set of reference slots of,and let.Then If is the?rst level in the strati?cation,it cannot refer to any undetermined classes.Thus,the number of potential objects in is simply the product of the number of objects in each determined class as speci?ed in the entity skeleton.Each term is?nite,so the product of the terms will be?nite. Next,assume by induction that all of the classes at strati?cation levels less than are?nite.If is at level in the strati?cation,the constraints imposed by the strati?cation constraints imply that the range type of all of its reference slots are at strati?cation levels.By our induction hypothesis, each of these classes is?nite.Hence,the cross product of the classes of the reference slots is?nite and the number of potential objects in is?nite.

As discussed,each undetermined has a special existence attribute whose values are

true false.For uniformity of notation,we introduce an attribute for all classes;for classes that are determined,the value is de?ned to be always true.We require that all of the reference slots of a determined class have a range type which is also a determined class.

For a PRM with strati?ed undetermined classes,we de?ne an instantiation to be an assignment of values to the attributes,including the Exists attribute,of all potential objects.

4.2Probabilistic model

We now specify the probabilistic model de?ned by the PRM.By treating the Exists attributes as standard descriptive attributes,we can essentially build our de?nition directly on top of the de?nition of standard PRMs.

Speci?cally,the existence attribute for an undetermined class is treated in the same way as a descriptive attribute in our dependency model,in that it can have parents and children,and has an associated CPD.Figure6(b)illustrates a CPD for the Cites.Exists attribute.In this example,the existence of a citation depends on the topic of the citing paper and the topic of the cited paper;e.g., it is more likely that citations will exist between papers with the same topic.5.

5.This is similar to the‘encyclopedic’links discussed by(Ghani et al.,2001).Our exists models can capture each of

the types of links(encyclopedic,co-referencing,and partial co-referencing)de?ned in(Ghani et al.,2001).Moreover our exists models are much more general,and can capture much richer patterns in the existence of links.

15

Using the induced relational skeleton,treating the existence events as descriptive attributes,we have set things up so that Eq.(1)applies with minor changes.There are two minor changes to the de?nition of the distribution:

We want to enforce that false if false for one of the slots of.Suppose that has the slots,we de?ne the effective CPD for as follows.Let Pa

Pa,and de?ne

Pa Pa if true

otherwise

We want to“decouple”the attributes of non-existent objects from the rest of the PRM.Thus, if is a descriptive attribute,we de?ne Pa Pa,and

Pa Pa if true

otherwise

It is easy to verify that in both cases Pa is a legal conditional distribution.

In effect,these constraints specify a new PRM,in which we treat as a standard descriptive attribute.For each attribute(including the Exists attribute),we de?ne the parents of in to be Pa and the associated CPD to be Pa.

Given an entity skeleton,a PRM with exists uncertainty speci?es a distribution over a set of instantiations consistent with:

Pa(4) We can similarly de?ne the instance dependency graph and the class dependency graph for a PRM with existence uncertainty using the corresponding notions for the standard PRM.As there, we require that the class dependency graph is acyclic.One immediate consequence of this requirement is that the schema is strati?ed.

Lemma14If the class dependency graph is acyclic,then there is a strati?cation of the unde-termined classes.

Proof:The strati?cation is given by an ordering of Exists attributes consistent with the class de-pendency graph.Because the class dependency graph has an edge from to for every slot whose range type is,will precede in the constructed ordering.Hence it is a strati?cation ordering.

Furthermore,based on this de?nition,we can now easily prove the following result:

Theorem15Let be a PRM with existence uncertainty and an acyclic class dependency graph. Let be an entity skeleton.Then Eq.(4)de?nes a coherent distribution on all instantiations of the induced relational skeleton.

16

Proof By Lemma14and Lemma13we have that is a well-de?ned relational https://www.wendangku.net/doc/918971742.html,ing the assumption that is acyclic,we can apply Theorem2to and conclude that de?nes a coherent distribution over instances to,and hence so does.

One potential shortcoming of our semantics is that it de?nes probabilities over instances that in-clude assignment of descriptive attributes to non-existent objects.This potentially presents a prob-lem.An actual instantiation(i.e.,a database)will contain value assignments only for the descriptive attributes of existing objects.This suggests that in order to compute the likelihood of a database we need to sum over all possible values of descriptive attributes of potential objects that do not exist. (As we shall see,such likelihood computations are integral part of our learning procedure.)Fortu-nately,we can easily see that the de?nition of ensures that if,then variables of the form are independent of all other variables in the instance.Thus,we can ignore such descriptive attributes when we compute the likelihood of a database.

The situation with Exists attribute is somewhat more complex.When we observe a database,we also observe that many potential objects do not exist.The non-existence of these objects can provide information about other attributes in the model,which is taken into consideration by the correlations between them and the Exists attributes in the PRM.At?rst glance,this idea presents computational dif?culties,as there can be a very large number of non-existent objects.However,we note that the de?nition of is such that we need to compute false Pa only for objects whose slots refer to existing objects,thereby bounding the number of non-existent objects we have to consider.

5.Example:Word models

Our two models of structural uncertainty induce simple yet intuitive models for link existence. We illustrate this by showing a natural connection to two common models of word appearance in documents.Suppose our domain contains two entity classes:Document,representing the set of documents in our corpus,and Words,representing the words contained in our dictionary.Doc-uments may have descriptive attributes such as Topic;dictionary entries have the attribute Word, which is the word itself,and may also have additional attributes such as the type of word.The relationship class Appearance represents the appearance of words in documents;it has two slots InDoc and HasWord.In this schema,structural uncertainty corresponds to a probabilistic model of the appearance of words in documents.

In existence uncertainty,the class Appearance is an undetermined class;the potential objects in this class correspond to document-word pairs,and the assertion true means that the particular dictionary entry appears in the particular document.Now,suppose that has the parents Appearance.InDoc.Topic and Appearance.HasWord.Word.This implies,that,for each word and topic,we have a parameter which is the probability that a word appears in a document of topic.Furthermore,the different events

are conditionally independent given the topic.It is easy to see that this model is equivalent to the model often called binary naive Bayes model(McCallum and Nigam,1998),where the class variable is the topic and the conditionally independent features are binary variables corresponding to the appearance of different dictionary entries in the document.

17

When using reference uncertainty,we can consider several modeling alternatives.The most

straightforward model is to view a document as a bag of words.Now,Appearance also in-

cludes an attribute that designates the position of the word in the document.Thus,a document

of words has related Appearance objects.We can provide a probabilistic model of word ap-

pearance by using reference uncertainty over the slot Appearance.HasWord.In particular,if we

choose HasWord Word,then we have a multinomial distribution over the

words in the dictionary.If we set Appearance.InDoc.Topic as the parent of the selector variable HasWord,then we get a different multinomial distribution over words for each topic. The result is a model where a document is viewed as a sequence of independent samples from a

multinomial distribution over the dictionary,where the sample distribution depends on the docu-

ment topic.This document model is called the multinomial Naive Bayesian model(McCallum and

Nigam,1998).

Thus,for this simple PRM structure,the two forms of structural uncertainty lead to models that

are well-studied within the statistical NLP community.However,the language of PRMs allows us

to represent more complex structures:Both the existence and reference uncertainty can depend on

properties of words rather than on the exact identity of the word;for example they can also depend

on other attributes,such as the research area of the document’s author.

6.Learning PRMs with Structural Uncertainty

In this section,we brie?y review the learning algorithm for the basic PRM framework in Friedman

et al.(1999)and describe the modi?cations needed to handle the two extensions of PRMs proposed

in the previous sections.Our aim is to learn such models from data:given a schema and an instance,

construct a PRM that captures the dependencies between objects in the schema.We stress that basic

PRMs and both proposed variants are learned using the same type of training data:a complete

instantiation that describes a set of objects,their attribute values and their reference slots.However,

in each variant,we attempt to learn somewhat different structure from this data.For basic PRMs,

we learn the probability of attributes given other attributes;for PRMs with reference uncertainty,we

also attempt to learn the rules that govern the choice of slot references;and for PRMs with existence

uncertainty,we attempt to learn the probability of existence of relationship objects.

6.1Learning basic PRMs

We separate the learning problem into two tasks:evaluating the“goodness”of a candidate structure,

and searching the space of legal candidate structures.

Model Scoring For scoring candidate structures,we adapt Bayesian model selection Heckerman

(1998).We compute the posterior probability of a PRM given an https://www.wendangku.net/doc/918971742.html,ing Bayes

rule we have that.This score is composed of two main parts:the

prior probability of,and the probability of the instantiation assuming the PRM is.By making

fairly reasonable assumptions about the prior probability of structures and parameters,this term can

be decomposed into a product of terms Friedman et al.(1999).As in Bayesian network learning,

each term in the decomposed form of the score measures how well we predict the values of

given the values of its parents.Moreover,the term for depends only on the suf?cient

statistics C,that count the number of entities with and Pa.

18

Model Search To?nd a high-scoring structure in basic PRM framework,we use a simple search procedure that considers operators such as adding,deleting,or reversing edges in the dependency model.The procedure performs greedy hill-climbing search,using the Bayesian score to evaluate structures.As in Bayesian network search,we can take advantage of score decomposibility to perform the hill-climbing ef?ciently:after adding or deleting a parent of an attribute,the only steps that need to be re-scored are other edges that add/delete parents for this attribute.

6.2Learning with reference uncertainty

The extension to scoring required to deal with reference uncertainty is not a dif?cult one.Once we ?x the partitions de?ned by the attributes,a CPD for compactly de?nes a distribution over values of.Thus,scoring the success in predicting the value of can be done ef?ciently using standard Bayesian methods used for attribute uncertainty(e.g.,using a standard Dirichlet prior over values of).

The extension to search the model space for incorporating reference uncertainty involves expand-ing our search operators to allow the addition(and deletion)of attributes to partition de?nition for each reference slot.Initially,the partition of the range class for a slot is not given in the model. Therefore,we must also search for the appropriate set of attributes.We introduce two new op-erators re?ne and abstract,which modify the partition by adding and deleting attributes from. Initially,is empty for each.The re?ne operator adds an attribute into;the abstract operator deletes one.As mentioned earlier,we can de?ne the partition simply by looking at the cross product of the values for each of the partition attributes,or using a decision tree.In the case of a decision tree,re?ne adds a split to one of the leaves and abstract removes a split.These newly introduced operators are treated by the search algorithm in exactly the same way as the standard edge-manipulation operators:the change in the score is evaluated for each possible operator,and the algorithm selects the best one to execute.

We note that,as usual,the decomposition of the score can be exploited to substantially speed up the search.In general,the score change resulting from an operator is re-evaluated only after applying an operator that modi?es the parent or partition set of an attribute that modi?es.This is also true when we consider operators that modify the parent of selector attributes.

6.3Learning with Existence Uncertainty

The extension of the Bayesian score to PRMs with existence uncertainty is straightforward;the ex-ists attribute is simply a new descriptive attribute.The only new issue is how to compute suf?cient statistics that include existence attributes without explicitly enumerating all the non-existent entities.We perform this computation by counting,for each possible instantiation of Pa, the number of potential objects with that instantiation,and subtracting the actual number of ob-jects with that parent instantiation.Let be a particular instantiation of Pa.To compute C true,we can use standard database query to compute how many objects have Pa.To compute C false,we need to compute the number of potential entities.We can do this without explicitly considering each by decomposing

the computation as follows:Let be a reference slot of with.Let Pa be the subset of parents of along slot and let be the corresponding instantiation.We count the number of consistent with.If Pa is empty,this count is simply.The product

19

Figure7:,the PRM learned using reference uncertainty.The reference slots are Role.Movie, Role.Actor,Vote.Movie,and Vote.Person.Dashed lines indicate attributes used in de?n-

ing the partition.

of these counts is the number of potential entities.To compute C false,we simply subtract C true from this number.

No extensions to the search algorithm are required to handle existence uncertainty.We simply introduce the new attributes,and integrate them into the search space.Our search algorithm now considers operators that add,delete or reverse edges involving the exist attributes.As usual, we enforce coherence using the class dependency graph.In addition to having an edge from to for every slot whose range type is,when we add an edge from to,we add an edge from to and an edge from to.

7.Experimental Results

We evaluated our learning algorithms on several real-world data sets.In this section,we describe the PRM learned for a domain using both of our models for representing structural uncertainty. In each case,we compare against a simple baseline model.Our experiments used the Bayesian score with a uniform Dirichlet parameter prior with equivalent sample size,and a uniform distribution over structures.The partitions are de?ned using the cross-product of values of the partition attributes;they are not with using decision trees.

7.1Predictive ability

We?rst tested whether the additional expressive power allows us to better capture regularities in the domain.Toward this end,we evaluated the likelihood of test data given our learned model. Unfortunately,we cannot directly compare the likelihood of the EU and RU models,since the

20

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当的人”,使集团全体员工掌握好企业知识,建立和强化企业的核心利润源,谋取企业长期的、稳定的、增长的利润。 1.1.2 较具体地, 要在这次知识管理的推动中,建立起集团的知识体系架构;整理出全集团各岗位工作所产生的知识、员工贡献的知识、员工所需求的知识、常用的知识、基础知识、专家知识、员工的工作经验和总结等知识内容;确定这些知识内容的管理方式;通过工具平台、组织和制度逐步使知识管理工作走向正规化。 1.2 策略 1.2.1 根据****集团业务和工作特点,进行知识管理信息化办公平台和知识管理组织和机制的建设,在专业咨询机构的指导下,分阶段稳步推进实施。 1.2.2 知识管理信息化办公平台选用蓝凌公司的LKS4.0系统。该系统以IBM/LOTUS 的DOMINO协作平台为基础,它是基于知识管理的工作平台,可以满足****集团的知识管理需求。

完善知识管理理论构建知识共享系统_王玉晶

完善知识管理理论构建知识共享系统 王玉晶 【摘 要】知识共享是知识管理的一个重要组成部分。本文从知识管理的概念入手,指出了知识共享在知识管理中的重要性和特殊地位,分析了企业中进行知识共享存在的障碍与不利因素,从建立知识共享技术支撑体系、构建知识共享组织结构、营造知识共享文化、完善知识共享激励机制等方面深入探讨了如何提高企业知识共享程度,加强企业竞争力。 【关键词】知识管理 知识共享 体系 Abstract:Kno wledge sharing is an important component of the kno wledge management.This paper obtained from the kno wledge management concept,has pointed out the importance and the special status of knowledge sharing in the knowledge manage ment,and analyzed the barrier and th e disadvantage factor of knowledge sharing in the enterprise.This article pointed out that the knowledge sharing should be established technical support system,built knowledge sharing structure,created a kno wledge sharing culture,and improved knowledge sharing incentive mechanism. Key words:kno wledge sharing knowledge management system 当今社会,企业竞争力已不局限于仅仅依赖其规模、信息和技术,而更注重其创新和应变能力。知识管理就是在知识经济大背景下,以当代信息技术为依托,着力于知识的开发和利用、积累和创新,帮助人们共享信息,进而对扩大了的知识资本进行有效运营,最终通过集体智慧提高企业创新和应变能力的一种全新的信息管理理论与方法。而创新本身,无论是技术创新还是管理创新,其实质就是一种新知识的创造,它要求企业内部各个部门之间以及各员工之间,企业内部与外部之间进行广泛的知识交流与共享。所以知识共享一直是知识管理的一个重要组成部分。它是发挥知识的效用,实现知识价值的必由之路,是实现知识共享的前提,是走向知识共享世界的先导。理解知识共享的内涵,分析企业知识共享存在的障碍与不利因素并提出解决的方案,对完善组织中的知识共享机制具有重要意义。 1 知识共享的含义 关于知识共享的概念,由于标准、角度的不同,学者对知识共享的界定也有所不同。知识共享是指个体知识、组织知识通过各种交流手段为组织中其他成员所共享。同时,通过知识创新,实现组织的知识增值。对知识共享的认识应从知识共享的对象———知识 内容,知识共享的手段———知识网络、会议及团队学习,知识共享的主体———个人、团队及组织这三个层面考虑。其中,人是知识共享的主体,文化是知识共享的背景,信息技术是知识共享的重要工具。 2 知识共享障碍因素分析 2.1 技术应用障碍 知识管理作为一种全新的管理模式,如果缺乏应有的技术支撑,将难以发挥其应有的效力,最终失之于形式,流于空泛。许多企业物质技术基础薄弱,缺少有效的计算机网络和通信系统,很多员工不知道到哪里去寻找所需要的知识。存在于员工头脑中的隐性知识难以明确的被他人观察、了解,也无法用言语表达或者只能用言语进行部分表达。因此,薄弱的技术基础不能够帮助人们跨越时间、空间和知识的数量及质量的限制,从而不能为有效地实现知识共享提供强有力的技术支持。 2.2 组织结构缺陷 传统的组织结构管理层次多,信息传递速度缓慢,信息衰退或信息失真现象非常严重,员工之间没有超越命令以外的直接接触和交流,无法实现面对面的互动式交流,无法突破岗位对个人的约束。多层管理结构森严,越级的知识传递几乎不可能实现;员工之间 27 RESEARCH ES I N LIBRARY SCIENCE  DOI:10.15941/https://www.wendangku.net/doc/918971742.html, ki.issn1001-0424.2008.05.027

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