Ranking prediction by online learning Rbert Plovics Informatics - PowerPoint PPT Presentation

Ranking prediction by online learning Róbert Pálovics Informatics Laboratory, Department of Computer and Automation Research Institute, Hungarian Academy of Sciences https://dms.sztaki.hu/en July 2, 2015

O UTLINE ◮ Online ranking prediction ◮ Exploiting social influence in online RS ◮ Location-aware online learning

R ECOMMENDER SYSTEMS ◮ Utility matrix R , only a few known values ◮ Rating prediction vs. ranking prediction ◮ Explicit vs implicit data ◮ Collaborative filtering vs. contend based

O NLINE RANKING PREDICTION ◮ Online recommendation – after each event recommend a new top list of items – after each event update the recommender model – implicit data ◮ Temporal evaluation – for each tuple < u , i , t > (user, item, timestamp) – evaluate the given single tuple in question against the recommended top list ◮ Iterate on the dataset only at once < u , i , t > tuple time

O NLINE RANKING PREDICTION ◮ Evaluate the given single tuple in question against the recommended top list ◮ There is only one single relevant item, use  0 if rank ( i ) > K ;   DCG@K ( a ) = 1 otherwise .  log 2 ( rank ( i ) + 1 )  top list for < u , i , t > i rank ( i )

M ATRIX FACTORIZATION R = P · Q , where P ∈ R n × k and Q ∈ R k × m , ˆ ◮ Model ˆ r ui = p u · q i ◮ Objective - mean squared error (MSE), for ( u , i ) ∈ Tr r ui ) 2 F ui = ( r ui − ˆ ◮ Optimization - stochastic gradient descent (SGD) p u ← p u − lrate · ∂ F = p u − lrate · Err · q i ∂ p u Items q p r Users

O NLINE M ATRIX F ACTORIZATION ◮ Single iteration over the training data in temporal order ◮ Updating after each new element ◮ High learning rates ◮ More emphasis on recent events ◮ Works well on non-stationary datasets

N ETWORK I NFLUENCE ◮ User-User social graph + User-Item activity time series (bipartite graph) ◮ Detect social influences, influential pairs ◮ Improve top- k recommendation Time User u Time series User v Social network

L AST . FM ◮ Online service in music based social networking ◮ "Scrobbling": collecting listening activity of users ◮ Music recommendation system ◮ Social network ◮ Users see each others scrobbling activity

I NFLUENCE P ROBABILITY ◮ Key concept: influence between neighbors u and v , a ;∆ t ≤ t – subsequent scrobble, v − − − − → u – and the reason is influence ◮ Influence probability a ;∆ t ≤ t a ;∆ t ≤ t a ;∆ t ≤ t P ( Influence , v − − − − → u ) = P ( Influence | v − − − − → u ) · P ( v − − − − → u ) v , a , t v scrobbles of user v subsequent scrobble, possible influence time scrobbles of user u < u , a , t u >

I NFLUENCE P ROBABILITY , L EFT T ERM a ;∆ t ≤ t a ;∆ t ≤ t a ;∆ t ≤ t P ( Influence , v − − − − → u ) = P ( Influence | v − − − − → u ) · P ( v − − − − → u ) ◮ Approximation by measurements a ;∆ t ≤ t P ( Influence | v − − − − → u ) ≈ P ( Influence | ∆ t ≤ t ) ≈ 1 − c log t ◮ Slowly decreasing logarithmic function

I NFLUENCE P ROBABILITY , R IGHT T ERM a ;∆ t ≤ t a ;∆ t ≤ t a ;∆ t ≤ t P ( Influence , v − − − − → u ) = P ( Influence | v − − − − → u ) · P ( v − − − − → u ) a ;∆ t ≤ t ◮ Probability of event v − − − − → u in the time series ◮ Learned by modeling v u a v a a u v u

E XPERIMENTS - A BOUT L AST . FM ◮ Available for us under NDA for Last.fm, selection criteria ◮ Structure: network + scrobbling time series – 71 , 000 users, 285 , 241 edges – 2 year scrobble timeline, 2 , 073 , 395 artists – between 01 January 2010 and 31 December 2011 – 979 , 391 , 001 scrobbles – 57 , 274 , 158 1st-time scrobbles ◮ We train factor models only on the 1st time scrobbles ◮ Artists with popularity less than 14 are excluded ◮ Evaluation on each 1st time scrobble in the second year

2 E XPERIMENTS - F INAL C OMBINATION ◮ Factor and influence models combine well, the average improvement is – 7 % for DCG@10 0.01 K =10 0.009 0.008 average DCG 0.007 0.006 0.005 factor factor + influence 0.004 0 20 40 60 80 100 time (days) factor factor + influence

L OCATION - AWARE ONLINE LEARNING ◮ Twitter dataset ◮ Temporal hashtag recommendation ◮ Twitter: highly non-stationary data ◮ ( u , h , l , t ) geoinfo ◮ Idea: tree structure of geographical areas number of records 6,978,478 number of unique user-hashtag pairs 2,993,183 number of users 792,860 number of items 268,489 number of countries 49

T REE CONSTRUCTION ◮ 214,230 nodes containing 190,315 leaves. ◮ The depth of the tree is 6 ◮ The hashtag time series data covered 30,450 leaves from the whole tree. World ... Europe Asia Africa ... Germany Austria ... Vienna Graz ... ...

R ECENCY 1e+06 100,000 N (IET = t ) 10,000 1,000 100 10 1 0.1 1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 1e+07 t (sec) P ( τ = t ) = ( α − 1 ) · t − α and P ( 1 ≤ τ ≤ t ) = 1 − t ( 1 − α ) � ( 1 − α ) P ( t < τ ≤ t + ∆ t | τ > t ) = P ( τ ≤ t +∆ t ) − P ( τ ≤ t ) 1 + ∆ t � = 1 − 1 − P ( τ ≤ t ) t

M ODELING ◮ Online MF as baseline → NOT working ! ◮ Tree + Recency + Bias model: � ˆ ˆ r ( u , h , t , l ) = w n · f ( t − t n , h ) n ∈ Path(l) ◮ ˆ w n node biases learned with SGD ◮ ˆ w n already includes node reliability and popularity ◮ Different heuristic baselines

3 3 3 3 3 3 R ESULTS 0.4 average cumlative DCG@100 0.35 0.3 0.25 0.2 world 0.15 leaves countries 0.1 countries without recency tree 0.05 tree with learned node weights 0 2 4 6 8 10 12 14 16 18 20 time (days)