Learning Optimal Subsets with Implicit User Preferences

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Learning Optimal Subsets with Implicit User
Preferences

• Presentation for NIPS SISO, 12/12/2008.
• Yunsong Guo
• Computer Science Department, Cornell University
• Joint work with Carla Gomes

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Motivation

• Many interesting problems can be abstracted
• as an optimal subset selection problem
• movie recommendation
• shopping
• knapsack
• set covering
• The optimal subset is often induced from a users
  preferences.

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Motivation

• Example 1 choosing photos
• (CMU Face Images Dataset)
• Preference 1
• All passport photos
• Preference 2
• If more angry faces than happy ones,
• choose all angry otherwise all happy faces
• that are with sunglasses or looking up

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Motivation

• Preference can take different forms.
• Subset items may depend on each other.
• Difficult to learn an explicit preference model
  with high accuracy in general.
• We hope to model preferences implicitly with
  better performance.

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Problem Formulation

• Let
• ground set refers to a collection of items
• be the space of possible ground sets
• S(x) be the space of subsets for ground set
• We assume S(x) is the power set, so
• Given
• n supervised training examples
• is a ground set, with the corresponding
  optimal subset
• Learn
• A function that minimizes the set
  similarity loss

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Set Loss Function

• The loss function measures the set
  dissimilarity between two chosen subsets.
• Two common examples of set loss functions
• A optimal subset B predicted subset.
• Jaccard Loss
• Dice Loss
• Equals the F1-loss if we interpret as
  precision and as recall.
• Do not encourage exploration when BltA,
  assuming a fixed .

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Set Loss Function

• We propose a new loss function the set loss
• The above is indifferent in B when BltA

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Loss Function Comparison

• We will train to minimize and report
  performance on all , , , precision
  and recall.

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Structured Learning Formulation

• Natural to formulate as a structured learning
  problem
• sets of items as input/output
• Items may depend on one another
• We solve this problem by a Structured SVM
  approach.

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Structured Learning Formulation
(Structured Support Vector Machine for Optimal
Subset selection)
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Structured Learning Optimization

• Cutting plane training method Tsochantaridis et
  al 05
• Training is in polynomial time if the most
  violated constraint can be computed efficiently
• Testing is in polynomial time if the inference
• Can be computed in polynomial time for a new
  ground set x.

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Structured Learning Optimization

• We define the feature map
• For a training instance (x,y), the set loss
  function can be rewritten as
• where

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Structured Learning Optimization

• Consequently
• can be obtained
  in time Joachims 05.
• in testing phase is also
  efficiently computable.

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Preference Formalism

• A preference is a function
• maps a ground set to its optimal subset
• Generally, given a ground set x and preference p,
  the decision problem of whether an item is in
  p(x) is
• NP-complete.
• Difficult even to compute the training set with a
  known preference.
• We assume in this work p(x) is easy to compute.

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Experiment

• Datasets
• CMU face images dataset
• Synthetic blocks dataset

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Experiment

• Preferences
• 8 different tasks (5 for Face, 3 for Blocks)
• Sample preferences
• (Task 1) All passport photos
• (Task 5) If open and happy images consist of more
  than 30 of ground set, and sad and sunglass
  images are less than open and happy, choose all
  sad, else all angry images.
• (Task 8) To build a uniform tower with large
  similar-sided blocks of the same color.

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Experiment

• Methods
• SVMos best performance for C in
• SVMcv 5-fold cross validation on trainset to
  select C
• DDpref best performance from varying and k
  parameters extensively desJardins et al 06

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Experiment Set Accuracy
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Experiment Other Performance Measures
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Experiment Runtime Comparison
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Conclusion

• We formulated the widely applicable subset
  selection problem as a structured learning
  problem.
• Our method learns to minimize a subset-specific
  loss function using structured SVM.
• The efficient training and testing is guaranteed
  by the loss function and feature map
  construction.
• Empirical results show that our method
  outperforms the existing competing method by
  multiple metrics.

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Future Work

• Ranking instead of rank(doc,que), we can model
  rank(doc,que,usr).
• Collaborative filtering Instead of modeling
  similarity among users by personal attributes, we
  can replace the similarity measure from learned
  set selection behaviors.
• A preference is like a relaxed version of a
  constraint (eg. Lagrangian relaxation). How to
  learn implicit and unknown constraints from
  subsets selection examples?

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Thank you

Questions?