Learning User Preferences

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Learning User Preferences
Jason Rennie MIT CSAIL jrennie_at_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
• Identifying Resolving Named Entites
• Tracking Context
• 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
• Translate text to partial ordering or rating
• 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
Ratings
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Single User, Item Features
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Preference Scores
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Many Users, No Features
Features
Weights
Ratings
Preference Scores
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Collaborative Filtering

• Possible goals
• Predict missing entries
• Cluster users or items
• Applications
• Movies, Books
• Genetic Interaction
• Network routing
• Sports performance

items
users
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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

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

• Convex function gt 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
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Immediate-Thresholds
Shashua Levin, 2003
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Some Errors are Better than Others
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Not a Bound on Absolute Diff.
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All-Thresholds Loss
Srebro, Rennie Jaakkola, NIPS 2004
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Experiments
Multi-Class Imm-Thresh All-Thresh p-value
MLS .7486 .7491 .6700 1.7e-18
Hinge .7433 .7628 .6702 6.6e-17
Logistic .7490 .7248 .6623 7.3e-22
Least Squares 1.3368
Rennie Srebro, IJCAI 2005
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Many Users, No Features
Features
Weights
Ratings
Preference Scores
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Background Lp-norms

• L0 non-zero entries lt0,2,0,3,4gt0 3
• L1 absolute value sum lt2,-2,1gt1 5
• L2 Euclidean length lt1,-1gt2 ?2
• General vp (?i vip)1/p

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Background Feature Selection

• Objective Loss Regularization

L1
L2 Squared
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Singular Value Decomposition

• XUSV
• U,V orthogonal (rotation)
• S diagonal, non-negative
• Eigenvalues of XXUSVVSUUSSU are squared
  singular values of X
• Rank s0
• SVD used to obtain least-squares low-rank
  approximation

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Low Rank Matrix Factorization
V
U

X rank k
¼

• Sum-Squared Loss
• Fully Observed Y
• Classification Error Loss
• Partially Observed Y

Use SVD to find Global Optimum
Non-convex No explicit soln.
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Low-Rank Non-Convex Set
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Trace Norm Regularization
Fazel et al., 2001
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Many Users, No Features
Features
V
X
U
Y
Weights
Ratings
Preference Scores
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Max Margin Matrix Factorization
Trace Norm
All-Thresholds Loss

• Convex function of X and ?
• Low rank in X

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(n3) per round
• Stationary points, but no local minima

Rennie Srebro, ICML 2005
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Collaborative Prediction Results
size, sparsity EachMovie 36656x1648, 96 EachMovie 36656x1648, 96 MovieLens 6040x3952, 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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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

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XUXV WUWV
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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-1VX 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. gt 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