Learning Bayesian Networks For
Managing Inventory Of Display
Advertisements
Max Chickering
Mad Scientist
Live Labs
Microsoft Corporation
Display Advertisements
AdExpert
Microsoft’s System for Delivering
Display Advertisements
Microsoft Properties Only
7.5 Billion Impressions/Day
$1 Billion/Year Revenue
AdExpert: Inventory
Health Pages Top
Inventory consists of impressions
of targetable attributes:
1. Page Groups
Set of pages + position
~6000 page groups
Health
Pages
Side
2. Geographic Targeting
3. Demographic Targeting
4. Behavioral Tags
Examples:
• 1M imp of males on the HealthTop page group
• 1M imp of sports enthusiast on the AutoSide page group
AdExpert: Selling Inventory
Charge per impression
Cost depends on page group and targets
High-touch market
Inventory is guaranteed
Guarantees Result In
Inventory Management Problems
Pricing: How much do we charge
per impression?
Remaining Inventory: Can we fill this order?
Selection: Do we want to?
(something better coming)
Delivery: Given that we have overbooked, how
do we prioritize orders?
Capacity Prediction
How many Old Males are coming next week?
Pricing
Remaining
Inventory
Selection
Capacity Prediction
Delivery
Capacity Prediction
Example: on a particular page group…
• Existing order: 1.2M impressions of Old
• New customer wants 1.2M impressions of Males
Can we satisfy new request?
1.5M
1.5M
Old
Male
Yes
1M
0.5M
No
0.5M
Old
Male
Capacity Prediction
Old
Male
Investor
Location
Autos Fan
Sports Fan
How Many Old Males Next Week?
Age Gender Sports
Volume Prediction
Past
Volume
Prediction
Old Male No
Young Female No
Population Prediction
Old Male Yes
p(Age,Gender,Sports)
Capacity Prediction
=
Volume Prediction
X
Population Prediction
p(Age=Old,Gender=Male)
Capacity Prediction In Earlier System
Not Many Targets
Random
Sample
Old Male No
Young Female No
Age
Gender
Sports
Old
Male
Yes
Old
Female
No
Young Male
No
Young Female
Yes
Old
No
Male
Young Female
Yes
Young Male
Yes
Old
No
Female
Young Male
Old Male Yes
Yes
N (Old , Male ) 2

p (Old , Male ) 
9
N
New Version Of AdExpert:
Increase Targeting
Current System Maxed Out
Earlier system could not handle any more targeting
Competitors adding more targeting
New Demographic Targets
300 Targets
Add Behavioral Targets
Capacity Prediction From Sample
300 Variables
Millions
of
Samples
B1
B2
…
Age
Gender
BN
Sports
Old
Male
Yes
Old
Female
No
Young Male
No
Young Female
Yes
Old
No
Male
Young Female
Yes
Young Male
Yes
Old
No
Female
Young Male
Yes
x 6000!
Compressing Tables With Bayesian Networks
Bayesian network:
Graphical model for representing a joint probability distribution
Age
Gender
Sports
Old
Male
Yes
Old
Female
No
Young Male
•
•
•
•
Yes
p(Age)
Age
p(Gender|Age)
Gender
p(Sports | Gender)
Sports
One node for each column
Edges represent probabilistic dependence
Each node stores p(node|parents)
Joint probability: product of conditionals:
p(Age, Sports, Gender)=p(Age) x p(Gender) x p(Sports|Gender)
•
More independence leads to more compression
Bayesian Network For Hotmail PG
1014 possible combinations
Only 119,350 parameters
Training:
Constructing The Model From Data
Age
Gender B1 B2 … BN Sports
Old
Male
Yes
Old
Female
No
Young Male
No
Young Female
Yes
Old
Male
No
Old
Female
No
Young Male
B2
OFFLINE
Training
Yes
Gender
B1
Efficient “Look up” Algorithms: p(Age=Old, Gender=Male)
Pre-release Validation:
Accuracy better than existing system
Timing requirements met
Age
B3
Sports
Bayesian Network: Updating Over Time
Easy to Update
Local Probabilities
B2
Age
Old Male No
B3
Gender
Young Female No
B1
Old Male Yes
Sports
Current Status
Capacity Prediction is working well
Valuable inventory is still selling out
Fewer under-delivered targeted orders
Targeting is increasing
Lessons Learned (I)
Include cost of probability “look up” in learning algorithm
Lessons Learned (II)
Allow “preferred edges” – Some dependences are
apriori important
B2
Age
B3
Gender
B1
Sports
Questions?
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