IntroductionRecommenderSystems_Petroni.pdf

Introduction to Recommender Systems
Fabio Petroni

About me
Fabio Petroni
Sapienza University of Rome, Italy
Current position:
PhD Student in Engineering in Computer Science
Research Interests:
data mining, machine learning, big data
petroni@dis.uniroma1.it
I slides available at
http://www.fabiopetroni.com/teaching
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Materials
I Xavier Amatriain Lecture at Machine Learning Summer
School 2014, Carnegie Mellon University
B https://youtu.be/bLhq63ygoU8
B https://youtu.be/mRToFXlNBpQ
I Recommender Systems course by Rahul Sami at Michigan’s
Open University
B http://open.umich.edu/education/si/si583/winter2009
I Data Mining and Matrices Course by Rainer Gemulla at
University of Mannheim
B http://dws.informatik.uni-mannheim.de/en/teaching/courses-
for-master-candidates/ie-673-data-mining-and-matrices/
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Age of discovery
The Age of Search has come to an end
• ... long live the Age of Recommendation!
• Chris Anderson in “The Long Tail”
• “We are leaving the age of information and entering the age
of recommendation”
• CNN Money, “The race to create a 'smart' Google”:
• “The Web, they say, is leaving the era of search and
entering one of discovery. What's the difference? Search is
what you do when you're looking for something. Discovery
is when something wonderful that you didn't know existed,
or didn't know how to ask for, finds you.”
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Web Personalization & Recommender Systems
I Most of todays internet businesses deeply root their success
in the ability to provide users with strongly personalized
experiences.
I Recommender Systems are a particular type of personalized
Web-based applications that provide to users personalized
recommendations about content they may be interested in.
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Example 2
Example: Amazon
Recommendations
http://www.amazon.com/
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The tyranny of choice
Information overload
“People read around 10 MB worth of material a day, hear 400 MB a
day, and see 1 MB of information every second” - The Economist, November 2006
In 2015, consumption will raise to 74 GB a day - UCSD Study 2014
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The value of recommendations
• Netflix: 2/3 of the movies watched are
recommended
• Google News: recommendations generate
38% more clickthrough
• Amazon: 35% sales from recommendations
• Choicestream: 28% of the people would buy
more music if they found what they liked.
u
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Recommendation process
users
items
feedback
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Input
Sources of information
• Explicit ratings on a numeric/ 5-star/3-star etc. scale
• Explicit binary ratings (thumbs up/thumbs down)
• Implicit information, e.g.,
– who bookmarked/linked to the item?
– how many times was it viewed?
– how many units were sold?
– how long did users read the page?
• Item descriptions/features
• User profiles/preferences
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Methods of a aggregating inputs
I Content-based filtering
B recommendations based on item descriptions/features, and
profile or past behavior of the “target” user only.
I Collaborative filtering
B look at the ratings of like-minded users to provide
recommendations, with the idea that users who have expressed
similar interests in the past will share common interests in the
future.
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Collaborative Filtering
I Collaborative Filtering (CF) represents today’s a widely
adopted strategy to build recommendation engines.
I CF analyzes the known preferences of a group of users to
make predictions of the unknown preferences for other users.
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Collaborative filtering
I problem
B set of users
B set of items (movies, books, songs, ...)
B feedback
I explicit (ratings, ...)
I implicit (purchase, click-through, ...)
I predict the preference of each user for each item
B assumption: similar feedback $ similar taste
I example (explicit feedback):
Avatar The Matrix Up
Marco 4 2
Luca 3 2
Anna 5 3
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Collaborative filtering
I problem
B set of users
B set of items (movies, books, songs, ...)
B feedback
I explicit (ratings, ...)
I implicit (purchase, click-through, ...)
I predict the preference of each user for each item
B assumption: similar feedback $ similar taste
I example (explicit feedback):
Marco ? 4 2
Luca 3 2 ?
Anna 5 ? 3
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Collaborative filtering taxonomy
SVD PMF
user based PLS(A/I)
memory
based
collaborative
filtering
item based
model
based
probabilistic
methods
neighborhood
models
dimensionality
reduction
matrix
completion
latent
Dirichlet
allocation
other machine
learning
methods
Bayesian
networks
Markov
decision
processes
neural
networks
I Memory-based use the ratings to compute similarities
between users or items (the “memory" of the system) that are
successively exploited to produce recommendations.
I Model-based use the ratings to estimate or learn a model
and then apply this model to make rating predictions.
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Memory based
neighborhood models
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The CF Ingredients
● List of m Users and a list of n Items
● Each user has a list of items with associated opinion
○ Explicit opinion - a rating score
○ Sometime the rating is implicitly – purchase records
or listen to tracks
● Active user for whom the CF prediction task is
performed
● Metric for measuring similarity between users
● Method for selecting a subset of neighbors
● Method for predicting a rating for items not currently
rated by the active user.
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Collaborative Filtering
The basic steps:
1. Identify set of ratings for the target/active user
2. Identify set of users most similar to the target/active user
according to a similarity function (neighborhood
formation)
3. Identify the products these similar users liked
4. Generate a prediction - rating that would be given by the
target user to the product - for each one of these products
5. Based on this predicted rating recommend a set of top N
products
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User-based Collaborative Filtering
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User-User Collaborative
Filtering
Target User
Weighted
Sum
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UB Collaborative Filtering
● A collection of user ui
, i=1, …n and a collection
of products pj
, j=1, …, m
● An n × m matrix of ratings vij
, with vij
= ? if user
i did not rate product j
● Prediction for user i and product j is computed
as
• Similarity can be computed by Pearson correlation
or
or
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Item-based Collaborative Filtering
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Item-Item Collaborative
Filtering
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Item Based CF Algorithm
● Look into the items the target user has rated
● Compute how similar they are to the target item
○ Similarity only using past ratings from other
users!
● Select k most similar items.
● Compute Prediction by taking weighted average
on the target user’s ratings on the most similar
items.
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Item Similarity Computation
● Similarity between items i & j computed by finding
users who have rated them and then applying a
similarity function to their ratings.
● Cosine-based Similarity – items are vectors in the m
dimensional user space (difference in rating scale
between users is not taken into account).
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Prediction Computation
● Generating the prediction – look into the target
users ratings and use techniques to obtain
predictions.
● Weighted Sum – how the active user rates the
similar items.
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Item-based CF Example
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Performance Implications
● Bottleneck - Similarity computation.
● Time complexity, highly time consuming with
millions of users and items in the database.
○ Isolate the neighborhood generation and
predication steps.
○ “off-line component” / “model” – similarity
computation, done earlier & stored in memory.
○ “on-line component” – prediction generation
process.
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Challenges Of User-based CF
Algorithms
● Sparsity – evaluation of large item sets, users purchases
are under 1%.
● Difficult to make predictions based on nearest neighbor
algorithms =>Accuracy of recommendation may be poor.
● Scalability - Nearest neighbor require computation that
grows with both the number of users and the number of
items.
● Poor relationship among like minded but sparse-rating
users.
● Solution : usage of latent models to capture similarity
between users & items in a reduced dimensional space.
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Model based
dimensionality reduction
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What we were interested in:
■ High quality recommendations
Proxy question:
■ Accuracy in predicted rating
■ Improve by 10% = $1million!
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SVD/MF
X[n x m] = U[n x r] S [ r x r] (V[m x r])T
● X: m x n matrix (e.g., m users, n videos)
● U: m x r matrix (m users, r factors)
● S: r x r diagonal matrix (strength of each ‘factor’) (r: rank of the
matrix)
● V: r x n matrix (n videos, r factor)
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Recap: Singular Value Decomposition
• SVD is useful in data analysis
Noise removal, visualization, dimensionality reduction, . . .
• Provides a mean to understand the hidden structure in the data
We may think of Ak and its factor matrices as a low-rank model
of the data:
• Used to capture the important aspects of the data
(cf. principal components)
• Ignores the rest
• Truncated SVD is best low-rank factorization of the data in
terms of Frobenius norm
• Truncated SVD Ak = Uk kV T
k of A thus satisfies
A Ak F = min
rank(B)=k
A B F
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SVD problems
I complete input matrix: all entries available and considered
I large portion of missing values
I heuristics to pre-fill missing values
B item’s average rating
B missing values as zeros
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Matrix completion
I Matrix completion techniques avoid the necessity of
pre-filling missing entries by reasoning only on the observed
ratings.
I They can be seen as an estimate or an approximation of the
SVD, computed using application specific optimization
criteria.
I Such solutions are currently considered as the best
single-model approach to collaborative filtering, as
demonstrated, for instance, by the Netflix prize.
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Matrix completion for collaborative filtering
I the completion is driven by a factorization
R P Q
I associate a latent factor vector with each user and each item
I missing entries are estimated through the dot product
rij ⇡ piqj
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Latent factor models (Koren et al., 2009)
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Latent factor models
Discover latent factors (r = 1)
Anni 4 2
Bob 3 2
Charlie 5 3
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(2.24) (1.92) (1.18)
Anni 4 2
(1.98)
Bob 3 2
(1.21)
Charlie 5 3
(2.30)
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(2.24) (1.92) (1.18)
Anni 4 2
(1.98) (3.8) (2.3)
Bob 3 2
(1.21) (2.7) (2.3)
Charlie 5 3
(2.30) (5.2) (2.7)
Minimum loss
min
Q,P
(i,j)
(vij [QT
P]ij )2
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(2.24) (1.92) (1.18)
Anni ? 4 2
(1.98) (4.4) (3.8) (2.3)
Bob 3 2 ?
(1.21) (2.7) (2.3) (1.4)
Charlie 5 ? 3
(2.30) (5.2) (4.4) (2.7)
Minimum loss
min
Q,P
(i,j)
(vij [QT
P]ij )2
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(2.24) (1.92) (1.18)
Anni ? 4 2
(1.98) (4.4) (3.8) (2.3)
Bob 3 2 ?
(1.21) (2.7) (2.3) (1.4)
Charlie 5 ? 3
(2.30) (5.2) (4.4) (2.7)
Minimum loss
min
Q,P,u,m
(i,j)
(vij µ ui mj [QT
P]ij )2
Bias
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(2.24) (1.92) (1.18)
Anni ? 4 2
(1.98) (4.4) (3.8) (2.3)
Bob 3 2 ?
(1.21) (2.7) (2.3) (1.4)
Charlie 5 ? 3
(2.30) (5.2) (4.4) (2.7)
Minimum loss
min
Q,P,u,m
(i,j)
(vij µ ui mj [QT
P]ij )2
+ ( Q + P + u + m )
Bias, regularization
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(2.24) (1.92) (1.18)
Anni ? 4 2
(1.98) (4.4) (3.8) (2.3)
Bob 3 2 ?
(1.21) (2.7) (2.3) (1.4)
Charlie 5 ? 3
(2.30) (5.2) (4.4) (2.7)
Minimum loss
min
Q,P,u,m
(i,j,t) t
(vij µ ui (t) mj (t) [QT
(t)P]ij )2
+ ( Q(t) + P + u(t) + m(t) )
Bias, regularization, time, . . .
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Example: Netflix prize data
Root mean square error of predictions
COVER FEATURE
M
collabor
mender
datasets s
data has
accuracy
nearest-n
the same
pact me
that syste
easily. W
niques ev
that mod
rally man
data, suc
feedback
and conf
40
60
90
128
180
50
100
200
50
100
200
100
200 500
50
100 200 500 1,000
1,500
0.875
0.88
0.885
0.89
0.895
0.9
0.905
0.91
10 100 1,000 10,000 100,000
Millionsofparameters
RMSE
Plain
With biases
With implicit feedback
With temporal dynamics (v.1)
With temporal dynamics (v.2)
Figure 4. Matrix factorization models’ accuracy. The plots show the root-mean-square 57 of 65

Matrix reconstruction (unregularized)
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Stochastic gradient descent
I parameters ⇥ = {P, Q}
I find minimum ⇥⇤
of loss
function L
I pick a starting point ⇥0
I iteratively update current
estimations for ⇥
6
7
0 5 10 15 20 25 30
loss
(×
10
7
)
iterations
⇥n+1 ⇥n ⌘
@L
@⇥
I learning rate ⌘
I an update for each given training point
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Stochastic updates
Lij (P, Q) = (rij pi qj )2
I SGD to minimize the squared loss iteratively computes:
pi pi ⌘
@Lij (P, Q)
@pi
= pi + ⌘("ij · qj )
qj qj ⌘
@Lij (P, Q)
@qj
= qj + ⌘("ij · pi )
I where "ij = rij pi qj
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Suggested reading
I G. Linden, B. Smith, and J. York. Amazon.com recommendations:
Item-to-item collaborative filtering. Internet Computing, IEEE,
7(1):76–80, 2003.
I Y. Koren, R. Bell, and C. Volinsky. Matrix factorization techniques
for recommender systems. Computer, 42(8):30–37, 2009.
I X. Su and T. M. Khoshgoftaar. A survey of collaborative filtering
techniques. Advances in Artificial Intelligence, 2009:4, 2009.
I F. Ricci, L. Rokach, and B. Shapira. Introduction to recommender
systems handbook. Springer, 2011.
I M. D. Ekstrand, J. T. Riedl, and J. A. Konstan. Collaborative filtering
recommender systems. Foundations and Trends in Human-Computer
Interaction, 4(2):81–173, 2011.
I J. A. Konstan and J. Riedl. Recommender systems: from algorithms to
user experience. User Modeling and User-Adapted Interaction,
22(1-2):101–123, 2012.
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