1

Intro to RecSys and CCF

Brian Ackerman

2

Roadmap

• Introduction to Recommender Systems & Collaborative Filtering

• Collaborative Competitive Filtering

3

Introduction to Recommender Systems & Collaborative Filtering

4

Motivation

• Netflix has over 20,000 movies, but you may only be interested in a small number of these movies

• Recommender systems can provide personalized suggestions based on a large set of items such as movies– Can be done in a variety of ways, the most popular

is collaborative filtering

5

Collaborative Filtering

• If two users rate a subset of items similarly, then they might rate other items similarly as well

Item A Item B Item C Item D Item EUser 1 ? 3 4 5 3User 2 1 3 4 5 ?

6

Roadmap (RS-CF)

• Motivation• Problem• Main CF Types– Memory-based – User-based– Model-based – Regularized SVD

7

Problem Setting

• Set of users, U• Set of items, I• Users can rate items where rui is user u’s rating

on item i• Ratings are often stored in a rating matrix– R|U|×|I|

8

Sample Rating MatrixItem A Item B Item C Item D Item E Item F Item G Item H Item I

User 1 - 5 - 3 - - 2 - -

User 2 4 - 5 - - 4 - 1 -

User 3 - 4 - 3 - - 2 - -

User 4 1 2 - - - 5 - 3 -

User 5 - - 3 - 4 - - 2 -

User 6 - 2 - - 1 - - 2 -

User 7 4 - - 5 - - 4 - 1

# is a user rating, - means a null entry, not rated

9

Problem

• Input– Rating matrix (R|U|×|I|)– Active user, a (user interacting with the system)

• Output– Prediction for all null entries of the active user

10

Roadmap (RS-CF)

• Motivation• Problem• Main CF Types– Memory-based – User-based– Model-based – Regularized SVD

11

Main Types

• Memory-based– User-based* [Resnick et al. 1994]– Item-based [Sarwar et al. 2001]– Similarity Fusion (User/Item-based) [Wang et al.

2006]• Model-based– SVD (Singular Value Decomposition) [Sarwar et al.

2000]– RSVD (Regularized SVD)* [Funk 2006]

12

User-based

• Find similar user’s– KNN or threshold

• Make prediction

Item A Item B Item C Item D Item E Item F Item G Item H Item I

Active ? 5 ? 3 ? ? 2 ? ?

User 2 4 - 5 - - 4 - 1 -

User 3 - 4 - 3 - - 2 - -

User 4 1 2 - - - 5 - 3 -

User 5 - - 3 - 4 - - 2 -

User 6 - 2 - - 1 - - 2 -

User 7 4 - - 5 - - 4 - 1

13

User-based – Similar Users

• Consider each user (row) to be a vector• Compare each vector to find the similarity

between two users– Let a be the vector for active user and u3 be the

vector for user 3– Cosine similarity can be used to compare vectors

14

User-based – Similar Users

• KNN (k-nearest neighbors or top-k)– Only find the k most similar users

• Threshold– Find all users that are at most θ level of similarity

Item A Item B Item C Item D Item E Item F Item G Item H Item I

User 1 ? 5 - 3 - - 2 - -

User 2 4 - 5 - - 4 - 1 -

User 3 - 4 - 3 - - 2 - -

User 4 1 2 - - - 5 - 3 -

User 5 - - 3 - 4 - - 2 -

User 6 - 2 - - 1 - - 2 -

User 7 4 - - 5 - - 4 - 1

15

User-based – Make Prediction

• Weighted by similarity– Weight each similar user’s rating based on

similarity to active user

Similar users

Prediction for active user on item i

16

Main Types

• Memory-based– User-based* [Resnick et al. 1994]– Item-based [Sarwar et al. 2001]– Similarity Fusion (User/Item-based) [Wang et al.

2006]• Model-based– SVD (Singular Value Decomposition) [Sarwar et al.

2000]– RSVD (Regularized SVD)* [Funk 2006]

17

Regularized SVD

• Netflix data has 8.5 billion entries based on 17 thousand movie and .5 million users

• Only 100 million ratings– 1.1% of all possible ratings

• Why do we need to operate on such a large matrix?

18

Regularized SVD – Setup

• Let each user and item be represented by a feature vector of length k– E.g. Item A may be vector Ak = [a1 a2 a3 … ak]

• Imagine the features for items were fixed– E.g. items are movies and each feature is a genre

such as comedy, drama, etc…• Features of the user vector are how well a

user likes that feature

19

Regularized SVD – Setup

• Consider the movie Die Hard– Its feature vector may be i = [1 0 0] if the features

are action, comedy, and drama• Maybe the user has the feature vector u =

[3.87 2.64 1.32]• We can try to predict a user’s rating using the

dot product of these two vectors– r’ui= u i = [1 0 0] [3.87 2.64 1.32] = 3.87∙ ∙

20

Regularized SVD – Goal

• Try to find values for each item vector that work for all users

• Try to find value for each user vector that can produce the actual rating when taking the dot product with the item vector

• Minimizing the difference between the actual and predicted (based on dot product) rating

21

Regularized SVD – Setup

• In reality, we cannot choose k to be large enough for a fixed number of features– There are too many to consider (e.g. genre, actors,

directors, etc…)• Usually k is only 25 to 50 which reduces the

total size of the matrices to only roughly 25 million to 50 million (compared to 8.5 billion)

• Because of the size of k, the values in the vectors are NOT directly tied to any feature

22

Regularized SVD – Goal

• Let u be a user, i be an item, rui is a rating by user u on item i where R is the set of all ratings, and φu, φi are the vectors

• At first thought, it seems simple to have the following optimization goal

23

Regularized SVD – Overfitting

• Problem is overfitting of the features– Solved by regularization

24

Regularized SVD – Regularization

• Introduce a new optimization goal including a term for regularization

• Minimizing the magnitude of the feature vectors– Controlled by fixed parameters λu and λi

25

Regularized SVD

• Many improvements have been proposed to improve the regularized optimization goal– RSVD2/NSVD1/NSVD2 [Paterek 2007]: added term

for user bias and a term for item bias, minimize number of parameters

– Integrated Neighborhood SVD++ [Koren 2008]: used a neighborhood-based approach to RSVD

26

Roadmap

• Introduction to Recommender Systems & Collaborative Filtering

• Collaborative Competitive Filtering

27

Collaborative Competitive Filtering: Learning Recommender Using Context of User Choice

Georgia Tech and Yahoo! LabsBest Student Paper at SIGIR’11

28

Motivation

• A user may be given 5 random movies and chooses Die Hard– This tells us the user prefers action movies

• A user may be given 5 actions movies and chooses Die Hard over Rocky and Terminator– This tells us the user prefers Bruce Willis

29

Roadmap (CCF)

• Motivation• Problem Setting & Input• Techniques• Extensions

30

Problem Setting

• Set of users, U• Set of items, I• Each user interaction has an offer set O and a

decision set D• Each user interaction is stored as a tuple (u, O,

D) where D is a subset of O

31

CCF InputItem A Item B Item C Item D Item E Item F Item G Item H Item I

U1-S1 1 - - -

U1-S2 - - 1 -

U1-S3 - - - 1

U2-S1 - 1 - - -

U2-S2 - 1 - -

U3-S1 - - - 1

U3-S2 - - - 1

1 means user interaction, - means it was in the offer set

32

Roadmap (CCF)

• Motivation• Problem Setting & Input• Techniques• Extensions

33

Local Optimality of User Choice

• Each item has a potential revenue to the user which is rui

• Users also consider the opportunity cost (OC) when deciding potential revenue– OC is what the user gives up for making a given

decision

• OC is cui = max( i’ | i’ in O \ i)

• Profit is πui= rui – cui

34

Local Optimality of User Choice

• A user interaction is an opportunity give and take process– User is given a set of opportunities– User makes a decision to select one of the many

opportunities– Each opportunity comes with some revenue

(utility or relevance)

35

Competitive Collaborative Filtering

• Local optimality constraint– Each item in the decision set has a revenue higher

than those not in the decision set

– Problem becomes intractable with only this constraint, no unique solution

36

CCF – Hinge Model

• Optimization goal– Minimize error (ξ, slack variable) & model

complexity

37

CCF – Hinge Model

• Find average potential utility– Average utility of non-chosen items

• Constraints– Chosen items have a higher utility– eui is an error term

38

CCF – Hinge Model

• Optimization Goal

– Assume ξ is 0

Average Relevance of Non-chosen Items

39

CCF – How to use results

• We can predict the relevance of all items based on user and item vectors– Can set threshold if more than one item can be

chosen (e.g. θ > .9 implies action)

Item User Action Predicted Relevance

A 1 .98

B - .93

C - .56

D - .25

E - .11

40

Roadmap (CCF)

• Motivation• Problem Setting & Input• Techniques• Extensions

41

Extensions

• Sessions without a response– User does not take any opportunity

• Adding content features– Fixed features for each item rather than a limited

number of parameters to improve accuracy of new item prediction