probabilistic methods for targeted advertising

Probabilistic Methods forTargeted Advertising

Max Chickering

Microsoft Research

Outline

• Targeted Mailing

To whom should you send a solicitation?

• Targeted Advertising on the Web

How should you display banner ads to maximize click-through?

Targeted Mailing• Given a population of potential customers.

Person X1 X2 … Xn

1 0 0 … red2 0 3.4 … blue. . . .. . . .. . . .m 1 7 … green

• Sending an advertisement costs money:

- Postage- Possible Discount

Which potential customers do you solicit?

Motivating Application

Advertisement:

MSN subscription

Potential customers:

People who registered Windows 95

Known variables:

15 from questionnaire (e.g. gender, RAM size)

Naïve Solutions

• Mail to those customers most likely to subscribe to MSN

Can waste money by targeting customers who wouldsubscribe anyway

• Mail to everyone

Even worse!

Response Behaviors

Mail Don’t Mail Always buyer Yes YesPersuadable Yes NoAnti-persuadable No YesNever buyer No No

Will the potential customer buy the product?

We only make money from mailing to the persuadablepotential customers

Expected Profit for a Population

Population of N potential cutomers Nalw, Nper, Nanti, Nnev

Cost of mailing cSolicited and unsolicited revenue r

Expected Profit from mailing

rN

NNc peralw

rN

NN antialw

Profit from not mailing

Lift in Profit From Mailing

Profit from mailing - Profit from not mailing

rN

NN

N

NNc antialwperalw

For any set of potential customers, we should onlymail if the lift is positive.

Learning Expected Lift

S {s0, s1} (did not subscribe, did subscribe)

M {m0, m1} (did not mail, did mail)

)|( 11 mMsSpN

NN peralw

)|( 01 mMsSpN

NN antialw

Identifiable ifS, M known in training data

Lift : -c + [ p(S=s1|M=m1) – p(S=s1|M=m0) ] r

Controlled Experiment: Identify Profitable Sub-Populations

1. Choose a small sample of the potential customers

2. Randomly divide those customers into a “treatment group” (M = m1) and a “control group” (M = m0)

3. Wait a specified period of time, and record S = s0 or S = s1 for each

Controlled Experiment

Person X1 X2 … Xn M S1 0 0 … red m1 s0

2 0 3.4 … blue m0 s1

. . . .

. . . .

. . . .m 1 7 … green m1 s1

Use machine-learning techniques to identify sub-populations with high positive lift, and then target those customers

Lift ( Sub-population corresponding to Xn=blue ) =

-c + [ p(S=s1|M=m1 , Xn=blue) – p(S=s1|M=m0 , Xn=blue) ] r

Identify Profitable Sub-Populations

Partitions of X define sub-populations and statistical model for p(S|M,X) defines the lift

Approach: Use Decision Trees

Known distinctions in our data : X = {X1, …, Xn}, S, M

X1 > 10, X4 = 2

X1 < 10, X12 = false

X1 < 10, X12 = true

Lift 2 Lift 3

Lift 4

X1 > 10, X4 2

Lift 1

Probabilistic Decision Trees

p(S | M=m0, X1=1, X2=2)

X2

M X1

M

Mp(S=subscribed) = 0.6p(S=not subscribed) = 0.4

21,3

mailednot

mailed 12

p(S=subscribed) = 0.5p(S=not subscribed) = 0.5



mailed notmailed

mailed

notmailedp(S=subscribed) = 0.7

p(S=not subscribed) = 0.3


p(S | M, X1, X2)

X2

M X1

M

Mp(S=subscribed) = 0.6p(S=not subscribed) = 0.4

21,3

mailednot

mailed 1 2




mailed notmailed

mailed

notmailed



Calculating Lift

Potential customer with {X1=1, X2=2}, Assume c = 0.50, r = 9

Lift = -0.5 + (0.4 – 0.2) 9 = 1.3

Mail to this person!

Traditional Learning Algorithm

X1

Score1(Data)

X2

Score2(Data)

Xn

Scoren(Data)

X2

X2

X1

Score1(Data)

X2

X3

Score3(Data)

X2

Xn

Scoren(Data)

Lift-Aware Learning Algorithm

Traditional Learning Algorithm

Identify a tree that represents p(S|M,X) well

Lift-Aware

Would like the tree to be good at modeling the difference:

p(S=s1|M=m1,X=x) - p(S=s1|M=m0,X=x)

A HeuristicOnly consider decision trees (for S) with the last split on M

M

X1

M M

X1

M M

Score1(Data)

Xn

M M

Scoren(Data)

X1

M

Score2(Data)

X2

M M

X1

M

Score2(Data)

X2

M M

Experiment: Real-world Dataset

Product of interest: MSN subscriptionPotential customers: Windows 95 registrantsKnown variables (X): 15 from questionnaire (e.g. gender, RAM size) Cost to Mail: 42 centsSubscription revenue: varied from 1 to 15 dollars

Data: sample of ~110,000 potential customers (70% train, 30% test)

Compared our algorithm (FORCE) with unconstrained greedyalgorithm (NORMAL) for various revenues

Results on Test Data:Per-person improvement over Mail-to-All

0

0.05

0.1

0.15

0.2

0.25

1 4 7 10 13 16 19 22 25

Benefit (Dollars)

Imp

rove

men

ts (

Do

llars

)

FORCE

NORMAL

Conclusions / Future Work

Marginal improvement over standard decision-tree algorithm:

Almost every path in the “standard” trees contained a split onM. We expect larger difference for other domains.

Algorithm works for discounted prices:

Expected Profit from mailing discountperalw r

N

NNc

rN

NN antialw

Profit from not mailing

Part II: Targeted Advertising on the Web

Given information about a visitor, how do you choosewhich advertisement to display?

???

Goals of Targeted Advertising

Maximize $$$

• Maximize Clicks

• Brand Presence

Naïve Targeting Scheme

Possible cluster attributes:

• Current page category

• Pages the user has visited on the site

• Known demographics

• Inferred demographics

• Previous advertisement clicks

Cluster 1 Cluster m

Step 1: cluster / segment users

Naïve Targeting Scheme

Step 2: Advertiser books ads into clusters

Step 3: Measure click probabilities

Step 4: Show best ad to each cluster

Problems: (Inventory management)

Ad Quotas

Cluster overbooking

Advertisement Allocation

Cluster 1 Cluster m

Ad 1

Ad 2

Ad n

x11

x21

xn1

x1m

x2m

xnm

Cluster 2

x12

x22

xn2

xij = Number of times to show advertisement i

to user cluster j

Maximize Expected Clicks

Cluster 1 Cluster m

Ad 1

Ad 2

Ad n

p11 x11

p21 x21

pn1 xn1

p1m x1m

p2m x2m

pnm xnm

Cluster 2

p12 x12

p22 x22

pn2 xn2

n

i

m

jijij xpE

1 1

)for Clicks#( X

Inventory-Management Constraints

Ad i xi1 xim

Cluster j

xij

xi1

xin

m

jiij qx

1

n

ijij cx

1

Linear ProgramFind the schedule X that maximizes:

Subject to:

n

i

m

jijij xp

1 1

iqxm

jiij

1

jcxn

ijij

1

Solve using (e.g.) the simplex algorithm

A Simple Targeting System

• Estimate probabilities

• Find the optimal schedule

• Serve ads to cluster j via

''

) Serve(

iji

ij

x

xip

Sensitivity to Estimates

Cluster 1

Ad 1

Ad 2

0.49

0.51

Cluster 2

0.51

0.49q1 = q2 = c1 = c2 =k

Cluster 1

Ad 1

Ad 2

0

k

Cluster 2

k

0

Probabilities:

Optimal Schedule:

Solution: BucketsCluster 1

Ad 1

Ad 2

0.5

0.5

Cluster 2

0.5

0.5q1 = q2 = c1 = c2 =k

Cluster 1

Ad 1

Ad 2

a

c

Cluster 2

b

d

Probabilities:

Optimal Schedule:

a+b+c+d = 2k

Secondary (linear) optimization: Ads are shown as close to uniform across all clusters

Passive Experiment: MSNBC(December 1998)

SportsNewsHealthOpinion

Clusters defined by the current page group

Manual approach: advertisers buy impressions on page groups

~20 clusters~500 advertisements~1.6 million impressions / day

Passive Experiment: MSNBC(December 1998)

Data from day 1:Estimate pij (ave ~4K data points per probability)Find optimal schedule (less than 1 minute – no buckets)

Data from day 2:Re-estimate pij

Evaluate schedule:

Result:

20 – 30 % increase over manual schedule

n

i

m

jijij xp

1 1

Particular advertiser: 5 ads

Data from weekend 1:Estimate pij (~15K data points per probability)Find optimal schedule (less than 1 second using buckets)

Rearrange advertisements for weekend 2

Data from weekend 2:

Count the number of clicks and compare to weekend 1

Active Experiment on MSNBC(May 1999)

0

advertiser control

Weekend 1 (pre target)

Weekend 2 (post target)

30% increase for the advertiser, negligible increase for othersPredicted a 20% increase on MSNBC

Active Experiment Results

Extensions

Problem:

Increasing total expected clicks across site may decrease clicks for particular advertiser

Solution:

Add (linear) constraint that expected clicks cannotdecrease

Passive experiment: MSNBC overall increase still ~20%

Extensions

Focus of talk: pij = expected #clicks from showing ad i to user jIn general: uij = expected utility from showing ad i to user j

Expected utility of X =

n

i

m

jijij xu

1 1

Alternative uij choicesWeighted probabilities: wi pij

Probability of purchaseIncrease in brand awarenessExpected revenue

My Home Page

http://research.microsoft.com/~dmax/

Results on Test Data:Per-person improvement over Mail-to-All

To evaluate test case given a model:

• Evaluate the lift given X (ignoring M and S)

• Recommend Mail if and only if Lift > 0

• If recommendation matches M from the test case, add r to the total revenue. Otherwise, ignore.

probabilistic methods for targeted advertising

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