IIR 2016, VENEZIA, ITALYCOMPUTING NEIGHBOURHOODS WITH LANGUAGEMODELS IN A COLLABORATIVE FILTERING SCENARIO

Daniel Valcarce, Javier Parapar, Álvaro Barreiro@dvalcarce @jparapar @AlvaroBarreiroG

Information Retrieval Lab@IRLab_UDC

University of A CoruñaSpain

Outline

1. Introduction to Recommender Systems

2. Neighbourhood-based Methods

3. Computing Neighbourhoods

4. Language Models for Neighbourhoods

5. Experiments

6. Conclusions and Future Directions

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INTRODUCTION TO RECOMMENDER SYSTEMS

Recommender Systems

Recommender systems provide personalised suggestions foritems that may be of interest to the users.

Top-N Recommendation: create a ranking of the N mostrelevant items for each user.

Different approaches:

# Content-based: exploit item description to recommenditems similar to those the target user liked in the past.

# Collaborative filtering: rely on the user feedback such asratings or clicks to generate recommendations.

# Hybrid: combination of content-based and collaborativefiltering approaches.

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Recommender Systems

Recommender systems provide personalised suggestions foritems that may be of interest to the users.

Top-N Recommendation: create a ranking of the N mostrelevant items for each user.

Different approaches:

# Content-based: exploit item description to recommenditems similar to those the target user liked in the past.

# Collaborative filtering: rely on the user feedback such asratings or clicks to generate recommendations.

# Hybrid: combination of content-based and collaborativefiltering approaches.

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Collaborative Filtering

Collaborative Filtering (CF) exploit feedback from users:

# Explicit: ratings or reviews.# Implicit: clicks or purchases.

Two main families of CF methods:

# Model-based: learn a model from the data and use it forrecommendation.

# Neighbourhood-based (or memory-based): computerecommendations using directly part of the ratings.

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Collaborative Filtering

Collaborative Filtering (CF) exploit feedback from users:

# Explicit: ratings or reviews.# Implicit: clicks or purchases.

Two main families of CF methods:

# Model-based: learn a model from the data and use it forrecommendation.

# Neighbourhood-based (or memory-based): computerecommendations using directly part of the ratings.

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NEIGHBOURHOOD-BASED METHODS

Neighbourhood-based Methods

Two perspectives:

# User-based: recommend items that users with commoninterests with you liked.

# Item-based: recommend items similar to those you liked.Similarity between items is computed using common usersamong items (not the content!).

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Weighted Sum Recommender (WSR)

Very simple but effective approach (Valcarce et al., ECIR 2016).

WSR computes a weighted sum of the ratings in theneighbourhood. Weights are calculated using cosine similarity.

Item-based version (WSR-IB):

r̂u ,i �∑j∈ Ji

cosine�i , j

�ru , j (1)

User-based version (WSR-UB):

r̂u ,i �∑v∈Vu

cosine (u , v) rv ,i (2)

The computation of neighbourhoods is crucial!

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Weighted Sum Recommender (WSR)

Very simple but effective approach (Valcarce et al., ECIR 2016).

WSR computes a weighted sum of the ratings in theneighbourhood. Weights are calculated using cosine similarity.

Item-based version (WSR-IB):

r̂u ,i �∑j∈ Ji

cosine�i , j

�ru , j (1)

User-based version (WSR-UB):

r̂u ,i �∑v∈Vu

cosine (u , v) rv ,i (2)

The computation of neighbourhoods is crucial!

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COMPUTING NEIGHBOURHOODS

Computing Neighbourhoods with k-NN algorithm

The effectiveness of neighbourhood-based methods relieslargely on how neighbours are computed.

The most common approach is to compute the k nearestneighbours (k-NN algorithm) using a pairwise similarity.

# The most common similarities are Pearson’s correlationcoefficient or cosine similarity.

# Cosine provides important improvements over Pearson’scorrelation coefficient (Cremonesi et al., RecSys 2010).

Let’s study cosine similarity from the perspective ofInformation Retrieval.

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Computing Neighbourhoods with k-NN algorithm

The effectiveness of neighbourhood-based methods relieslargely on how neighbours are computed.

The most common approach is to compute the k nearestneighbours (k-NN algorithm) using a pairwise similarity.

# The most common similarities are Pearson’s correlationcoefficient or cosine similarity.

# Cosine provides important improvements over Pearson’scorrelation coefficient (Cremonesi et al., RecSys 2010).

Let’s study cosine similarity from the perspective ofInformation Retrieval.

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Cosine Similarity and the Vector Space Model

Recommendation Information Retrieval

Target user QueryRest of users Documents

Items Terms

Under this scheme, using cosine similarity for findingneighbours is equivalent to search in the Vector Space Model.

If we swap users and items, we can derive an analogousitem-based approach.

We can use sophisticated search techniques for findingneighbours!

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Cosine Similarity and the Vector Space Model

Recommendation Information Retrieval

Target user QueryRest of users Documents

Items Terms

Under this scheme, using cosine similarity for findingneighbours is equivalent to search in the Vector Space Model.

If we swap users and items, we can derive an analogousitem-based approach.

We can use sophisticated search techniques for findingneighbours!

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Cosine Similarity and the Vector Space Model

Recommendation Information Retrieval

Target user QueryRest of users Documents

Items Terms

Under this scheme, using cosine similarity for findingneighbours is equivalent to search in the Vector Space Model.

If we swap users and items, we can derive an analogousitem-based approach.

We can use sophisticated search techniques for findingneighbours!

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Cosine Similarity and the Vector Space Model

Recommendation Information Retrieval

Target user QueryRest of users Documents

Items Terms

Under this scheme, using cosine similarity for findingneighbours is equivalent to search in the Vector Space Model.

If we swap users and items, we can derive an analogousitem-based approach.

We can use sophisticated search techniques for findingneighbours!

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LANGUAGE MODELS FOR NEIGHBOURHOODS

Language Models

Statistical language models are a state-of-the-art framework fordocument retrieval.

Documents are ranked according to their posterior probabilitygiven the query:

p(d |q) � p(q |d) p(d)p(q)

rank� p(q |d) p(d)

The query likelihood, p(q |d), is based on a unigram model:

p(q |d) �∏t∈q

p(t |d)c(t ,d)

The document prior, p(d), is usually considered uniform.

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Language Models

Statistical language models are a state-of-the-art framework fordocument retrieval.

Documents are ranked according to their posterior probabilitygiven the query:

p(d |q) � p(q |d) p(d)p(q)

rank� p(q |d) p(d)

The query likelihood, p(q |d), is based on a unigram model:

p(q |d) �∏t∈q

p(t |d)c(t ,d)

The document prior, p(d), is usually considered uniform.

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Language Models

Statistical language models are a state-of-the-art framework fordocument retrieval.

Documents are ranked according to their posterior probabilitygiven the query:

p(d |q) � p(q |d) p(d)p(q)

rank� p(q |d) p(d)

The query likelihood, p(q |d), is based on a unigram model:

p(q |d) �∏t∈q

p(t |d)c(t ,d)

The document prior, p(d), is usually considered uniform.

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Language Models for Finding Neighbourhoods (I)

Information Retrieval:

p(d |q) rank� p(d)

∏t∈q

p(t |d)c(t ,d)

User-based collaborative filtering:

p(v |u) rank� p(v)

∏i∈Iu

p(i |v)rv ,i

Item-based collaborative filtering:

p( j |i) rank� p( j)

∏u∈Ui

p(u | j)ru , j

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Language Models for Finding Neighbourhoods (II)

User-based collaborative filtering:

p(v |u) rank� p(v)

∏i∈Iu

p(i |v)rv ,i

We assume a multinomial distribution over the count of ratings.The maximum likelihood estimate (MLE) is:

pmle(i |v) � rv ,i∑j∈Iv rv , j

However it suffers from sparsity. We need smoothing!

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Language Models for Finding Neighbourhoods (II)

User-based collaborative filtering:

p(v |u) rank� p(v)

∏i∈Iu

p(i |v)rv ,i

We assume a multinomial distribution over the count of ratings.The maximum likelihood estimate (MLE) is:

pmle(i |v) � rv ,i∑j∈Iv rv , j

However it suffers from sparsity. We need smoothing!

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Smoothing Methods for Language Models

Absolute Discounting (AD)

pδ(i |u) � max(ru ,i − δ, 0) + δ |Iu | p(i |C)∑j∈Iu ru , j

Jelinek-Mercer (JM)

pλ(i |u) � (1 − λ) ru ,i∑j∈Iu ru , j

+ λ p(i |C)

Dirichlet Priors (DP)

pµ(i |u) � ru ,i + µ p(i |C)µ +∑

j∈Iu ru , j

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EXPERIMENTS

Experimental settings

Baselines:

# Pearson’s correlation coefficient# RM1Sim: user-based similarity (Bellogín et al., RecSys ’13)# Cosine similarity

Our similarities are Language Models using:

# Absolute Discounting smoothing# Jelinek-Mercer smoothing# Dirichlet Priors smoothing

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Parameter Sensibility of WSR-UB on MovieLens 100k

0.18

0 1k 2k 3k 4k 5k 6k 7k 8k 9k 10k

0.280.300.320.340.360.380.40

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

µ

nDC

G@

10

λ, δ

PearsonCosine

RM1Sim (λ)LM-Absolute Discounting (δ)

LM-Jelinek-Mercer (λ)LM-Dirichlet Priors (µ)

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Parameter Sensibility of WSR-IB on R3-Yahoo!

0.0120.0140.0160.0180.0200.0220.0240.0260.0280.030

100 101 102 103 104 105 106

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

nDC

G@

10

µ

λ, δ

PearsonCosine

LM-Absolute Discounting (δ)LM-Jelinek-Mercer (λ)

LM-Dirichlet Priors (µ)

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Precision (nDCG@10)

Algorithm ML 100k ML 1M R3-Yahoo LibraryThing

NNCosNgbr 0.1427 0.1042 0.0138 0.0550PureSVD 0.3595a 0.3499ac 0.0198a 0.2245a

Cosine-WSR 0.3899ab 0.3430a 0.0274ab 0.2476ab

LM-DP-WSR 0.4017abc 0.3585abc 0.0271ab 0.2464ab

LM-JM-WSR 0.4013abc 0.3622abcd 0.0276ab 0.2537abcd

Table: Values of precision in terms of normalised discountedcumulative gain at 10. Statistical significance is superscripted(Wilcoxon two-sided p < 0.01). Pink = best algorithm. Blue = notsignificantly different to the best.

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Diversity (Gini@10)

Algorithm ML 100k ML 1M R3-Yahoo! LibraryThing

Cosine-WSR 0.0549 0.0400 0.0902 0.1025LM-DP-WSR 0.0659 0.0435 0.1557 0.1356LM-JM-WSR 0.0627 0.0435 0.1034 0.1245

Table: Values of the complement of the Gini index at 10.Pink = best algorithm.

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Novelty (MSI@10)

Algorithm ML 100k ML 1M R3-Yahoo! LibraryThing

Cosine-WSR 11.0579 12.4816 21.1968 41.1462LM-DP-WSR 11.5219 12.8040 25.9647 46.4197LM-JM-WSR 11.3921 12.8417 21.7935 43.5986

Table: Values of novelty in terms of Mean Self Information at 10.Pink = best algorithm.

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CONCLUSIONS AND FUTURE DIRECTIONS

Conclusions

Statistical language models are a powerful tool for computingneighbourhoods in a collaborative filtering scenario. Combinedwith WSR, language models:

# Provide highly accurate recommendations.# Improve novelty and diversity figures compared to cosine.# Have low computational complexity.

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Future work

Explore other probability distributions:

# Multivariate Bernoulli.# Multivariate Poisson.

Evaluate the use of inverted indexes to computeneighbourhoods:

# Efficiency.# Scalability.

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THANK YOU!

@DVALCARCEhttp://www.dc.fi.udc.es/~dvalcarce