F. Petroni, L. Querzoni, R. Beraldi, M. Paolucci: "LCBM: Statistics-Based Parallel Collaborative Filtering." In: Proceedings of the 17th International Conference on Business Information Systems (BIS), 2014. Abstract: "In the last ten years, recommendation systems evolved from novelties to powerful business tools, deeply changing the internet industry. Collaborative Filtering (CF) represents today’s a widely adopted strategy to build recommendation engines. The most advanced CF techniques (i.e. those based on matrix factorization) provide high quality results, but may incur prohibitive computational costs when applied to very large data sets. In this paper we present Linear Classifier of Beta distributions Means (LCBM), a novel collaborative filtering algorithm for binary ratings that is (i) inherently parallelizable and (ii) provides results whose quality is on-par with state-of-the-art solutions (iii) at a fraction of the computational cost."

1. LCBM: Statistics-based Parallel
Collaborative Filtering
Fabio Petroni 1, Leonardo Querzoni 1, Roberto Beraldi 1, Mario Paolucci 2
Cyber Intelligence and information Security
CIS Sapienza
1
Department of Computer Control and
Management Engineering Antonio Ruberti,
Sapienza University of Rome -
petroni|querzoni|beraldi@dis.uniroma1.it
2
Institute of Cognitive Sciences
and Technologies, CNR -
mario.paolucci@istc.cnr.it
Larnaca, Cyprus
22-23 May, 2014

2. Personalization
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 subclass of information filtering
system that seek to predict the rating or preference that user
would give to an item.
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3. 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.
Filtering
filter the user data stream
satisfying user personal interests
Discovery
recommends new content to the
user that matches his interests
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4. Challenges
I Key factors for recommendation e↵ectiveness:
amount of data available
larger data-sets improve quality
more than better algorithms
timeliness
timely deliver output to users
constitutes a business advantage
7 Most CF algorithms typically need to go through a very lengthy
training stage, incurring in prohibitive computational costs and
large time-to-prediction intervals when applied on large data sets.
7 This lack of e ciency is going to quickly limit the applicability of
these solutions at the current rates of data production growth.
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5. Taxonomy Of CF Algorithms
MEMORY-
BASED
MODEL-
BASED
Collaborative
Filtering
neighborhood
models
user-oriented item-oriented
Pearson
Correlation
Similarity
Cosine
Similarity
cluster
models
Bayesian
networks
linear
regression
LATENT
FACTORS
MODELS
pLSA
neural
networks
Latent
Dirichlet
Allocation
MATRIX
FACTORIZATION
ALS SGD SVD
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6. Memory-Based CF Algorithms
I Operate on the entire set of ratings to generate predictions:
B compute a similarity score, which reflects the distance between two
users or two items.
- Pearson Correlation Similarity
- Cosine Similarity
B Predictions are computed by looking at the ratings of the k most
similar users or items (k-nearest neighbor).
3 Simple design and implementation;
3 used in a lot of real-world systems.
7 Impose several scalability limitations;
7 their use is impractical when dealing with large amounts of data.
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7. Model-Based CF Algorithms
I Use the set of available ratings to estimate or learn a model and
then apply this model to make rating predictions.
I The most successful are based on matrix factorization models.
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8. Matrix Factorization 1/2
LOSS(P, Q) =
X
(Rij Pi Qj )2
I The most popular techniques to minimize LOSS are Alternating
Least Squares (ALS) and Stochastic Gradient Descent (SGD).
ALS
ALS alternates between keeping
P and Q fixed, solving from time
to time a least-squares problem.
SGD
SGD works by taking steps
proportional to the negative of the
gradient of the LOSS function.
I Both algorithms need several passes through the set of ratings.
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9. Matrix Factorization 2/2
3 Provide high quality results;
3 SGD was chosen by the top three solutions of KDD-Cup 2011;
3 there exist parallel and distributed implementations.
7 High computational costs;
7 large time-to-prediction intervals;
7 especially when applied on large data sets.
SGD ALS LCBM
training time O(X · K · E) ⌦(K3
(N + M) + K2
X) O(X)
prediction time O(K) O(K) O(1)
memory usage O(K(N + M)) O(M2 + X) O(N + M)
In the table X is the number of collected ratings, K the number of hidden
features, E the iterations, N and M the number of users and items respectively.
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10. Contributions
In this paper we present:
LCBM: Linear Classifier of Beta distributions Means
a novel collaborative filtering algorithm for binary ratings that:
3 is inherently parallelizable;
3 provides results whose quality is on-par with state-of-the-art
solutions;
3 in shorter time;
3 using less computational resources.
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11. Overview
LCBM
Working phase
ratings
Training phase
Item rating PDF
inferenceratings per
item
User profiler
ratings per
user
standard
error
mean
>
predictions
threshold
I We consider:
B items as elements whose tendency to be rated positively/negatively
can be statistically characterized using a probability density function;
B users as entities with di↵erent tastes that rate the same items using
di↵erent criteria and that must thus be profiled;
I The algorithm needs two passes over the set of available ratings
to train the model (build users and items profiles).
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12. Item Rating PDF Inference
I Beta distribution:
B X = the relative frequency of positive
votes that the item will receive.
B ↵ = OK + 1, = KO + 1
Item profile
MEAN = ↵
↵+ = OK+1
OK+KO+2
SE = 1
OK+KO+2
q
(OK+1)(KO+1)
(OK+KO)(OK+KO+3)
I Chebyshev’s inequality:
Pr(MEAN SE  X  MEAN+ SE) 1
1
2
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
PDF
X
I Example:
B OK = 8, KO = 3
B MEAN ⇡ 0.7
B SE ⇡ 0.04
– Pr(0.62  X  0.78) 0.75
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13. User Profiler
0.1 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.65 0.7 0.8 0.85
discriminant function
OK errors KO errors
I Every rating is represented by a point with two attributes:
B a boolean value containing the rating (OK or KO).
B a key 2 [0, 1] that gives the point’s rank in the order;
I if value = OK ! key = MEAN + SE
I if value = KO ! key = MEAN SE
User profile
Quality threshold (QT) = the discriminant function of a 1D linear
classifier that separates the points with a minimal number of errors.
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14. Working Phase
LCBM
Working phase
ratings
Training phase
Item rating PDF
inferenceratings per
item
User profiler
ratings per
user
standard
error
mean
>
predictions
threshold
I In order to produce a prediction the algorithm simply compares
QT values from the user profiler with MEAN values from the
item’s rating PDF inference block:
B if MEAN > QT ! prediction = OK
B if MEAN  QT ! prediction = KO
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15. Experiments: Setting and The Data Sets
Dataset MovieLens 100k MovieLens 10M Netflix
users 943 69878 480189
items 1682 10677 17770
ratings 100000 10000054 100480507
I 5-fold cross-validation approach:
B This technique divides the dataset in 5 folds and then uses in turn
one of the folds as test set and the remaining ones as training set.
I We compared LCBM against CF
implementations in Apache Mahout:
B ParallelSGDFactorizer: lock-free and parallel implementation of SGD
B ALSWRFactorizer: ALS with Weighted- -Regularization
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16. Experiments: Performance Metrics
I Confusion matrix: true positives (TP) false negatives (FN)
false positives (FP) true negatives (TN)
I Matthews correlation coe cient (MCC) 2 [ 1, 1]
MCC =
TP ⇥ TN FP ⇥ FN
p
(TP + FP) ⇥ (TP + FN) ⇥ (TN + FP) ⇥ (TN + FN)
B 1 ! perfect prediction;
B 0 ! no better than random prediction;
B 1 ! total disagreement between prediction and observation.
I time needed to run the test;
I the peak memory load during the test.
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17. Results: Accuracy
0
0.1
0.2
0.3
0.4
0.5
0.6
MovieLens (105
) MovieLens (107
) Netflix (108
)
MCC
number of ratings
LCBM
SGD K=256
SGD K=32
SGD K=8
ALS
0
0.1
0.2
0.3
0.4
0.5
0.6
MovieLens (105
) MovieLens (107
) Netflix (108
)
MCC
number of ratings
LCBM
SGD K=256
SGD K=32
SGD K=8
ALS
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18. Results: Computational Resources
0
2
4
6
8
10
12
14
16
18
20
MovieLens (105
) MovieLens (107
) Netflix (108
)
memory(GB)
number of ratings
LCBM
SGD K=256
SGD K=32
SGD K=8
ALS
0
2
4
6
8
10
12
14
16
18
20
MovieLens (105
) MovieLens (107
) Netflix (108
)
memory(GB)
number of ratings
LCBM
SGD K=256
SGD K=32
SGD K=8
ALS
0
0.2
Zoom
0
0.2
Zoom
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19. Results: Timeliness
0
500
1000
1500
2000
2500
3000
3500
4000
4500
MovieLens (105
) MovieLens (107
) Netflix (108
)
time(s)
number of ratings
LCBM
SGD K=256
SGD K=32
SGD K=8
ALS
0
500
1000
1500
2000
2500
3000
3500
4000
4500
MovieLens (105
) MovieLens (107
) Netflix (108
)
time(s)
number of ratings
LCBM
SGD K=256
SGD K=32
SGD K=8
ALS
0
10
Zoom
0
10
Zoom
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20. Conclusions
I LCBM is a novel CF algorithm with binary ratings.
I It works by analyzing collected ratings to:
B infer a probability density function of the relative frequency of
positive votes that the item will receive;
B compute a personalized quality threshold for each user.
I These two information are used to predict missing ratings.
I LCBM is inherently parallelizable.
Future works:
I Handle multidimensional ratings.
I Provide recommendations: a list of items the user will like the
most.
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21. Thank you!
Questions?
Fabio Petroni
Rome, Italy
Current position:
PhD Student in Computer Engineering, Sapienza University of Rome
Research Areas:
Recommendation Systems, Collaborative Filtering, Distributed Systems
petroni@dis.uniroma1.it
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