The Dynamics of Repeat Consumption Ashton Anderson Stanford University Ravi Kumar, Andrew Tomkins, Sergei Vassilvitskii Google Thursday, April 10, 14
repeat consumption a lot of consumption is repeat consumption what factors determine what we reconsume? given a set of previously-consumed candidates, predict which item a user will choose to reconsume 2 Thursday, April 10, 14
consumption data BrightKite : location checkins G+ : public location checkins MapClicks : clicks on Google Maps businesses MapClicks - Food : clicks on Google Maps restaurants 3 Thursday, April 10, 14
consumption data WikiClicks : all clicks on English Wikipedia pages by Google users ouTube : last 10K video watches of users Y ouTube - Music : Y ouTube restricted to Y music videos 4 Thursday, April 10, 14
baselines es : radio playlists from hundreds of Y US radio stations * (to compare against non-individual consumption data) Shakespeare : full text of Shakespeare’s works, with each letter considered an item (to compare against data with repetitions) * available at http://www.cs.cornell.edu/~shuochen/ 5 Thursday, April 10, 14
the dynamics of repeat consumption 1. empirical analysis 2. models 3. experiments 6 Thursday, April 10, 14
the dynamics of repeat consumption 1. empirical analysis 2. models 3. experiments 7 Thursday, April 10, 14
empirical analysis what are the empirical traits of reconsumed items? 8 Thursday, April 10, 14
popularity individual popularity: are users generally exploiting or exploring? 9 Thursday, April 10, 14
popularity more frequently consumed items are more likely to be reconsumed 10 Thursday, April 10, 14
recency how does the recency of consumption affect the likelihood of reconsumption? to answer this question, we use a cache-based analysis technique 11 Thursday, April 10, 14
recency consider a cache of size k= 3: 12 Thursday, April 10, 14
recency process a consumption history using optimal offline caching (replace item that occurs furthest in the future) 13 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c 14 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a Hits: 0 Misses: 1 15 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a b Hits: 0 Misses: 2 16 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a b Hits: 1 Misses: 2 17 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a c b Hits: 1 Misses: 3 18 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a b d Hits: 1 Misses: 4 19 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c e b d Hits: 1 Misses: 5 20 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c e b d Hits: 2 Misses: 5 21 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c e b d Hits: 3 Misses: 5 22 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a b d Hits: 3 Misses: 6 23 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a c d Hits: 3 Misses: 7 24 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a c d Hits: 4 Misses: 7 25 Thursday, April 10, 14
recency consumption history: a b b c d e b d a c d c a c d Hits: 5 Misses: 7 26 Thursday, April 10, 14
recency the hit ratio is an indication of the degree to which recency is displayed in a consumption history 27 Thursday, April 10, 14
recency Real consumption sequences display a significant amount of recency 28 Thursday, April 10, 14
recency Baseline datasets don’t display recency ( Y es even shows anti-recency) 29 Thursday, April 10, 14
empirical analysis user-level item popularity generally positive predictor recency is the strongest effect 30 Thursday, April 10, 14
the dynamics of repeat consumption 1. empirical analysis 2. models 3. experiments 31 Thursday, April 10, 14
models goal: develop a simple mathematical framework powerful enough to explain patterns of reconsumption we observe in real data 32 Thursday, April 10, 14
models first, fix vocabulary of items E a consumption history for user is X u = x 1 , . . . u where each x i ∈ E at each step, user picks next item to consume using some function of consumption history 33 Thursday, April 10, 14
quality model natural hypothesis: item quality dictates consumption behavior associate score for each , and at each s ( e ) e ∈ E step next item is chosen proportionally to its score: X s ( e 0 ) P ( x i = e ) = s ( e ) / e 0 2 E 34 Thursday, April 10, 14
recency model since recency is the strongest empirical effect, we formulate a copying model based on it at every step i , user copies item at position i-j proportional to weight w(i-j) 35 Thursday, April 10, 14
recency model recency model since recency is the strongest empirical effect, we formulate a copying model based on it at every step i , user picks item at position i-j proportional to weight w(i-j) a b b c d e b d a c d c ? consumption history 36 Thursday, April 10, 14
recency model recency model since recency is the strongest empirical effect, we formulate a copying model based on it at every step i , user picks item at position i-j proportional to weight w(i-j) a b b c d e b d a c d c ? consumption history weights w w(12) w(11) w(10) w(9) w(8) w(7) w(6) w(5) w(4) w(3) w(2) w(1) 37 Thursday, April 10, 14
recency model recency model since recency is the strongest empirical effect, we formulate a copying model based on it at every step i , user picks item at position i-j proportional to weight w(i-j) a b b c d e b d a c d c ? consumption history e.g.: P ( x i = d ) ∼ + + w(8) w(5) w(2) 38 Thursday, April 10, 14
recency model recency model since recency is the strongest empirical effect, we formulate a copying model based on it at every step i , user picks item at position i-j proportional to weight w(i-j) P j<i I ( x i = e ) w ( i − j ) P ( x i = e ) = P j<i w ( i − j ) 39 Thursday, April 10, 14
recency model we assume additivity in weights thought experiment: learn weights, and compare additivity prediction to actual likelihoods from copying 40 Thursday, April 10, 14
recency model very small deviations from additivity 41 Thursday, April 10, 14
hybrid model combination of recency and quality ) · ( e.g.: P ( x i = d ) ∼ + + w(8) w(5) w(2) s(d) P j<i I ( x j = e ) w ( i − j ) s ( x j ) P ( x i = e ) = P j<i w ( i − j ) s ( x i − j ) 42 Thursday, April 10, 14
learning model parameters quality model: simply the empirical fraction of occurrences k s ( e ) = 1 X I ( x i = e ) k i =1 43 Thursday, April 10, 14
learning model parameters recency and hybrid models: maximize likelihood with stochastic gradient ascent Y ! P j<i I ( x i = x j ) w ( i − j ) s ( x j ) LL = log P j<i w ( i − j ) s ( x j ) i ∈ R 44 Thursday, April 10, 14
learning model parameters weight update: A i ( x i = x j ) − s ( x i ) s ( x i ) ( if x i = x i − δ , ∂ LL X A i (1) ∂ w ( δ ) = − s ( x i ) otherwise A i (1) i ∈ R score update: 1 − A i ( x j = e ) ( if x i = e, ∂ LL X A i (1) ∂ s ( e ) = − A i ( x j = e ) otherwise. A i (1) i ∈ R alternating updates to local maximum (not jointly convex) 45 Thursday, April 10, 14
the dynamics of repeat consumption 1. empirical analysis 2. models 3. experiments 46 Thursday, April 10, 14
experiments scores for quality model 47 Thursday, April 10, 14
experiments learned recency weights 48 Thursday, April 10, 14
experiments log-likelihood per item of models, normalized by log-likelihood of hybrid model (which is 1.0) 49 Thursday, April 10, 14
experiments hybrid always wins, but recency model is close 50 Thursday, April 10, 14
experiments recency beats quality 51 Thursday, April 10, 14
experiments learning per-item quality scores always beats setting scores to be equal to popularity 52 Thursday, April 10, 14
experiments recency without scores > recency using popularity as quality scores 53 Thursday, April 10, 14
experiments learned quality scores are quite different from popularity (Kendall-Tau coefficient of 0.44) 54 Thursday, April 10, 14
experiments currently, we learn a weight for each possible previous position can our weights be compressed? 55 Thursday, April 10, 14
experiments weights follow power law with exponential cutoff Pr[ x ] ∝ ( x + γ ) − α e − β x 56 Thursday, April 10, 14
experiments log-likelihood of variants of recency model (full recency model set to 1.0) similar results for hybrid model 57 Thursday, April 10, 14
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