research at the decision making lab
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Research at the Decision Making Lab. Fabio Cozman Universidade de São Paulo. Decision Making Lab (2002). Research tree. Bayes nets. Sets of probabilities. Robotics (a bit). Anytime, anyspace (embedded systems). Classification. Algorithms independence. MCMC algorithms - PowerPoint PPT PresentationTRANSCRIPT
Research at the Decision Making Lab
Fabio CozmanUniversidade de São Paulo
Decision Making Lab (2002)
Research tree
Robotics (a bit)
Bayes netsSets of probabilities
Algorithmsindependence
ApplicationsMDPs, robustness analysis, auctions
Anytime, anyspace(embedded systems)
Classification
ApplicationsMedical decisions
MCMC algorithmsinference & 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 netsSets of probabilities
Algorithmsindependence
ApplicationsMDPs, robustness analysis, auctions
Anytime, anyspace(embedded systems)
Classification
ApplicationsMedical decisions
MCMC algorithmsinference & 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.) p(label) i=0…N p(attr. i | Class)
Attribute 1
Class
Attribute 2 Attribute N
The TAN classifier
Attribute NXN
Attribute 1X1
Class
Attribute 2X2
Attribute 3X3
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):
100
101
102
103
104
0.06
0.07
0.08
0.09
0.1
0.11
Number of Unlabeled records
Pro
ba
bil
ity
of
err
or
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
101
102
103
104
105
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2Classification error: 0%, 50%, 99% unlabeled records
Number of records (log)
Cla
ssifi
catio
n er
ror
0%, complete 50%, only labeled50%, complete 99%, only labeled99%, 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/perror
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 netsSets of probabilities
Algorithmsindependence
ApplicationsMDPs, robustness analysis, auctions
Anytime, anyspace(embedded systems)
Classification
ApplicationsMedical decisions
MCMC algorithmsinference & 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(1) p(2), p(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