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Refining Rules Incorporated into Knowledge-Based Support Vector Learners

This paper presents a method for refining rules incorporated into knowledge-based support vector learners through successive linear programming. The approach allows users to specify advice and then refine it with the data, resulting in more accurate models. The algorithm, called Rule-Refining Support Vector Machines (RRSVM), adjusts the thresholds of rules to improve performance. Experimental results on artificial and real-world data sets demonstrate the effectiveness of the approach.

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Refining Rules Incorporated into Knowledge-Based Support Vector Learners

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  1. Refining Rules Incorporated into Knowledge-Based Support Vector Learners via Successive Linear Programming Richard Maclin University of Minnesota - Duluth Edward Wild, Jude Shavlik, Lisa Torrey, Trevor Walker University of Wisconsin - Madison

  2. The Setting Given • Examples for classification/regression task • Advice from an expert about the task Do • Learn an accurate model • Refine the advice (if needed) Knowledge-Based Support Vector Classification/Regression

  3. Motivation • Advice-taking methods incorporate human user’s knowledge • But users may not be able to precisely define advice • Idea: allow users to specify advice but refine the advice with the data

  4. An Example of Advice True concept IF(3x1 – 4x2) > -1 THENclass = +ELSEclass =- Examples 0.8 , 0.7 , 0.3 , 0.2 , + 0.2 , 0.6 , 0.8 , 0.1 , - Advice IF(3x1 – 4x2) > 0 THENclass = + ELSEclass =- (wrong, threshold should be -1)

  5. Knowledge-Based Classification

  6. Knowledge Refinement

  7. SVM Formulation min (model complexity) + C (penalties for error) such that model fits data (with slack vars for error)

  8. Knowledge-Based SVMs[Fung et al., 2002, 2003 (KBSVM), Mangasarian et al., 2004 (KBKR)] min (model complexity) + C (penalties for error) +(µ1,µ2) (penalties for not following advice) such that model fits data (with slack vars for error) + model fits advice (also with slacks)

  9. Refining Advice min (model complexity) + C (penalties for error) + (µ1,µ2) (penalties for not following advice) + ρ(penalties for changing advice) such that model fits data (with slack vars for error) + model fits advice (also with slacks) + variables to refine advice

  10. Advice format Bx ≤ df(x) ≥  Incorporating Advice in KBKR IF(3x1 – 4x2) > 0 THENclass = + (f(x)≥ 1) f(x)≥ 1

  11. Linear Programming with Advice Advice Bx ≤ d f(x) ≥  IF(3x1 – 4x2) > 0 THENclass = + KBSVMs: min ||w||1 + |b| + C||s||1 sum per advice k µ1||zk||1+µ2ζk such that Y(wTx +b) + s ≥ 1 for each advice k wk+BkTuk = zk -dTuk + ζk ≥ βk – bk (s,uk,ζk)≥0

  12. Refining Advice Advice Bx ≤ (d - δ) f(x) ≥  Would like to just add to linear programming formulation, but KBSVMs: min ||w||1 + |b| + C||s||1 sum per advice k µ1||zk||1+µ2ζk+ρ||δ||1 such that Y(wTx +b) + s ≥ 1 for each advice k wk+BkTuk = zk (δ-d)Tuk + ζk ≥ βk – bk (s,uk,ζk)≥0 Cannot solve for δ and u simultaneously!

  13. Solution: Successive Linear Programming Rule-Refining Support Vector Machines (RRSVM) algorithm: Set δ=0 Repeat Fix value of δ and solve LP for u Fix value of u and solve LP for δ Until no change to δ or max # of repeats

  14. Experiments Artificial data sets IF(3x1–4x2)>-1 THENclass = + ELSEclass = - Data randomly generated (with and w/o noise) Errors added (e.g., -1 dropped) to make advice Promoter data set Data: Towell et al. (1990) Domain theory: Ortega (1995)

  15. Methodology • Experiments repeated twenty times • Artificial data results – training and test set randomly generated (separately) • Promoter data – ten fold cross validation • Parameters chosen using cross validation (ten folds) on training data Standard SVMs: C KBSVMs: C, µ1, µ2 RRSVMs: C, µ1, µ2 , ρ

  16. Related Work • Knowledge-Based Kernel Methods • Fung et al., NIPS 2002, COLT 2003 • Mangasarian et al., JMLR 2005 • Maclin et al., AAAI 2005, 2006 • Le et al., ICML 2006 • Mangasarian and Wild, IEEE Trans Neural Nets 2006 • Knowledge Refinement • Towell et al., AAAI 1990 • Pazzani and Kibler, MLJ 1992 • Ourston and Mooney, AIJ 1994 • Extracting Learned Knowledge from Networks • Fu, AAAI 1991 • Towell and Shavlik, MLJ 1993 • Thrun, 1995 • Fung et al., KDD 2005

  17. Future Work • Test on other domains • Address limitations (speed, # of parameters) • Refine multipliers of antecedents • Add additional terms to rules • Investigate rule extraction methods

  18. Conclusions RRSVM • Key idea: refine advice by adjusting thresholds of rules • Can produce more accurate models • Able to produce changes to advice • Have shown that RRSVM converges

  19. Acknowledgements • US Naval Research Laboratory grant N00173-06-1-G002 (to RM) • DARPA grant HR0011-04-1-0007 (to JS)

  20. Questions?

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