1. Transfer Learning for Link Prediction
Qiang Yang, 楊強，香港科大
Hong Kong University of Science and Technology
Hong Kong, China

2. We often find it easier …

3. We often find it easier…

4. We often find it easier…

5. We often find it easier…
自行车
三轮车
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6. Transfer Learning? 迁移学习…
People often transfer knowledge to novel situations
Chess  Checkers
C++  Java
Physics  Computer Science
Transfer Learning:
The ability of a system to recognize and apply knowledge and skills learned in previous tasks to novel tasks (or new domains)
Seems the changes is involved in moving to new tasks is more radical than moving to new domains.

7. But, direct application will not work
Machine Learning:
Training and future (test) data
follow the same distribution, and
are in same feature space

8. When distributions are different
Classification Accuracy (+, -)
Training: 90%
Testing: 60%
Move to front? As distribution. Animation: applictation/tracking 8

9. When features and distributions are different
Classification Accuracy (+, -)
Training: 90%
Testing: 10%
Move to front? As distribution. Animation: applictation/tracking 9 9

10. Cross-Domain Sentiment Classification
Training
Test
Classifier
82.55%
DVD
DVD
Training
Test
Classifier
71.85%
Electronics
DVD

11. When distributions are different
Wireless sensor networks
Different time periods, devices or space
Move to front? As distribution. Animation: applictation/tracking
Device,
Space, or
Time
Day time
Night time
Device 2
Device 1 11

12. When Features are different
Heterogeneous: different feature spaces
Training: Text
Future: Images
The apple is the pomaceous fruit of the apple tree, species Malus domestica in the rose family Rosaceae ...
Apples
Banana is the common name for a type of fruit and also the herbaceous plants of the genus Musa which produce this commonly eaten fruit ...
Bananas

13. Transfer Learning: Source Domains
Input
Output
Source Domains
Source Domain
Target Domain
Training Data
Labeled/Unlabeled
Test Data
Unlabeled

14. Inductive Transfer Learning 目標數據
An overview of
various settings of
transfer learning
Self-taught Learning
源數據
Case 1
No labeled data in a source domain
Inductive Transfer Learning
目標數據
Labeled data are available in a source domain
Labeled data are available in a target domain
Source and target tasks are learnt simultaneously
Multi-task Learning
Case 2
Transfer Learning
Labeled data are available only in a source domain
Assumption: different domains but single task
Transductive Transfer Learning
Domain Adaptation
No labeled data in both source and target domain
Assumption: single domain and single task
Unsupervised Transfer Learning
Sample Selection Bias /Covariance Shift

15. Feature-based Transfer Learning (Dai, Yang et al. ACM KDD 2007)
Source:
Many labeled instances
Target:
All unlabeled instances
Distributions
Feature spaces can be different, but have overlap
Same classes
P(X,Y): different!
CoCC Algorithm (Co-clustering based)
bridge

16. Document-word co-occurrenceDi
Source
Knowledge
transfer
Target Do

17. Co-Clustering based Classification (on 20 News Group dataset)
Using Transfer Learning

18. Talk Outline Transfer Learning: A quick introduction
Link prediction and collaborative filtering problems
Transfer Learning for Sparsity Problem
Codebook Method
CST Method
Collective Link Prediction Method
Conclusions and Future Works 18

19. Network Data Social Networks Information Networks Biological Networks
Facebook, Twitter, Live messenger, etc.
Information Networks
The Web (1.0 with hyperlinks and 2.0 with tags)
Citation network, Wikipedia, etc.
Biological Networks
Gene network, etc.
Other Networks

20. A Real World Study [Leskovec-Horvitz WWW ‘08]
Who talks to whom on MSN messenger
Network: 240M nodes, 1.3 billion edges
Conclusions:
Average path length is 6.6
90% of nodes is reachable <8 steps

21. Global Network Structures
Small world
Six degrees of separation [Milgram 60s]
Clustering and communities
Evolutionary patterns
Long tail distributions
However, the understanding of the global network structures do help us on working with local network structures.

22. Local Network Structures
Link Prediction
A form of Statistical Relational Learning (Taskar and Getoor)
Object classification: predict category of an object based on its attributes and links
Is this person a student?
Link classification: predict type of a link
Are they co-authors?
Link existence: predict whether a link exists or not
(credit: Jure Leskovec, ICML ‘09)

23. Link Prediction Task: predict missing links in a network
Main challenge: Network Data Sparsity

24. Long Tail in Era of Recommendation
Help users discover novel/rare items
The long-tail  recommendation systems

25. Product Recommendation (Amazon.com)25 25

26. Collaborative Filtering (CF)
Wisdom of the crowd, word of mouth,…
Your taste in music/products/movies/… is similar to that of your friends (Maltz & Ehrlich, 1995)
Key issue: who are your friends?
There are many popular . People help people. Reference other people. There may be tons of web pages a particular user havn’t read, or tons of produces not purchased.

27. Taobao.com

29. CF: Neighborhood Based Models
User-based Model
Item-based Model

30. Matrix Factorization model for Link Prediction
We are seeking a low rank approximation for our target matrix
Such that the unknown value can be predicted by ? 1
Low rank Approximation x
m x k
k x n
m x n

31. Examples: Collaborative Filtering1 3 5 2 4 ?
Ideal Setting
Training Data:
Dense Rating Matrix
Density >=2.0%,
Test Data:
Rating Matrix
CF model
RMSE:0.8721

32. Data Sparsity in Collaborative Filtering1 5 3 4 ?
Realistic Setting
Training Data:
Sparse Rating Matrix
Density <=0.6%,
Test Data:
Rating Matrix
CF model
RMSE:0.9748
10%

33. Neighborhood Based Models
User-based Model
Item-based Model
Unified User-Item Model

34. CF as Matrix Factorization
Approximate each rating by the product between the k-dimensional latent feature vector of each user and item
Learning the user and item latent features via minimizing regularized approximation error:

35. Sparsity Problem in Collaborative Filtering
However, in real-world recommender systems ...
Users can rate a limited number of ratings
So rating matrix is too sparse to cluster well

36. Transfer Learning for Collaborative Filtering?
IMDB Database
Amazon.com 36 36

37. Codebook Transfer Bin Li, Qiang Yang, Xiangyang Xue.
Can Movies and Books Collaborate? Cross-Domain Collaborative Filtering for Sparsity Reduction.
In Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence (IJCAI '09), Pasadena, CA, USA, July 11-17, 2009.

38. Main Idea Observations - What “Relatedness” Approach - How to “Relate”
Take MOVIES & BOOKS for example
Users are related in Interest; Items are related in Genre
Approach - How to “Relate”
To MATCH user/item-groups across domains

39. Transfer CF: Problem Setting
Goal
Alleviate the sparsity problem in the target domain by transferring rating knowledge from a related auxiliary (dense) domain
Target task: A sparse p × q rating matrix Xtgt
Auxiliary task: A dense n × m rating matrix Xaux
Xtgt and Xaux are related in user/item categories
Learn informative & compact rating patterns (codebook) from Xaux
Transfer the learned rating patterns to Xaux

40. Codebook Construction
Definition 2.1 (Codebook). A k × l matrix which compresses the cluster-level rating patterns of k user clusters and l item clusters.
Codebook: User prototypes rate on item prototypes
Encoding: Find prototypes for users and items and get indices
Decoding: Recover rating matrix based on codebook and indices

41. Knowledge Sharing via Cluster-Level Rating Matrix
Source (Dense): Encode cluster-level rating patterns
Target (Sparse): Map users/items to the encoded prototypes

42. Step 1: Codebook Construction
Co-cluster rows (users) and columns (items) in Xaux
Get user/item cluster indicators Uaux ∈ {0, 1}n×k, Vaux ∈ {0, 1}m×l

43. Step 2: Codebook Transfer
Objective
Expand target matrix, while minimizing the difference between Xtgt and the reconstructed one
User/item cluster indicators Utgt and Vtgt for Xtgt
Binary weighting matrix W for observed ratings in Xtgt
Alternate greedy searches for Utgt and Vtgt to a local minimum

44. Codebook Transfer Each user/item in Xtgt matches to a prototype in B
Duplicate certain rows & columns in B to reconstruct Xtgt
Codebook is indeed a two-sided data representation

45. Experimental Setup Data Sets Compared Methods Evaluation Protocol
EachMovie (Auxiliary): 500 users × 500 movies
MovieLens (Target): 500 users × 1000 movies
Book-Crossing (Target): 500 users × 1000 books
Compared Methods
Pearson Correlation Coefficients (PCC)
Scalable Cluster-based Smoothing (CBS)
Weighted Low-rank Approximation (WLR)
Codebook Transfer (CBT)
Evaluation Protocol
First 100/200/300 users for training; last 200 users for testing
Given 5/10/15 observable ratings for each test user

46. Experimental Results (1): Books  Movies
MAE Comparison on MovieLens
average over 10 sampled test sets
Lower is better

47. Experimental Results (2)
MAE Comparison on Book-Crossing
average over 10 sampled test sets
Lower is better

48. Limitations of Codebook Transfer
Same rating range
Source and target data must have the same range of ratings [1, 5]
Homogenous dimensions
User and item dimensions must be similar
In reality
Range of ratings can be 0/1 or [1,5]
User and item dimensions may be very different

49. Coordinate System Transfer
Weike Pan, Evan Xiang, Nathan Liu and Qiang Yang.
Transfer Learning in Collaborative Filtering for Sparsity Reduction. 
In Proceedings of the 24th AAAI Conference on Artificial Intelligence (AAAI-10). Atlanta, Georgia, USA. July 11-15, 2010.

50. Types of User Feedback
Explicit feedback: express preferences explicitly
1-5: Rating
?: Missing
Implicit feedback: express preferences implicitly
1: Observed browsing/purchasing
0: Unobserved browsing/purchasing

51. One auxiliary domain (two or more data sources)
Target domain
R: explicit ratings
One auxiliary domain (two or more data sources)
: user u has implicitly browsed/purchased item j

52. Problem Formulation One target domain
, n users and m items.
One auxiliary domain (two data sources)
user side: , shares n common users with R.
item side: , shares m common items with R.
Goal: predict the missing values in R.

53. Our Solution: Coordinate System Transfer
Step 1: Coordinate System Construction ( )
Step 2: Coordinate System Adaptation

54. Step 1: Coordinate System Construction
Coordinate System Transfer
Step 1: Coordinate System Construction
Sparse SVD on auxiliary data
where the matrices give the top d principle coordinates.
Definition (Coordinate System):
A coordinate system is a matrix with columns of orthonormal bases (principle coordinates), where the columns are located in descending order according to their corresponding eigenvalues.

55. Step 1: Coordinate System Adaptation
Coordinate System Transfer
Step 1: Coordinate System Adaptation
Adapt the discovered coordinate systems from the auxiliary domain to the target domain,
The effect from the auxiliary domain
Initialization: take as seed model in target domain,
Regularization:

56. Coordinate System Transfer
Algorithm

57. Data Sets and Evaluation Metrics
Experimental Results
Data Sets and Evaluation Metrics
Data sets (extracted from MovieLens and Netflix)
Mean Absolute Error (MAE) and Root Mean Square Error (RMSE),
Where and are the true and predicted ratings, respectively,
and is the number of test ratings.

58. Baselines and Parameter Settings
Experimental Results
Baselines and Parameter Settings
Baselines
Average Filling
Latent Matrix Factorization (Bell and Koren, ICDM07)
Collective Matrix Factorization (Singh and Gordon, KDD08)
OptSpace (Keshavan, Montanari and Oh, NIPS10)
Average results over 10 random trials are reported

59. Results(1/2) Observations:
CST performs significantly better (t-test) than all baselines at all sparsity levels,
Transfer learning methods (CST, CMF) beat two non-transfer learning methods (AF, LFM).

60. Results(2/2) Experimental Results Observations:
CST consistently improves as d increases, demonstrating the usefulness in avoid overfitting using the auxiliary knowledge,
The improvement (CST vs. OptSpace) is more significant with fewer observed ratings, demonstrating the effectiveness of CST in alleviating data sparsity.

61. Related Work (Transfer Learning)
Cross-domain collaborative filtering
Domain adaptation methods
One-sided:
Two-sided:

62. Limitation of CST and CBT
Different source domains are related to the target domain differently
Book to Movies
Food to Movies
Rating bias
Users tend to rate items that they like
Thus there are more rating = 5 than rating = 2

63. Our Solution: Collective Link Prediction (CLP)
Jointly learn multiple domains together
Learning the similarity of different domains
consistency between domains indicates similarity.
Introduce a link function to correct the bias

64. Bin Cao, Nathan Liu and Qiang Yang.
Transfer Learning for Collective Link Prediction in Multiple Heterogeneous Domains.
In Proceedings of 27th International Conference on Machine Learning (ICML 2010), Haifa, Israel. June 2010.

65. Recommendation with Heterogeneous Domains
Items span multiple, heterogeneous domains for many recommendation systems.
ebay, GoogleReader, douban, etc.

66. Example: Collective Link Prediction1 5 3 4 2 3 1 5 4
Sparse Training Movie Rating Matrix
Dense Auxiliary Book Rating Matrix
Training
Different Rating
Domains
Transfer Learning 1
Different
User behaviors ?
RMSE:0.8855
Predicting
Dense Auxiliary Movie Tagging Matrix
Test Data:
Rating Matrix

67. Inter-task Similarity
Based on Gaussian process models
Key part is the kernel modeling user relation as well as task relation
Darkness indicates the similarity 67

68. Making Prediction Similar to memory-based approach
Similarity between items
Mean of prediction
Similarity between tasks

69. Experimental Settings
Datasets
Movielens, Book-crossing: 5 largest categories
Douban: 3 domains (movie+book+music)
Evaluation metric
Mean Average Precision
Baselines
I-GP: treating domains independently
M-GP: treating domains as one
CMF: Collective Matrix Factorization [Singh & Gordon’08]

70. Experimental Results (I)

71. Experimental Results
The left figure is the case where all task are sparse and evaluated on all tasks; the right figure is the case only the target task is sparse and evaluated on the target task. 71

72. Conclusions and Future Work
Transfer Learning (舉一反三 )
Link prediction is an important task in graph/network data mining
Key Challenge: sparsity
Transfer learning from other domains helps improve the performance

73. Source Information Network Target Information Network
Future Work
Scenario 1:
Our objective is to use the dense source network to help reduce the sparsity of the entire target network
Sparse
Dense
Source Information Network
Target Information Network

74. Source Information Network Target Information Network
Future Work
Scenario 2:
To use a dense source network as a bridge to help connect parts of the target network.
Dense
Dense
Source Information Network
Target Information Network
Sparse

75. Future: Negative Transfer
Helpful: positive transfer
Harmful:
negative transfer
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Neutral:
zero transfer 75

76. Future: Negative Transfer
“To Transfer or Not to Transfer”
Rosenstein, Marx, Kaelbling and Dietterich
Inductive Transfer Workshop, NIPS (Task: meeting invitation and acceptance)

77. Acknowledgement HKUST: Shanghai Jiaotong University: Visiting Students
Sinno J. Pan, Huayan Wang, Bin Cao, Evan Wei Xiang, Derek Hao Hu, Nathan Nan Liu, Vincent Wenchen Zheng
Shanghai Jiaotong University:
Wenyuan Dai, Guirong Xue, Yuqiang Chen, Prof. Yong Yu, Xiao Ling, Ou Jin.
Visiting Students
Bin Li (Fudan U.), Xiaoxiao Shi (Zhong Shan U.),
Group Pictures…