Yehuda Koren

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Collaborative Filtering with Temporal Dynamics

• Yehuda Koren

2
Recommender systems
We Know What You OughtTo Be Watching This Summer
3
Collaborative filtering

• Recommend items based on past transactions of
  users
• Specific data characteristics are irrelevant
• Domain-free
• Can identify elusive aspects
• Two popular approaches
• Matrix factorization
• Neighborhood

4
Movie rating data
Training data
Test data
score date movie user
1 5/7/02 21 1
5 8/2/04 213 1
4 3/6/01 345 2
4 5/1/05 123 2
3 7/15/02 768 2
5 1/22/01 76 3
4 8/3/00 45 4
1 9/10/05 568 5
2 3/5/03 342 5
2 12/28/00 234 5
5 8/11/02 76 6
4 6/15/03 56 6
score date movie user
? 1/6/05 62 1
? 9/13/04 96 1
? 8/18/05 7 2
? 11/22/05 3 2
? 6/13/02 47 3
? 8/12/01 15 3
? 9/1/00 41 4
? 8/27/05 28 4
? 4/4/05 93 5
? 7/16/03 74 5
? 2/14/04 69 6
? 10/3/03 83 6
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Achievable RMSEs on the Netflix data
Global average 1.1296
Find better items
User average 1.0651
Movie average 1.0533
Personalization
Cinematch 0.9514 baseline
Algorithmics
Static neighborhood 0.9002
Static factorization 0.8911
Time effects
Leader 0.8558 10.05 improvement
Inherent noise ????
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Something Happened in Early 2004
2004
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Are movies getting better with time?
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Multiple sources of temporal dynamics

• Item-side effects
• Product perception and popularity are constantly
  changing
• Seasonal patterns influence items popularity
• User-side effects
• Customers ever redefine their taste
• Transient, short-term bias anchoring
• Drifting rating scale
• Change of rater within household

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Temporal dynamics - challenges

• Multiple sources Both items and users are
  changing over time
• Multiple targets Each user/item forms a unique
  time series ? Scarce data per target
• Inter-related targets Signal needs to be shared
  among users foundation of collaborative
  filtering ? cannot isolate multiple problems
• ? Common concept drift methodologies wont
  hold.E.g., underweighting older instances is
  unappealing

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Basic matrix factorization model
users
4 5 5 3 1
3 1 2 4 4 5
5 3 4 3 2 1 4 2
2 4 5 4 2
5 2 2 4 3 4
4 2 3 3 1

items
users
-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1
1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8
.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1
.2 -.4 .1
.5 .6 -.5
.5 .3 -.2
.3 2.1 1.1
-2 2.1 -.7
.3 .7 -1

items
A rank-3 SVD approximation
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Estimate unknown ratings as inner-products of
factors
users
4 5 5 3 1
3 1 2 4 4 5
5 3 4 3 2 1 4 2
2 4 5 4 2
5 2 2 4 3 4
4 2 3 3 1
?

items
users
-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1
1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8
.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1
.2 -.4 .1
.5 .6 -.5
.5 .3 -.2
.3 2.1 1.1
-2 2.1 -.7
.3 .7 -1

items
A rank-3 SVD approximation
12
Estimate unknown ratings as inner-products of
factors
users
4 5 5 3 1
3 1 2 4 4 5
5 3 4 3 2 1 4 2
2 4 5 4 2
5 2 2 4 3 4
4 2 3 3 1
?

items
users
-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1
1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8
.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1
.2 -.4 .1
.5 .6 -.5
.5 .3 -.2
.3 2.1 1.1
-2 2.1 -.7
.3 .7 -1

items
A rank-3 SVD approximation
13
Estimate unknown ratings as inner-products of
factors
users
4 5 5 3 1
3 1 2 4 4 5
5 3 4 3 2 1 4 2
2 4 5 4 2
5 2 2 4 3 4
4 2 3 3 1
2.4

items
users
-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1
1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8
.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1
.2 -.4 .1
.5 .6 -.5
.5 .3 -.2
.3 2.1 1.1
-2 2.1 -.7
.3 .7 -1

items
A rank-3 SVD approximation
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Matrix factorization model
.2 -.4 .1
.5 .6 -.5
.5 .3 -.2
.3 2.1 1.1
-2 2.1 -.7
.3 .7 -1
4 5 5 3 1
3 1 2 4 4 5
5 3 4 3 2 1 4 2
2 4 5 4 2
5 2 2 4 3 4
4 2 3 3 1
-.9 2.4 1.4 .3 -.4 .8 -.5 -2 .5 .3 -.2 1.1
1.3 -.1 1.2 -.7 2.9 1.4 -1 .3 1.4 .5 .7 -.8
.1 -.6 .7 .8 .4 -.3 .9 2.4 1.7 .6 -.4 2.1

• Properties
• SVD isnt defined when entries are unknown ? use
  specialized methods
• Can easily overfit, sensitive to regularization
• Need to separate main effects

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Baseline predictors

• Mean rating 3.7 stars
• The Sixth Sense is 0.5 stars above avg
• Joe rates 0.2 stars below avg
• ?Baseline predictionJoe will rate The Sixth
  Sense 4 stars
• No user-item interaction

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Factor model correction

• Both The Sixth Sense and Joe are placed high on
  the Supernatural Thrillers scale
• ?Adjusted estimateJoe will rate The Sixth Sense
  4.5 stars

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Matrix factorization with biases
Baseline predictors µ global average bu
bias of u bi bias of i
User-item interaction pu user us factors qi
item is factors
?Minimization problem
regularization
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Addressing temporal dynamics

• Factor model conveniently allows separately
  treating different aspects
• We observe changes in
• Rating scale of individual users
• Popularity of individual items
• User preferences

Baseline predictors
User factors
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Parameterizing the model

• Use functional forms bu(t)f(u,t), bi(t)g(i,t),
  pu(t)h(u,t)
• Need to find adequate f(), g(), h()
• General guidelines
• Items show slower temporal changes
• Users exhibit frequent and sudden changes
• Factors pu(t) are expensive to model
• Gain flexibility by heavily parameterizing the
  functions

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Achievable RMSEs on the Netflix data
Global average 1.1296
Find better items
User average 1.0651
Movie average 1.0533
Personalization
Cinematch 0.9514 baseline
Algorithmics
Static neighborhood 0.9002
Static factorization 0.8911
Time effects
Dynamic factorization 0.8794
Grand Prize 0.8563 10 improvement
Inherent noise ????
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Neighborhood-based CF

• Earliest and most common collaborative filtering
  method
• Derive unknown ratings from those of similar
  items (item-item variant)

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Neighborhood modeling
Use item-item weights - wij - to relate items
Need to estimate rating of user u for item i
Deviation from baseline estimate for item j
Baseline predictor
Weight from j to i
Set of items rated by u
constants
learned from the data through optimization
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Optimizing the model
Minimize the squared error function
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Making the model time-aware

• A popular scheme instance weightingdecay the
  significance of outdated events within cost
  function

time decay
Dont do this!
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Why instance weighting isnt suitable?

• Not enough data per user need to exploit all
  signal, including old one
• The learnt parameters wij represent time
  invariant item-item relations. Can be also
  deduced from older actions.
• Two items are related when users rated them
  similarly within a short timeframe, even if this
  happened long ago
• How to do it right?

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Time-aware neighborhood model

• Decay item-item relations based on time distance
• User-specific decay rate controlled by ßu
• All past user behavior is equally considered,
  through cost function

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Temporal neighborhood model delivers same
relative RMSE improvement (0.0117) as temporal
factor model (!)
Global average 1.1296
Find better items
User average 1.0651
Movie average 1.0533
Personalization
Cinematch 0.9514 baseline
Algorithmics
Static neighborhood 0.9002
Static factorization 0.8911
Dynamic neighborhood 0.8885
Time effects
Dynamic factorization 0.8794
Grand Prize 0.8563 10 improvement
Inherent noise ????
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Lessons

• Modeling temporal effects is significant in
  improving recommenders accuracy
• Allow multiple time drifting patterns across
  users and items
• Integrate all users within a single model to
  allow crucial cross-user collaboration
• Model user behavior along full history, do not
  over-emphasize recent actions
• Separate long term values, while excluding
  transient fluctuations from the model
• Sudden, single-day effects are significant
• Modeling past temporal fluctuations helps in
  predicting future behavior, even though we do not
  extrapolate future temporal dynamics

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4 5 5 3 1
3 1 2 4 4 5
5 3 4 3 2 1 4 2
2 4 5 4 2
5 2 2 4 3 4
4 2 3 3 1
3 4 3 2 1
4 5 4
2 4 3 4
3 2
5
2 4
Yehuda Koren Yahoo! Research yehuda_at_yahoo-inc.com