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Overview • Matrix Factoriza<on Model • asymmetric MF
• Objec<ve: op<mize various Ranking Metrics • exploit proper<es of MF model & implicit data
• Training: pointwise & listwise • Related Work • Experiments
Basic Idea:
data .
items i
users u
≈ users u
Low-‐rank Matrix Factoriza<on Model
Basic Idea:
-‐ latent user vector: -‐ by [Paterek 07], extended to SVD++ [Koren 08]
Asymmetric Matrix Factoriza<on
Overview • Matrix Factoriza<on Model • asymmetric MF
• Objec5ve: op5mize various Ranking Metrics • exploit proper5es of MF model & implicit data
• Training: pointwise & listwise • Related Work • Experiments
AMF as Neural Network
rank loss = f (ranks)
items i … click history
… user vec.
… scores … ranks
AMF as Neural Network
rank loss = f (ranks)
items i … click history
… user vec.
… scores … ranks
1st term: Rank Loss example 1: AUC • pairwise comparisons ! (linear) sum of ranks
example 2: nDCG (for binary relevance) • emphasizes top of ranked list • also a func<on of the ranks of the posi<ves
1st term: Rank Loss
2nd term: Ac<va<on Func<on
T
Scores ! Ranks: + + + -‐ binary data: nega<ves and posi<ves -‐ sparse data: many few ! MF scores: Gaussian distrib. assumed
scores i
score
rank
1
N
Scores ! Ranks:
2nd term: Ac<va<on Func<on
score
score
… piecewise quadra<c
2nd term: Ac<va<on Func<on
3rd term • score:
• deriva<ve:
Pueng it All Together
training objec<ve func<on: rank prior on param’s scores of loss " lambda nega<ves "gamma -‐ minimized by stochas<c gradient descent
Overview • Matrix Factoriza<on Model • asymmetric MF
• Objec<ve: op<mize various Ranking Metrics • exploit proper<es of MF model & data
• Training: pointwise & listwise • Related Work • Experiments
Listwise Approach
• consider ALL items for each user:
-‐ es<mate standard devia<on of scores for each user ! width of ac<va<on func<on
Listwise Approach
• consider ALL items for each user: -‐ sort by scores ! exact ranks -‐ using logis<c ac<va<on func<on: 2nd term in chain rule
AUC
nDCG
Listwise Approach
deriva5ves L’: 1st & 2nd terms top of ranked list
! between nDCG and AUC: L’ = constant ! use very large std. for ac<va<on func<on in pointwise approach
AUC
nDCG
Pointwise Approach
deriva5ves L’: top of ranked list
Overview • Matrix Factoriza<on Model • asymmetric MF
• Objec<ve: op<mize various Ranking Metrics • exploit proper<es of MF model & data
• Training • Related Work • Experiments
Related Work
• various learning-‐to-‐rank approaches exist • ogen tailored to specific ranking losses • mostly pairwise approaches, eg: • AUC: BPR [Rendle et al. ’09] • MRR: CLiMF [Shi et al. ’12] used as • MAP: TFMAP [Shi et al. ‘12] baselines
• listwise approaches, eg: • top-‐1 [Shi et al. ’10] ... like neural network
• … addi<onal references in the paper
Overview • Matrix Factoriza<on Model • basic MF ! asymmetric MF ! Neural Network
• Objec<ve: op<mize various Ranking Metrics • exploit proper<es of MF model & data
• Training • Related Work • Experiments
10 m MovieLens Data
• 10k movies & 70k users • 1% dense data • binarized: 3+ star ra<ng ! 1, otherwise 0 • 5-‐fold cross-‐valida<on
10 m MovieLens Data
5-‐fold cross-‐valida<on std : 0.001
10 m MovieLens Data
std=0.002
Nellix Play Data • Test day: 4/9/2014 • rela(ve improvement to RMSE training
std=1%
Nellix Play Data
std=2%
Conclusions • learning-‐to-‐rank approach: – implicit feedback data – proper<es of MF model ! Gaussian distribu<on of scores ! non-‐linear ac<va<on func<ons derived for ranking
• pointwise and listwise training • various ranking metrics can be used: – compe<<ve for op<mizing AUC – par<cularly effec<ve at head of ranked list
Thank You ! Ques5ons ?
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