The Dynamics of Repeat Consumption Ashton Anderson Stanford - - PowerPoint PPT Presentation

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The Dynamics of Repeat Consumption Ashton Anderson Stanford - - PowerPoint PPT Presentation

Apr 06, 2023 185 likes •841 views

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

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The Dynamics of Repeat Consumption

Ashton Anderson

Stanford University

Ravi Kumar, Andrew Tomkins, Sergei Vassilvitskii

Google

Thursday, April 10, 14

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repeat consumption

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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

Thursday, April 10, 14

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consumption data

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BrightKite: location checkins G+: public location checkins MapClicks: clicks on Google Maps businesses MapClicks-Food: clicks on Google Maps restaurants

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consumption data

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WikiClicks: all clicks on English Wikipedia pages by Google users Y

  • uTube: last 10K video watches of users

Y

  • uTube-Music: Y
  • uTube restricted to

music videos

Thursday, April 10, 14

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SLIDE 5

baselines

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Y es: radio playlists from hundreds of 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/

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SLIDE 6

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the dynamics of repeat consumption

  • 1. empirical analysis
  • 2. models
  • 3. experiments

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SLIDE 7

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the dynamics of repeat consumption

  • 1. empirical analysis
  • 2. models
  • 3. experiments

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SLIDE 8

empirical analysis

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what are the empirical traits of reconsumed items?

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individual popularity: are users generally exploiting or exploring?

popularity

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popularity

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more frequently consumed items are more likely to be reconsumed

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recency

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how does the recency of consumption affect the likelihood of reconsumption? to answer this question, we use a cache-based analysis technique

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recency

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consider a cache of size k=3:

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recency

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process a consumption history using

  • ptimal offline caching (replace item

that occurs furthest in the future)

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recency

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a b b c d e b a c d c d

consumption history:

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recency

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a b b c d e b a c d c d

consumption history:

a

Hits: 0 Misses: 1

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recency

16

a b b c d e b a c d c d

consumption history:

a b

Hits: 0 Misses: 2

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recency

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a b b c d e b a c d c d

consumption history:

a b

Hits: 1 Misses: 2

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recency

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a b b c d e b a c d c d

consumption history:

a b

Hits: 1 Misses: 3

c

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recency

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a b b c d e b a c d c d

consumption history:

a b

Hits: 1 Misses: 4

d

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recency

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a b b c d e b a c d c d

consumption history:

e b

Hits: 1 Misses: 5

d

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recency

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a b b c d e b a c d c d

consumption history:

e b

Hits: 2 Misses: 5

d

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recency

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a b b c d e b a c d c d

consumption history:

e b

Hits: 3 Misses: 5

d

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recency

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a b b c d e b a c d c d

consumption history:

a b

Hits: 3 Misses: 6

d

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recency

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a b b c d e b a c d c d

consumption history:

a c

Hits: 3 Misses: 7

d

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recency

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a b b c d e b a c d c d

consumption history:

a c

Hits: 4 Misses: 7

d

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recency

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a b b c d e b a c d c d

consumption history:

a c

Hits: 5 Misses: 7

d

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recency

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the hit ratio is an indication of the degree to which recency is displayed in a consumption history

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recency

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Real consumption sequences display a significant amount of recency

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recency

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Baseline datasets don’t display recency (Y es even shows anti-recency)

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empirical analysis

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user-level item popularity generally positive predictor recency is the strongest effect

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the dynamics of repeat consumption

  • 1. empirical analysis
  • 2. models
  • 3. experiments

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models

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goal: develop a simple mathematical framework powerful enough to explain patterns

  • f reconsumption we observe in real data

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models

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first, fix vocabulary of items E a consumption history for user is where each Xu = x1, . . . xi ∈ E u at each step, user picks next item to consume using some function of consumption history

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quality model

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natural hypothesis: item quality dictates consumption behavior associate score for each , and at each step next item is chosen proportionally to its score: s(e) e ∈ E P(xi = e) = s(e)/ X

e02E

s(e0)

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recency model

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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)

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recency model

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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 a c d c d ?

consumption history

recency model

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recency model

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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 a c d c d ?

consumption history weights w

w(1) w(2) w(3) w(4) w(5) w(6) w(7) w(8) w(9) w(10) w(11) w(12)

recency model

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recency model

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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 a c d c d ?

consumption history

w(2) w(5) w(8)

e.g.: P(xi = d) ∼ + +

recency model

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recency model

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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(xi = e) = P

j<i I(xi = e)w(i − j)

P

j<i w(i − j)

recency model

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recency model

we assume additivity in weights thought experiment: learn weights, and compare additivity prediction to actual likelihoods from copying

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recency model

very small deviations from additivity

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hybrid model

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combination of recency and quality P(xi = e) = P

j<i I(xj = e)w(i − j)s(xj)

P

j<i w(i − j)s(xi−j)

w(2) w(5) w(8)

e.g.: P(xi = d) ∼ + +

( )·

s(d)

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learning model parameters

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quality model: simply the empirical fraction of occurrences s(e) = 1 k

k

X

i=1

I(xi = e)

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learning model parameters

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recency and hybrid models: maximize likelihood with stochastic gradient ascent LL = log Y

i∈R

P

j<i I(xi = xj)w(i − j)s(xj)

P

j<i w(i − j)s(xj)

!

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weight update: score update:

∂LL ∂w(δ) = X

i∈R

(

s(xi) Ai(xi=xj) − s(xi) Ai(1)

if xi = xi−δ, − s(xi)

Ai(1)

  • therwise

∂LL ∂s(e) = X

i∈R

( 1 − Ai(xj=e)

Ai(1)

if xi = e, − Ai(xj=e)

Ai(1)

  • therwise.

alternating updates to local maximum (not jointly convex)

learning model parameters

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the dynamics of repeat consumption

  • 1. empirical analysis
  • 2. models
  • 3. experiments

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experiments

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scores for quality model

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experiments

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learned recency weights

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experiments

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log-likelihood per item of models, normalized by log-likelihood of hybrid model (which is 1.0)

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experiments

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hybrid always wins, but recency model is close

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experiments

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recency beats quality

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experiments

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learning per-item quality scores always beats setting scores to be equal to popularity

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experiments

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recency without scores > recency using popularity as quality scores

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experiments

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learned quality scores are quite different from popularity (Kendall-Tau coefficient of 0.44)

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experiments

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can our weights be compressed? currently, we learn a weight for each possible previous position

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experiments

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weights follow power law with exponential cutoff Pr[x] ∝ (x + γ)−αe−βx

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experiments

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log-likelihood of variants of recency model (full recency model set to 1.0) similar results for hybrid model

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conclusion

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studied repeat consumption across many domains found recency and quality to be strong empirical effects in characterizing reconsumption developed quality, recency, and hybrid models validated these models on lots of real data

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thanks!

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recency

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two problems:

  • 1. hit ratio depends on number of unique

items in the sequence

  • 2. some number of hits is expected

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recency

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solutions:

  • 1. use normalized hit ratio: divide hit ratio

by , the upper bound on hit ratio

  • 2. compare to normalized hit ratios on

randomly shuffled version of sequences 1 − u/c

another baseline: compare to optimal stable cache (fraction of consumptions accounted for by top k items)

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satiation

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no evidence of satiation in our data

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