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A Hierarchy of Independence Assumptions for Multi-Relational Bayes Net Classifiers

School of Computing Science Simon Fraser University Vancouver, Canada. A Hierarchy of Independence Assumptions for Multi-Relational Bayes Net Classifiers. Outline. Multi- R elational Classifiers Multi-Relational Independence Assumptions Classification Formulas Bayes Nets Evaluation.

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A Hierarchy of Independence Assumptions for Multi-Relational Bayes Net Classifiers

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  1. School of Computing Science • Simon Fraser University • Vancouver, Canada A Hierarchy of Independence Assumptions for Multi-Relational Bayes Net Classifiers

  2. Outline • Multi-Relational Classifiers • Multi-Relational Independence Assumptions • Classification Formulas • Bayes Nets • Evaluation A Hierarchy of Independence Assumptions

  3. Database Tables • Tables for Entities, Relationships • Can visualize as network Ranking = 1 Diff = 1 Jack 101 Registration Link-based ClassificationTarget table: Student Target entity: Jack Target attribute (class): Intelligence A Hierarchy of Independence Assumptions

  4. Extended Database Tables A Hierarchy of Independence Assumptions

  5. Multi-Relational Classifiers Count relational features Aggregate relational features • Propositionalization • Example: use average grade • Disadvantages: • loses information • slow to learn (up to several CPU days) Log-Linear Models Example: use number of A,s number of Bs,… ln(P(class)) = Σ xiwi – Z Disadvantage: slow learning + Independence Assumptions • Log-Linear Models With Independencies • Fast to learn • −Independence Assumptions may be only approximately true A Hierarchy of Independence Assumptions

  6. Independence Assumptions A Hierarchy of Independence Assumptions

  7. Independence Assumptions: Naïve Bayes Naive Bayes: non-class attributes are independent of each other, given the target class label. Legend: Given the blue information, the yellow columns are independent. A Hierarchy of Independence Assumptions

  8. Path Independence Naive Bayes: non-class attributes are independent of each other, given the target class label. Legend: Given the blue information, the yellow rows are independent. Path Independence: Links/paths are independent of each other, given the attributes of the linked entities.

  9. Influence Independence Legend: Given the blue information, the yellow columns are independent from the orange columns Influence Independence: Attributes of the target entity are independent of attributes of related entities, given the target class label. Naive Bayes: non-class attributes are independent of each other, given the target class label. Path Independence: Links/paths are independent of each other, given the attributes of the linked entities. Path-Class Independence: the existence of a link/path is independent of the class label.

  10. Classification Formulas • Can rigorously derive log-linear prediction formulas from independence assumptions. • Path Independence: predict max class for: log(P(class|target attributes)) + sum over each table, each row: [log(P(class|information in row)) – log(P(class|targetatts))] • PI + Influence Independence:predict max class for: log(P(class|target attributes)) + sum over each table, each row: [log(P(class|information in row)) – log(prior P(class))] A Hierarchy of Independence Assumptions

  11. Relationship to Previous Formulas A Hierarchy of Independence Assumptions

  12. Evaluation A Hierarchy of Independence Assumptions

  13. Data Sets and Base Classifier • Standard DatabasesKDD Cup, UC Irvine • MovieLens not shown. Country Continent Hepatitis In-Hosp Economy Out-Hosp Mondial Biopsy Patient Government Interferon Borders • Classifier • Can plug in any single-table probabilistic base classifier with classification formula . • We use Bayes nets. Country2 Transaction Loan Account Financial Order Disposition District Card Client

  14. Family of Alarm Burglary Earthquake E B P(A | E,B) e b 0.9 0.1 e b 0.2 0.8 Radio Alarm e b 0.9 0.1 0.01 0.99 e b Call What is a Bayes net? Compact representation of joint probability distributions via conditional independence • Qualitative part: • Directed acyclic graph (DAG) • Nodes - random vars. • Edges - direct influence Quantitative part: Set of conditional probability distributions Together: Define a unique distribution in a factored form Figure from N. Friedman

  15. Independence-Based Learning is Fast strongest assumption weakest assumption Training Time in seconds A Hierarchy of Independence Assumptions

  16. Independence-Based Models are Accurate strongest assumption weakest assumption • Similar results for F-measure, Area Under Curve A Hierarchy of Independence Assumptions

  17. Conclusion • Several plausible independence assumptions/classification formulas investigated in previous work. • Organized in unifying hierarchy. • New assumption: multi-relational path independence. • most general, implicit in other models. • Big advantage: Fast scalable simple learning. • Plug in single-table probabilistic classifier. • Limitation: no pruning or weighting of different tables.Can use logistic regression to learn weights (Bina, Schulte et al. 2013). Bina, B.; Schulte, O.; Crawford, B.; Qian, Z. & Xiong, Y. “Simple decision forests for multi-relational classification”, Decision Support Systems, 2013

  18. Thank you! • Any questions? A Hierarchy of Independence Assumptions

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