Research at the
Decision Making Lab
Fabio Cozman
Universidade de São Paulo
Decision Making Lab (2002)
Research tree
Robotics
(a bit)
Bayes nets
Sets of probabilities
Algorithms
independence
Applications
MDPs, robustness analysis, auctions
Anytime, anyspace
(embedded systems)
Classification
Applications
Medical decisions
MCMC algorithms
inference & testing
Some (bio)robotics
Bayesian networks
Decisions in medical domains
(with the University Hospital)
Idea:
To improve decisions at medical posts in urban,
poor areas
We are building networks that represent cardiac arrest
—
can be caused by stress, cardiac problems,
respiratory problems, etc
–
Support by FAPESP
The HU

network
A better interface for teaching
Embedded Bayesian networks
Challenge:
to implement inference algorithms
compactly and efficiently
Real challenge
: to develop anytime anyspace
inference algorithms
Idea:
decompose networks, apply several
algorithms (UAI2002 workshop on RT)
–
Support by HP Labs
Decomposing networks
How to decompose and assign algorithms to
meet space and time constraints with
reasonable accuracy
Application: Failure analysis in
car

wash systems
The car

wash network
Generating random networks
Problem is easy to state, hard to solve: critical
properties of DAGs are not known
Method based
on MCMC simulation,
with constraints on
induced width and
degree
–
Support by FAPESP
Research tree (again)
Biorobotics
(a bit of it)
Bayes nets
Sets of probabilities
Algorithms
independence
Applications
MDPs, robustness analysis, auctions
Anytime, anyspace
(embedded systems)
Classification
Applications
Medical decisions
MCMC algorithms
inference & testing
Bayesian network classifiers
Goal is to use probabilistic models for
classification
–
to “learn” classifiers using
labeled and unlabeled data
Work with Ira Cohen, Alex Bronstein and
Marsha Duro (UIUC and HP Labs)
Using Bayesian networks to learn
from labeled and unlabeled data
Suppose we want to classify events based on
observations; we have recorded data that are
sometimes labeled and sometimes unlabeled
What is the value of unlabeled data?
The Naïve Bayes classifier
A Bayesian

network like classifier with excellent
credentials:
Use Bayes rule to get classification
p(label  attrs.)
a
p(label)
P
i=0…N
p(attr. i  Class)
Attribute 1
Class
Attribute 2
Attribute N
The TAN classifier
Attribute N
X
N
Attribute 1
X
1
Class
Attribute 2
X
2
Attribute 3
X
3
Now, let’s consider unlabeled data
Our database:
–
American
baseball
hamburger
–
Brazilian
soccer
rice and beans
–
American
golf
apple pie
–
?
saloon soccer
rice and beans
–
?
golf
rice and beans
Question: How to use the unlabeled data?
Unlabeled data can help…
Learning a Naïve Bayes for data generated
from a Naïve Bayes model (10 attributes):
10
0
10
1
10
2
10
3
10
4
0.06
0.07
0.08
0.09
0.1
0.11
Number of Unlabeled records
Probability of error
30 Labeled
300 Labeled
3000 Labeled
… but unlabeled data may degrade
performance!
Surprising fact:
more data may
not help; more
data may hurt
Some math: asymptotic analysis
Asymptotic bias:
Variance decreases with more data
A very simple example
Consider the following situation:
Class
X
Y
Class
X
Y
“Real”
“Assumed”
X and Y are Gaussian given Class
Effect of unlabeled data
–
a
different perspective
10
1
10
2
10
3
10
4
10
5
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Classification error: 0%, 50%, 99% unlabeled records
Number of records (log)
Classification error
0%, complete
50%, only labeled
50%, complete
99%, only labeled
99%, complete
Searching for structures
Previous tests suggest that we should pay
attention to modeling assumptions when
dealing with unlabeled data
In the context of Bayesian network classifiers,
we must look for structures
This is not easy; worse, existing algorithms do
not focus on classification
Stochastic Structure Search (SSS)
Idea:
search for structures using classification
error
Hard:
search space is too messy
Solution:
Metropolis

Hastings sampling with
underlying measure proportional to 1/p
error
Some classification results
Some words on unlabeled data
Unlabeled data can improve performance, can
degrade performance
—
really hard!
Current understanding about this problem is
shaky
–
people think outliers or mismatches between
labeled and unlabeled data cause the problem
Research tree (once again)
Biorobotics
(a bit of it)
Bayes nets
Sets of probabilities
Algorithms
independence
Applications
MDPs, robustness analysis, auctions
Anytime, anyspace
(embedded systems)
Classification
Applications
Medical decisions
MCMC algorithms
inference & testing
Sets of probabilities
Instead of
probability of rain is 0.2,
say
probability of rain is [0.1, 0.3]
Instead of
expected value of stock is 10
,
admit
expected value of stock is [0, 1000]
An example
Consider a set of probabilities
p(
q
1
) p(
q
2
), p(
q
3
)
Set of
probabilities
Why?
More realistic and quite expressive as
representation language
Excellent tool for
–
robustness/sensitivity analysis
–
modeling incomplete beliefs (probabilistic logic)
–
group decision

making
–
analysis of economic interactions
–
for example, to
study arbitrage and design auctions
What we have been doing
Trying to formalize and apply “interval”
reasoning, particularly
independence
Building algorithms for manipulation of these
intervals and sets
–
To deal with independence and networks
–
JavaBayes is the only available software that can
deal with this (to some extent!)
Credal networks
Using graphical models
to represent sets of joint
probabilities
Question: what do the
networks represent?
Several open questions
and need for algorithms
Family In?
Dog Sick?
Lights On?
Dog Barking?
Dog Out?
Concluding
To summarize, we want to understand how to
use probabilities in AI, and then we add a bit of
robotics
Support from FAPESP and HP Labs has been
generous
Visit the lab in your next trip to São Paulo
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