Intro to RecSys and CCF

Brian Ackerman 1

Roadmap

• •

Introduction to Recommender Systems & Collaborative Filtering

Collaborative Competitive Filtering 2

Introduction to Recommender Systems & Collaborative Filtering

3

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 4

Collaborative Filtering

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

User 1 User 2 Item A ?

1

Item B

3 3

Item C

4 4

Item D

5 5

Item E

3

?

5

Roadmap (RS-CF)

• • • Motivation

Problem

Main CF Types – Memory-based – User-based – Model-based – Regularized SVD 6

Problem Setting

• • • • Set of users, U Set of items, I Users can rate items where r

ui

on item i is user u’s rating Ratings are often stored in a rating matrix –

R

|U|×|I| 7

Sample Rating Matrix

User 1 User 2 User 3 User 4 User 5 User 6 User 7 Item A Item B Item C Item D Item E Item F Item G Item H

5 3 2 1 4 4 2 5 3 3 4 4 5 2 1 3 2 4 2 5 1 4 2

Item I

1 # is a user rating, - means a null entry, not rated 8

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 9

Roadmap (RS-CF)

• • • Motivation Problem

Main CF Types

– Memory-based – User-based – Model-based – Regularized SVD 10

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] 11

User-based

Active User 2 User 3 User 4 User 5 User 6 User 7 Item A Item B Item C Item D Item E Item F Item G Item H

?

5 ?

3 ?

?

2 ?

4 4 5 3 4 2 1 1 4 2 2 3 5 4 1 5 4 3 2 2 • • Find similar user’s – KNN or threshold Make prediction

Item I

?

1 12

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 u

3

vector for user 3 be the – Cosine similarity can be used to compare vectors 13

User-based – Similar Users

User 1 User 2 User 3 User 4 User 5 User 6 Item A Item B Item C Item D Item E Item F Item G Item H

?

5 3 2 4 4 5 3 4 2 1 1 2 2 3 4 1 5 3 2 2 • •

User 7

– 4 5 KNN (k-nearest neighbors or top-k) Only find the k most similar users 4 Threshold – Find all users that are at most θ level of similarity 1

Item I

14

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 15

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]

16

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?

17

Regularized SVD – Setup

• • • Let each user and item be represented by a feature vector of length k – E.g. Item A may be vector A k = [a 1 a 2 a 3 … a k ] 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 18

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

19

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 20

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 21

Regularized SVD – Goal

• • Let u be a user, i be an item, r

ui

is a rating by user u on item i where R is the set of all ratings, and φ u , φ i are the vectors At first thought, it seems simple to have the following optimization goal 22

Regularized SVD – Overfitting

• Problem is overfitting of the features – Solved by regularization 23

Regularized SVD – Regularization

• Introduce a new optimization goal including a term for regularization • Minimizing the magnitude of the feature vectors – Controlled by fixed parameters λ u and λ i 24

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 25

Roadmap

• • Introduction to Recommender Systems & Collaborative Filtering

Collaborative Competitive Filtering

26

Collaborative Competitive Filtering: Learning Recommender Using Context of User Choice Georgia Tech and Yahoo! Labs Best Student Paper at SIGIR’11 27

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 28

Roadmap (CCF)

• • • • Motivation

Problem Setting & Input

Techniques Extensions 29

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 30

CCF Input

U1-S1 U1-S2 U1-S3 U2-S1 U2-S2 U3-S1 U3-S2 Item A Item B Item C Item D Item E Item F Item G Item H

1 1 1 1 1 1 1

Item I

1 means user interaction, - means it was in the offer set 31

Roadmap (CCF)

• • • • Motivation Problem Setting & Input

Techniques

Extensions 32

Local Optimality of User Choice

• • • • Each item has a potential revenue to the user which is r ui 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 c ui = max( i’ | i’ in O \ i) Profit is π ui = r ui – c ui 33

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) 34

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 35

CCF – Hinge Model

• Optimization goal – Minimize error (ξ, slack variable) & model complexity 36

CCF – Hinge Model

• Find average potential utility – Average utility of non-chosen items • Constraints – Chosen items have a higher utility – e ui is an error term 37

CCF – Hinge Model

• Optimization Goal – Assume ξ is 0 Average Relevance of Non-chosen Items 38

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

A 1 B C D E -

Predicted Relevance

.98

.93

.56

.25

.11

39

Roadmap (CCF)

• • • • Motivation Problem Setting & Input Techniques

Extensions

40

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 41