Collaborative Competitive Filtering: Learning

Report
Intro to RecSys and CCF
Brian Ackerman
1
Roadmap
• Introduction to Recommender Systems &
Collaborative Filtering
• Collaborative Competitive Filtering
2
Introduction to Recommender
Systems & Collaborative Filtering
3
Motivation
• Netflix has over 20,000 movies, but you may
only be interested in a small number of these
movies
• Recommender systems can provide
personalized suggestions based on a large set
of items such as movies
– Can be done in a variety of ways, the most
popular is collaborative filtering
4
Collaborative Filtering
• If two users rate a subset of items similarly,
then they might rate other items similarly as
well
User 1
User 2
Item A
?
1
Item B
3
3
Item C
4
4
Item D
5
5
Item E
3
?
5
Roadmap (RS-CF)
• Motivation
• Problem
• Main CF Types
– Memory-based – User-based
– Model-based – Regularized SVD
6
Problem Setting
• Set of users, U
• Set of items, I
• Users can rate items where rui is user u’s rating
on item i
• Ratings are often stored in a rating matrix
– R|U|×|I|
7
Sample Rating Matrix
Item A Item B Item C Item D Item E Item F Item G Item H
Item I
User 1
-
5
-
3
-
-
2
-
-
User 2
4
-
5
-
-
4
-
1
-
User 3
-
4
-
3
-
-
2
-
-
User 4
1
2
-
-
-
5
-
3
-
User 5
-
-
3
-
4
-
-
2
-
User 6
-
2
-
-
1
-
-
2
-
User 7
4
-
-
5
-
-
4
-
1
# is a user rating, - means a null entry, not rated
8
Problem
• Input
– Rating matrix (R|U|×|I|)
– Active user, a (user interacting with the system)
• Output
– Prediction for all null entries of the active user
9
Roadmap (RS-CF)
• Motivation
• Problem
• Main CF Types
– Memory-based – User-based
– Model-based – Regularized SVD
10
Main Types
• Memory-based
– User-based* [Resnick et al. 1994]
– Item-based [Sarwar et al. 2001]
– Similarity Fusion (User/Item-based) [Wang et al.
2006]
• Model-based
– SVD (Singular Value Decomposition) [Sarwar et al.
2000]
– RSVD (Regularized SVD)* [Funk 2006]
11
User-based
Item A Item B Item C Item D Item E Item F Item G Item H
Item I
Active
?
5
?
3
?
?
2
?
?
User 2
4
-
5
-
-
4
-
1
-
User 3
-
4
-
3
-
-
2
-
-
User 4
1
2
-
-
-
5
-
3
-
User 5
-
-
3
-
4
-
-
2
-
User 6
-
2
-
-
1
-
-
2
-
User 7
4
-
-
5
-
-
4
-
1
• Find similar user’s
– KNN or threshold
• Make prediction
12
User-based – Similar Users
• Consider each user (row) to be a vector
• Compare each vector to find the similarity
between two users
– Let a be the vector for active user and u3 be the
vector for user 3
– Cosine similarity can be used to compare vectors
13
User-based – Similar Users
Item A Item B Item C Item D Item E Item F Item G Item H
Item I
User 1
?
5
-
3
-
-
2
-
-
User 2
4
-
5
-
-
4
-
1
-
User 3
-
4
-
3
-
-
2
-
-
User 4
1
2
-
-
-
5
-
3
-
User 5
-
-
3
-
4
-
-
2
-
User 6
-
2
-
-
1
-
-
2
-
User 7
4
-
-
5
-
-
4
-
1
• KNN (k-nearest neighbors or top-k)
– Only find the k most similar users
• Threshold
– Find all users that are at most θ level of similarity
14
User-based – Make Prediction
• Weighted by similarity
– Weight each similar user’s rating based on
similarity to active user
Similar users
Prediction for active
user on item i
15
Main Types
• Memory-based
– User-based* [Resnick et al. 1994]
– Item-based [Sarwar et al. 2001]
– Similarity Fusion (User/Item-based) [Wang et al.
2006]
• Model-based
– SVD (Singular Value Decomposition) [Sarwar et al.
2000]
– RSVD (Regularized SVD)* [Funk 2006]
16
Regularized SVD
• Netflix data has 8.5 billion entries based on 17
thousand movie and .5 million users
• Only 100 million ratings
– 1.1% of all possible ratings
• Why do we need to operate on such a large
matrix?
17
Regularized SVD – Setup
• Let each user and item be represented by a
feature vector of length k
– E.g. Item A may be vector Ak = [a1 a2 a3 … ak]
• Imagine the features for items were fixed
– E.g. items are movies and each feature is a genre
such as comedy, drama, etc…
• Features of the user vector are how well a
user likes that feature
18
Regularized SVD – Setup
• Consider the movie Die Hard
– Its feature vector may be i = [1 0 0] if the features
are action, comedy, and drama
• Maybe the user has the feature vector u =
[3.87 2.64 1.32]
• We can try to predict a user’s rating using the
dot product of these two vectors
– r’ui= u ∙ i = [1 0 0] ∙ [3.87 2.64 1.32] = 3.87
19
Regularized SVD – Goal
• Try to find values for each item vector that
work for all users
• Try to find value for each user vector that can
produce the actual rating when taking the dot
product with the item vector
• Minimizing the difference between the actual
and predicted (based on dot product) rating
20
Regularized SVD – Setup
• In reality, we cannot choose k to be large
enough for a fixed number of features
– There are too many to consider (e.g. genre, actors,
directors, etc…)
• Usually k is only 25 to 50 which reduces the
total size of the matrices to only roughly 25
million to 50 million (compared to 8.5 billion)
• Because of the size of k, the values in the
vectors are NOT directly tied to any feature
21
Regularized SVD – Goal
• Let u be a user, i be an item, rui is a rating by
user u on item i where R is the set of all
ratings, and φu, φi are the vectors
• At first thought, it seems simple to have the
following optimization goal
22
Regularized SVD – Overfitting
• Problem is overfitting of the features
– Solved by regularization
23
Regularized SVD – Regularization
• Introduce a new optimization goal including a
term for regularization
• Minimizing the magnitude of the feature
vectors
– Controlled by fixed parameters λu and λi
24
Regularized SVD
• Many improvements have been proposed to
improve the regularized optimization goal
– RSVD2/NSVD1/NSVD2 [Paterek 2007]: added term
for user bias and a term for item bias, minimize
number of parameters
– Integrated Neighborhood SVD++ [Koren 2008]:
used a neighborhood-based approach to RSVD
25
Roadmap
• Introduction to Recommender Systems &
Collaborative Filtering
• Collaborative Competitive Filtering
26
Collaborative Competitive Filtering:
Learning Recommender Using
Context of User Choice
Georgia Tech and Yahoo! Labs
Best Student Paper at SIGIR’11
27
Motivation
• A user may be given 5 random movies and
chooses Die Hard
– This tells us the user prefers action movies
• A user may be given 5 actions movies and
chooses Die Hard over Rocky and Terminator
– This tells us the user prefers Bruce Willis
28
Roadmap (CCF)
•
•
•
•
Motivation
Problem Setting & Input
Techniques
Extensions
29
Problem Setting
• Set of users, U
• Set of items, I
• Each user interaction has an offer set O and a
decision set D
• Each user interaction is stored as a tuple (u, O,
D) where D is a subset of O
30
CCF Input
Item A Item B Item C Item D Item E Item F Item G Item H
U1-S1
1
-
U1-S2
-
-
U1-S3
-
-
-
1
-
-
-
-
U2-S2
U3-S2
1
-
U2-S1
U3-S1
-
Item I
1
1
-
-
-
-
-
1
-
-
1
1 means user interaction, - means it was in the offer set
31
Roadmap (CCF)
•
•
•
•
Motivation
Problem Setting & Input
Techniques
Extensions
32
Local Optimality of User Choice
• Each item has a potential revenue to the user
which is rui
• Users also consider the opportunity cost (OC)
when deciding potential revenue
– OC is what the user gives up for making a given
decision
• OC is cui = max( i’ | i’ in O \ i)
• Profit is πui= rui – cui
33
Local Optimality of User Choice
• A user interaction is an opportunity give and
take process
– User is given a set of opportunities
– User makes a decision to select one of the many
opportunities
– Each opportunity comes with some revenue
(utility or relevance)
34
Competitive Collaborative Filtering
• Local optimality constraint
– Each item in the decision set has a revenue higher
than those not in the decision set
– Problem becomes intractable with only this
constraint, no unique solution
35
CCF – Hinge Model
• Optimization goal
– Minimize error (ξ, slack variable) & model
complexity
36
CCF – Hinge Model
• Find average potential utility
– Average utility of non-chosen items
• Constraints
– Chosen items have a higher utility
– eui is an error term
37
CCF – Hinge Model
• Optimization Goal
– Assume ξ is 0
Average Relevance of
Non-chosen Items
38
CCF – How to use results
• We can predict the relevance of all items
based on user and item vectors
– Can set threshold if more than one item can be
chosen (e.g. θ > .9 implies action)
Item User Action
Predicted Relevance
A
1
.98
B
-
.93
C
-
.56
D
-
.25
E
-
.11
39
Roadmap (CCF)
•
•
•
•
Motivation
Problem Setting & Input
Techniques
Extensions
40
Extensions
• Sessions without a response
– User does not take any opportunity
• Adding content features
– Fixed features for each item rather than a limited
number of parameters to improve accuracy of
new item prediction
41

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