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Discriminative Probabilistic Models for Relational Data. Ben Taskar, Pieter Abbeel, Daphne Koller. Tradition statistic classification Methods. Dealing with only ‘ flat ’ data – IID
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Discriminative Probabilistic Models for Relational Data Ben Taskar, Pieter Abbeel, Daphne Koller
Tradition statistic classification Methods • Dealing with only ‘flat’ data – IID • In many supervised learning tasks, entities to be labeled are related to each other in complex way and their labels are not independent • This dependence is an important source of information to achieve better classification Guohua Hao
Collective Classification • Rather than classify each entity separately • Simultaneously decide on the class label of all the entities together • Explicitly take advantage of the correlation between the labels of related entitiies Guohua Hao
Undirected vs. directed graphical models • Undirected graphical models do not impose the acyclicity constraint, but directed ones need acyclicity to define a coherent generative model • Undirected graphical models are well suited for discriminative training, achieving better classification accuracy over generative training Guohua Hao
Our Hypertext Relational Domain Label Label ... ... HasWordk HasWord1 HasWordk HasWord1 Doc Doc From To Link Guohua Hao
Schema • A set of entity types • Attribute of each entity type • Content attribute E.X • Label attribute E.Y • Reference attribute E.R Guohua Hao
Instantiation • Provide a set of entities I(E) for each entity type E • Specify the values of all the attribute of the entities, I.x, I.y, I.r • I.r is the instantiation graph, which is call relational skeleton in PRM Guohua Hao
Markov Network • Qualitative component – Cliques • Quantitative component – Potentials Guohua Hao
Cliques • A set of nodes in the graph G such that for each are connected by an edge in G Guohua Hao
Potentials • The potential for the clique c defines the compatibility between values of variables in the clique • Log-linearly combination of a set of features Guohua Hao
Probability in Markov Network • Given the values of all nodes in the Markov Network Guohua Hao
Conditional Markov Network • Specify the probability of a set of target variables Y given a set of conditioning variables X Guohua Hao
Relational Markov Network (RMN) • Specifies the conditional probability over all the labels of all the entities in the instantiation given the relational structure and the content attributes • Extension of the Conditional Markov Networks with a compact definition on a relational data set Guohua Hao
Relational clique template • F --- a set of entity variables (From) • W--- the condition about the attributes of the entity variables (Where) • S --- subset of attributes (content and label attribute) of the entity variables (Select) Guohua Hao
Relationship to SQL query SELECT doc1.Category,doc2.Category FROM doc1,doc2,Link link WHERE link.From=doc1.key and link.To=doc2.key Doc1 Doc1 Doc2 Link Guohua Hao
Potentials • Potentials are defined at the level of relational clique template • The cliques of the same relational clique template have the same potential functions Guohua Hao
Unrolling the RMN • Given an instantiation of a relational schema, unroll the RMN as follows • Find all the cliques in the unrolled the relational schema where the relational clique templates are applicable • The potential of a clique is the same as that of the relational clique template which this clique belongs to Guohua Hao
link1 Doc1 Doc2 link2 Doc3 Guohua Hao
Probability in RMN Guohua Hao
Learning RMN • Given a set of relational clique templates • Estimate feature weight w using conjugate gradient • Objective function--Product of likelihood of instantiation and parameter prior • Assume a shrinkage prior over feature weights Guohua Hao
Learning RMN (Cont’d) • The conjugate gradient of the objective function where Guohua Hao
Inference in RMN • Exact inference • Intractable due to the network is very large and densely connected • Approximate inference • Belief propagation Guohua Hao
Experiments • WebKB dataset • Four CS department websites • Five categories (faculty,student,project,course,other) • Bag of words on each page • Links between pages • Experimental setup • Trained on three universities • Tested on fourth Guohua Hao
Flat Models • Based only on the text content on the WebPages • Incorporate meta-data Guohua Hao
Relational model • introduce relational clique template over the labels of two pages that are linked Doc1 Doc2 Link Guohua Hao
Relational model (Cont’d) • relational clique template over the label of section and the label of the pages it is on • Relational clique template over the label of the section containing the link and the label of the target page Guohua Hao
Discriminative vs. Generative • Exit+Naïve Bayes: a complete generative model proposed by Getoor et al • Exit+logistic: using logistic regression for the conditional probability distribution of page label given words • Link: a fully discriminative training model Guohua Hao
Thank You! Guohua Hao