Fabio Cozman - Research Overview

It makes sense to classify my interests into a few topics:

Extending the theory of probability: credal sets, full conditional measures, etc

Mostly I explore the theory of sets of probability measures. There is not a single, stable name for this theory: some people use "theory of imprecise probabilities"; others say "theory of credal sets", or "Quasi-Bayesian theory", or "theory of lower expectations", or ... several other names. I'm a founding member of the Society for Imprecise Probability Theory and Applications; I also helped organize some of the International Symposium for Imprecise Probabilities and Their Applications (ISIPTA) and edited some of its proceedings.

I have developed graph-based models that represent sets of probability measures over sets of variables; these are often called credal networks:

Through the years I have produced many algorithms for inference with credal networks, most of them with collaborators. A collection of still useful algorithms can be found in

Additionaly, we have investigated combinations of graph-based modeling with various concepts of independence, various kinds of assessments, and with propositional/relational logic:

Another interest of mine is the definition of independence between variables when uncertainty is represented using sets of probability mesures. Some thoughts on this can be found in:

Here is an interesting piece on laws of large numbers for very general concepts of independence:

Still on concepts of independence, I have considered such concepts in the realm of full conditional measures (that is, measures that extend standard probability by adopting conditional probability as the primary object of interest, and hence allowing conditioning on events of probability zero):

I have also looked at sequential decision making (that is, planning) under uncertainty. An interesting idea is to merge "probabilistic" and "nondeterministic" planning using the theory of sets of probabilities and Markov Decision Processes:

This work was followed up by papers that investigated computational issues:

Still on sequential decision making, here are publications that deal with decision trees and sets of probability measures:

And here is an older effort, looking at the problem of sequential-decision making associated with observations:

Changing the subject a little, here is a paper that summarizes old work on calculations with sets of probability measures:

Finally, a long time ago I explored with Lonnie Chrisman the possibility of learning convex sets of probability from data; that old work has been picked up by Terry Fine and his collaborators.

Probabilistic reasoning: knowledge representation, and machine learning

I am quite interested in probabilistic models in knowledge representation and machine learning.

Relational Bayesian networks and description logics

I have been interested, together with several students, in languages for knowledge representation and machine learning that combine graph-based modeling, in particular Bayesian networks, with logical structures, in particular description logics. Perhaps the most interesting language we have developed is

We have also looked at algorithms that learn descriptions in this language from data:

We have also looked at a variety of applications, from social network analysis, to localization in mobile robotics, to spatial reasoning. Here are some representative publications:

Semi-supervised learning

One of the most important situations where we make decisions and use our beliefs and sensory information is when we classify data. I have worked with classification problems where one must build ("learn") a classifier using observed data that can be labeled or unlabeled; that is, the data points themselves may be classified or not. This is often called semi-supervised learning.

Relevant publications are:

This was joint work with Ira Cohen, at HP Labs Palo Alto. Other people at HP Labs contributed a lot, particularly Marsha Duro and Alex Bronstein.

JavaBayes and Bayesian networks

I developed, between 1996 and 2002, the JavaBayes system, a general purpose inference engine for graphical models. The engine computes posterior probabilities and expectations for probabilistic models represented as directed acyclic graphs. The system is distributed freely (under the GNU license) in the spirit of fostering teaching and research. JavaBayes is now used in many university and research labs around the world. A summary can be found in: In the process of putting together JavaBayes, I have developed a very general, yet easy to understand, inference algorithm for Bayesian networks. The method is suited for teaching due to its simplicity. You can get it:

While JavaBayes is a complete system, with graphical interface, parsers, etc, the EBayes package was an early effort to produce a lightweight Bayesian network engine that is appropriate to the growing market of embedded devices. A much more complete algorithm for probabilistic inference under time and space constraints has been developed with my former student Fabio Ramos:

Still on Bayesian networks, I have worked with my former student Jaime S. Ide on methods for generating random Bayesian networks:

Robotics and Computer Vision: Teleoperation, mobile robots, automated orthosis...

Third, I was involved for a long time, in one way or another, with robotic devices, mostly with mobile robots. I have not worked on these topics for a while.

My involvement with robotics started quite a while ago.

Right after my undergraduate course, I took a Master of Engineering in Brazil, and worked in the first Brazilian mobile robot, called Ariel. We produced a complete system, from the mechanical structure to the planning software; the result was very impressive and we ended up showing it off in the Jornal da Globo (Brazil's second most important TV news source at the time). Unfortunately, that material is not online. Here are two representative papers, perhaps of historic value:

I worked, for two years, in the Lunar Rover project during my PhD years at Carnegie Mellon. My main contribution to the Lunar Rover project was the Viper system, a piece of technology that was used in the Atacama desert for tests. The Viper system, estimates position from a stream of images, by matching images to a previously constructed map of the environment. The estimator builds an occupancy map for the position of the robot; the catch is that the occupancy maps actually represents a full density ratio familiy of distributions which generate both the estimates and the confidence on the estimates. The system is described in:

There is also a description of an old version of the Viper system in:

The vision algorithms developed for the Viper system are reported in the following papers.

During a few years at CMU I worked with the Ratler robot. We actually had it rolling for some fifty kilometers in our outdoor tests; you can take a look at the following paper.

I also worked on a variety of other problems. For instance, once I wrote a line linker based on the Akaike Information Criterion, that was distributed in the web. Another example was the investigation of celestial data as a source of position estimates for mobile robots:

I was interested for some time in the problem of calculating bounds for dynamical systems; there is a huge literature in this area. I have published some work on the specific topic of manipulating ellipsoidal models of error in Robotics:

Yet another example was the study of atmospheric scattering as a clue for depth in outdoor environments; as far as I know, the first study of scattering in the context of image understanding.

Finally, during 2000-2002, I participated in an effort to develop devices that can help the disabled walk with less effort and discomfort. The project started from interactions with doctors and engineers at the Associação de Assistência a Criança Defeituosa and was supported by FAPESP. A former advisee involved with this project, Marco Ackermann, received the prize of Best Master Thesis in Mechanical Engineering in Brazil 2003, granted by the Brazilian Association for the Mechanical Sciences (ABCM), for this work. You can read about it:

Since then I have occasionally returned to robotics and computer vision when dealing with uncertain reasoning and knowledge representation; my focus has been on the latter topics and not so much on the robots themselves. For instance: