BBM: Bayesian Browsing Model from Petabyte-scale

DataChao Liu, MSR-Redmond

Fan Guo, Carnegie Mellon UniversityChristos Faloutsos, Carnegie Mellon University

Massive Log Streams

• Search log– 10+ terabyte each day (keeps increasing!)– Involves billions of distinct (query, url)’s

• Questions– Can we infer user-perceived relevance for

each (query, url) pair?– How many passes of the data are needed? Is

one enough?– Can the inference be parallel?

• Our answer: Yes, Yes, and Yes!

BBM: Bayesian Browsing Model

query URL1 URL2 URL3 URL4

C1 C2 C3 C4

S1 S2 S3 S4 Relevance

E1 E2 E3 E4Examine Snippet

ClickThroughs

Dependencies in BBM

S1

E1 E2

C1

S2

C2

…

…

…

Si

Ei

Ci

the preceding click position before i

i id i r

Road Map

• Exact Model Inference

• Algorithms through an Example

• Experiments

• Conclusions

Notations

• For a given query– Top-M positions, usually M=10• Positional relevance• M(M+1)/2 combinations of (r, d)’s

– n search instances

– N documents impressed in total: • Document relevance•

1 2( , ,..., )Nd d d

1 2( , ,..., )NR R R R

1 2( , ,..., ) 1, 2,...,k k k kMC C C C k n

1 2( , ,..., )MS S S S

Model Inference

• Ultimate goal

• Observation: conditional independence

P(C|S) by Chain Rule

• Likelihood of search instance

• From S to R:

kC

Putting things together

• Posterior with

• Re-organize by Rj’s

How many times dj

was clicked

How many times dj was not clicked when it is at position (r + d) and the preceding click is on position r

1:nC

What Tells US

• Exact inference with joint posterior in closed form

• Joint posterior factorizes and hence mutually independent

• At most M(M+1)/2 + 1 numbers to fully characterize each posterior– Count vector:

1:( | )np R C

0 1 2 ( 1) 2( , , ,..., )M Me e e e e

Road Map

• Exact Model Inference

• Algorithms through an Example

• Experiments

• Conclusions

LearnBBM: One-Pass Counting

Find Rj

An Example

• Compute• Count vector for

R4

r

0 0

0 0 0

0

0 1 2

d

3 2 1

0

N4

N4, r, d

1

1

LearnBBM on MapReduce

• Map: emit((q,u), idx)

• Reduce: construct the count vector

Example on MapReduce

(U1, 0)(U2, 4)(U3, 0)

Map

(U1, 1)(U3, 0)(U4, 7)

Map

(U1, 1)(U3, 0)(U4, 0)

Map

21 1 1( ) (1 )p R R R 2 2( ) 1 0.98p R R 3

3 3( )p R R 4 4 4( ) (1 )p R R R (U1, 0, 1, 1) (U2,

4)(U4, 0, 7)

(U3, 0, 0, 0)

Reduce

Road Map

• Exact Model Inference

• Algorithms through an Example

• Experiments

• Conclusions

Experiments• Compare with the User Browsing Model (Dupret and

Piwowarski, SIGIR’08)– The same dependence structure– But point-estimation of document relevance rather than

Bayesian– Approximate inference through iterations

• Data:– Collected from Aug and Sept 2008– 10 algorithmic results only– Split to training/test sets according

to time stamps for each query– 51 million search instances of

1.15 million distinct queries, 10X larger than the SIGIR’08 study

Overall Comparison on Log-Likelihood

• Experiments in 20 batches• LL Improvement Ratio = 2 1( 1)*100%ll lle

Comparison w.r.t. Frequency

• Intuition– Hard to predict clicks for infrequent

queries– Easy for frequent ones

Model Comparison on Efficiency

57 times faster

Petabyte-Scale Experiment

• Setup:– 8 weeks data, 8

jobs– Job k takes first

k-week data

• Experiment platform– SCOPE: Easy and Efficient Parallel Processing of

Massive Data Sets [Chaiken et al, VLDB’08]

Scalability of BBM

• Increasing computation load – more queries, more urls, more impressions

• Near-constant elapse time

Computation Overload Elapse Time on SCOPE

• 3 hours• Scan 265 terabyte data• Full posteriors for 1.15 billion (query, url) pairs

Road Map

• Exact Model Inference

• Algorithms through an Example

• Experiments

• Conclusions

Conclusions

• Bayesian Browsing Model for Search streams– Exact Bayesian inference– Joint posterior in closed form– A single pass suffices– Map-Reducible for Parallelism– Admissible to incremental updates– Perfect for mining click streams

• Models for other stream data– Browsing, twittering, Web 2.0, etc?

Thanks!