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Learning User Preferences Jason Rennie MIT CSAIL jrennie@gmail.com Advisor: Tommi Jaakkola

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Information Extraction Informal Communication: e-mail, mailing lists, bulletin boards Issues: –Context switching –Abbreviations & shortened forms –Variable punctuation, formatting, grammar

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Thesis Advertisement: Outline Thesis is not end-to-end IE system We address some IE problems: 1.Identifying & Resolving Named Entites 2.Tracking Context 3.Learning User Preferences

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Identifying Named Entities Rialto is now open until 11pm Facts/Opinions usually about a named entity Tools typically rely on punctuation, capitalization, formatting, grammar We developed criterion to identify topic- oriented words using occurrence stats [Rennie & Jaakkola, SIGIR 2005]

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Resolving Named Entites Theyre now open until 11pm What does they refer to? Clustering –Group noun phrases that co-refer McCallum & Wellner (2005) –Excellent for proper nouns Our contribution: better modeling of non- proper nouns (incl. pronouns)

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Tracking Context The Swordfish was fabulous –Indirect comment on restaurant. –Restaurant identifed by context. Use word statistics to find topic switches Contribution: new sentence clustering algorithm

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Learning User Preferences Examples: –I loved Rialto last night. –Overall, Oleana was worth the money –Radius wasnt bad, but wasnt great –Om was purely pretentious Issues: 1.Translate text to partial ordering or rating 2.Predict unobserved ratings

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Preference Problems Single User w/ Item Features Multi-user, no features –Aka Collaborative Filtering

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Single User, Item Features -0.1 +10+500+2 User Weights +8-4+1-7-6-3 Preference Scores Capacity Price French? New American? Ethnic? Formality Location 10 Tables#9 ParkLumiereTanjoreChennaiRndzvous 309060804080 306050302040 101000 010001 000110 243102 231202 Feature Values 4 =6 3 =3 2 =-2 1 =-5 5 1 3 2 4 Ratings

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Single User, Item Features ??????? User Weights ?????? Preference Scores Capacity Price French? New American? Ethnic? Formality Location 10 Tables#9 ParkLumiereTanjoreChennaiRndzvous 309060804080 306050302040 101000 010001 000110 243102 231202 Feature Values 5231?? Ratings

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-2.51.4-0.95.63.1-1.8 -2.70.2-4.22.10.2-4.2 2.1-2.51.4-0.95.63.1 -1.8-2.70.2-4.22.1-2.5 1.4-0.95.63.1-1.8-2.7 0.2-4.2-1.40.73.4-0.8 1.9-2.24.72.6-3.5-2.1 Many Users, No Features 232323 215124 121313 523524 425215 333532 452435 ? ???? ?? ?? ???? ??? ??? Weights Features Preference Scores Ratings ?? ?

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Possible goals: –Predict missing entries –Cluster users or items Applications: –Movies, Books –Genetic Interaction –Network routing –Sports performance Collaborative Filtering 232323 215124 121313 523524 425215 333532 452435 users items

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Outline Single User, Features –Loss functions, Convexity, Large Margin –Loss function for Ratings Many Users, No Features –Feature Selection, Rank, SVD –Regularization: tie together multiple tasks –Optimization: scale to large problems Extensions

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This Talk: Contributions Implementation and systematic evaluation of loss functions for Single User prediction. Scaling Multi-user regularization to large (thousands of users/items) problems –Analysis of optimization Extensions –Hybrid: features + multiple users –Observation model & multiple ratings

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Rating Classification n ordered classes Learn weight vector, thresholds 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 w

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Loss Functions 0-1Hinge Logistic Margin Agreement Smooth Hinge Mod. Least Squares

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Convexity Convex function => no local minima Set convex if all line segments within set

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Convexity of Loss Functions 0-1 loss is not convex –Local minima, sensitive to small changes Convex Bound –Large margin solution with regularization –Stronger guarantees

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Proportional Odds McCullagh introduced original rating model –Linear interaction: weights & features –Thresholds –Maximum likelihood [McCullagh, 1980] 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 w

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Immediate-Thresholds 1 2 3 4 5 [Shashua & Levin, 2003]

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Some Errors are Better than Others User: System 1:System 2:

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Not a Bound on Absolute Diff. 1 2 3 4 5

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All-Thresholds Loss 1 2 3 4 5 [Srebro, Rennie & Jaakkola, NIPS 2004]

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Experiments Multi- Class Imm- Thresh All- Thresh p-value MLS.7486.7491.67001.7e-18 Hinge.7433.7628.67026.6e-17 Logistic.7490.7248.66237.3e-22 Least Squares: 1.3368 [Rennie & Srebro, IJCAI 2005]

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Many Users, No Features 232323 215124 121313 523524 425215 333532 452435 ? ???? ?? ?? ???? ??? ??? -2.51.4-0.95.63.1-1.8 -2.70.2-4.22.10.2-4.2 2.1-2.51.4-0.95.63.1 -1.8-2.70.2-4.22.1-2.5 1.4-0.95.63.1-1.8-2.7 0.2-4.2-1.40.73.4-0.8 1.9-2.24.72.6-3.5-2.1 Weights Features Preference Scores Ratings ?? ?

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Background: L p -norms L 0 : # non-zero entries: || || 0 = 3 L 1 : absolute value sum: || || 1 = 5 L 2 : Euclidean length: || || 2 = 2 General: ||v|| p = ( i |v i | p ) 1/p

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Background: Feature Selection Objective: Loss + Regularization L 2 Squared L1L1

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Singular Value Decomposition X=USV –U,V: orthogonal (rotation) –S: diagonal, non-negative Eigenvalues of XX=USVVSU=USSU are squared singular values of X Rank = ||s|| 0 SVD: used to obtain least-squares low- rank approximation

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Low Rank Matrix Factorization V U × ¼ X rank k = 245142 312254 424131 33424 231432 22145 241423 131143 422531 Y Use SVD to find Global Optimum Non-convex No explicit soln. Sum-Squared Loss Fully Observed Y Classification Error Loss Partially Observed Y

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Low-Rank: Non-Convex Set Rank 1 Rank 2

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Trace Norm Regularization [Fazel et al., 2001] Trace Norm: sum of singular values y

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Many Users, No Features 232323 215124 121313 523524 425215 333532 452435 -2.51.4-0.95.63.1-1.8 -2.70.2-4.22.10.2-4.2 2.1-2.51.4-0.95.63.1 -1.8-2.70.2-4.22.1-2.5 1.4-0.95.63.1-1.8-2.7 0.2-4.2-1.40.73.4-0.8 1.9-2.24.72.6-3.5-2.1 Weights Features Preference Scores Ratings U V X Y

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Max Margin Matrix Factorization Convex function of X and Low rank in X All-Thresholds Loss Trace Norm [Srebro, Rennie & Jaakkola, NIPS 2004]

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Properties of the Trace Norm The factorization: U S, V S minimizes both quantities

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Factorized Optimization Factorized Objective (tight bound): Gradient descent: O(n 3 ) per round Stationary points, but no local minima [Rennie & Srebro, ICML 2005]

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Collaborative Prediction Results size, sparsity: EachMovie 36656x1648, 96% MovieLens 6040x3952, 96% Algorithm Weak Error Strong Error Weak Error Strong Error URP.8596.8859.6946.7104 Attitude.8787.8845.6912.7000 MMMF.8548.8439.6650.6725 [URP & Attitude: Marlin, 2004] [MMMF: Rennie & Srebro, 2005]

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Extensions Multi-user + Features Observation model –Predict which restaurants a user will rate, and –The rating she will make Multiple ratings per user/restaurant –E.g. Food, Service and Décor ratings SVD Parameterization

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Fixed Features Learned Features Multi-User + Features Feature parameters (V): –Some are fixed –Some are learned Learn weights (U) for all features Fixed part of V does not affect regularization V

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Observation Model Common assumption: ratings observed at random Restaurant selection: –Geography, popularity, price, food style Remove bias: model observation process

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Observation Model Model as binary classification Add binary classification loss Tie together rating and observation models X=U X V W=U W V

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Multiple Ratings Users may provide multiple ratings: –Service, Décor, Food Add in loss functions Stack parameter matrices for regularization

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SVD Parameterization Too many parameters: UAA -1 V=X is another factorization of X Alternate: U,S,V –U,V orthogonal, S diagonal Advantages: –Not over-parameterized –Exact objective (not a bound) –No stationary points

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Summary Loss function for ratings Regularization for multiple users Scaled MMMF to large problems (e.g. > 1000x1000) Trace norm: widely applicable Extensions Code: http://people.csail.mit.edu/jrennie/matlab

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Thanks! Helen, for supporting me for 7.5 years! Tommi Jaakkola, for answering all my questions and directing me to the end! Mike Collins and Tommy Poggio for addl guidance. Nati Srebro & John Barnett for endless valuable discussions and ideas. Amir Globerson, David Sontag, Luis Ortiz, Luis Perez-Breva, Alan Qi, & Patrycja Missiuro & all past members of Tommis reading group for paper discussions, conference trips and feedback on my talks. Many, many others who have helped me along the way!

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Low-Rank Optimization Low-Rank Minimum Objective Minimum Low-Rank Local Minimum Low- Rank Low- Rank

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