Probabilistic Group Recommendationvia Information Matching

Jagadeesh Gorla (@jgorla)1 Neal Lathia (@neal lathia)2 Stephen Robertson3 Jun Wang (@seawan)1

1University College London

2University of Cambridge

3Microsoft Research Cambridge

What is the problem?• Group recommendation

• How to computePr(group relevance | group, activity)?

• A probabilistic group recommendation model!

What is the problem?

• Group recommendation

• Individual users preferences?• Type of the group (group preferences)?

Type of the groups

• Consensus preferences group

• Relevant to every group member

Type of the groups

• Shared preferences group

• Relevant to every group member, or at-least notdisliked by majority of the group members

Type of the groups

• Split preferences group

• Relevant to at-least one group member• e.g., Group of household members sharing the same

TV but consume at different times

Individual vs. Group preferences

• Individual preferences

Individual vs. Group preferences

• Individual preferences

Individual vs. Group preferences

What if they decide to watch a movie together?

Group recommendations?

Merging individual preferences• Merge and create group profile• Generate recommendations for group

Problem: May present unwanted items, e.g.,Spartacus

Merging individual recommendations• Compute a list of recommendations for each member• Merge the individual lists

Problem: May lose preferences as part of a group

Group recommendations?

Merging individual preferences• Merge and create group profile• Generate recommendations for group

Problem: May present unwanted items, e.g.,Spartacus

Merging individual recommendations• Compute a list of recommendations for each member• Merge the individual lists

Problem: May lose preferences as part of a group

Group recommendations?

Merging individual preferences• Merge and create group profile• Generate recommendations for group

Problem: May present unwanted items, e.g.,Spartacus

Merging individual recommendations• Compute a list of recommendations for each member• Merge the individual lists

Problem: May lose preferences as part of a group

Group recommendations?

Merging individual preferences• Merge and create group profile• Generate recommendations for group

Problem: May present unwanted items, e.g.,Spartacus

Merging individual recommendations• Compute a list of recommendations for each member• Merge the individual lists

Problem: May lose preferences as part of a group

Group recommendations?

Individual preference in a group may vary

Group recommendation should consider,• Individual preferences• Group preferences

Hypothesis,• Group relevance is a function of “individual group

member preferences”

Group recommendations?

Individual preference in a group may vary

Group recommendation should consider,• Individual preferences• Group preferences

Hypothesis,• Group relevance is a function of “individual group

member preferences”

Group recommendations?

Individual preference in a group may vary

Group recommendation should consider,• Individual preferences• Group preferences

Hypothesis,• Group relevance is a function of “individual group

member preferences”

Probabilistic model

Some notation:1 G is a set of users ({u1, u2 · · · , uh})2 Rg = 1 if the item is relevant to the group, and 0

otherwise3 < is a binary vector of individual relevance

Probabilistic model• Group relevance

P (Rg = 1|G, i) ∝Rg∑<

∏hj=1 P (Rj, uj, i|Rg = 1) ×

∏hj=1 P (Rj|uj, i)

• Individual relevance

• Least misery strategy:

P (Rg = 1|G, i) ∝Rg

min{P (R1 = 1|u1, i), · · · , P (Rh = 1|uh, i)}

Probabilistic model• Group relevance

P (Rg = 1|G, i) ∝Rg∑<

∏hj=1 P (Rj, uj, i|Rg = 1) ×

∏hj=1 P (Rj|uj, i)

• Individual relevance

• Least misery strategy:

P (Rg = 1|G, i) ∝Rg

min{P (R1 = 1|u1, i), · · · , P (Rh = 1|uh, i)}

Probabilistic model• Group relevance

P (Rg = 1|G, i) ∝Rg∑<

∏hj=1 P (Rj, uj, i|Rg = 1) ×

∏hj=1 P (Rj|uj, i)

• Individual relevance

• Least misery strategy:

P (Rg = 1|G, i) ∝Rg

min{P (R1 = 1|u1, i), · · · , P (Rh = 1|uh, i)}

Probabilistic model• Group relevance

P (Rg = 1|G, i) ∝Rg∑<

∏hj=1 P (Rj, uj, i|Rg = 1) ×

∏hj=1 P (Rj|uj, i)

• Individual relevance

• Least misery strategy:

P (Rg = 1|G, i) ∝Rg

min{P (R1 = 1|u1, i), · · · , P (Rh = 1|uh, i)}

Relevance to an individual

Name: Jane SmithSex: FemaleAge: 27Location: Ipanema

Product: ShoeType: FormalBrand: ChanelColour: Red

How to compute the relevance between Jane (“girl fromIpanema”) & Shoe?

Relevance to an individual

Name: Jane SmithSex: FemaleAge: 27Location: Ipanema

Product: ShoeType: FormalBrand: ChanelColour: Red

How to compute the relevance between Jane (“girl fromIpanema”) & Shoe?

Relevance to an individual

Traditional approaches:• Neighbourhood approaches

• Assume common feature space• matrix factorisation (e.g., PureSVD)

• Model features as a user/item

Relevance to an individual

Traditional approaches:• Neighbourhood approaches• Assume common feature space

• matrix factorisation (e.g., PureSVD)

• Model features as a user/item

Relevance to an individual

Traditional approaches:• Neighbourhood approaches• Assume common feature space

• matrix factorisation (e.g., PureSVD)

• Model features as a user/item

Relevance to an individual

We want a framework with:• No explicit similarity

• No common feature space• Interpretable features

Information Matching Model (IMM)or

Bi-directional Unified Model

Relevance to an individual

We want a framework with:• No explicit similarity• No common feature space

• Interpretable features

Information Matching Model (IMM)or

Bi-directional Unified Model

Relevance to an individual

We want a framework with:• No explicit similarity• No common feature space• Interpretable features

Information Matching Model (IMM)or

Bi-directional Unified Model

Relevance to an individual

We want a framework with:• No explicit similarity• No common feature space• Interpretable features

Information Matching Model (IMM)or

Bi-directional Unified Model

Idea ...

• Find a best match for Me

• man −−−−→ woman︸ ︷︷ ︸man preferences

+ man←−−−−woman︸ ︷︷ ︸woman preferences

Idea ...

• Find a best match for Me

• man −−−−→ woman︸ ︷︷ ︸man preferences

+ man←−−−−woman︸ ︷︷ ︸woman preferences

Idea ...

• Find a best match for Me

• man −−−−→ woman︸ ︷︷ ︸man preferences

+ man←−−−−woman︸ ︷︷ ︸woman preferences

IMM

U/Q/P α3

α2

α4

α1

. . .

αl

β3

β2

β4

β1

. . .

βk

Pro/D/P/Ad

1

IMM

U/Q/P α3

α2

α4

α1

. . .

αl

β3

β2

β4

β1

. . .

βk

Pro/D/P/Ad

1

IMM

U/Q/P α3

α2

α4

α1

. . .

αl

β3

β2

β4

β1

. . .

βk

Pro/D/P/Ad

1

IMM

U1

U2

. . .

α3

α2

α4

α1

. . .

αl

β3

β2

β4

β1

. . .

βk

Pr1

Pr2

. . .

1

It solves the problem of “Unified Model for InformationRetrieval”

S.E. Robertson, M.E. Maron and W.S. Cooper, Theunified probabilistic model for IR, 1982.

Data

Dataset Users Movies Ratings scaleMovieLens1 1K 1.7K 100K [1-5]MovieLens2 6K 4K 1M [1-5]MoviePilot (Tr) 171K 24K 4.4M [0-100]MoviePilot (Eva) 594 811 4,482 [0-100]

Number of households: 290

Evaluation Methodology

Evaluation:• Individual recommendation• Household recommendation

Individual recommendation• Randomly divide the data (60% training and 40%

testing) – Movie Lens• Rank all the items• Precision@N, NDCG@N and Mean Average

Precision (MAP)

Individual recommendation

Figure: Recommending to Individuals.

Performance Loss

Figure: PureSVD Figure: IMM

Conclusion

• Can develop powerful group recommendation modelswithin the framework

• Take advantage of probabilistic modelling• Individual recommendation is crucial for group

recommendation• Information Matching Model (IMM) framework can

be used to build:• Search• Job matching• People matching (e.g., dating)• Product recommendation (ads, retail, etc.)• Targeted marketing

Thank You & Questions

Acknowledgements:

• This work has been sponsored by• My personal thanks to Ulrich Paquet ( )

Graphical Model

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