We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: Online learning with a simple square loss and finding a symmetric positive definite matrix subject to symmetric linear constraints. The updates generalize the Exponentiated Gradient (EG) update and AdaBoost, respectively: the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector (which in this context is a diagonal positive definite matrix with trace one). The generalized updates use matrix logarithms and exponentials to preserve positive definiteness. Most importantly, we show how the analysis of each algorithm generalizes to the non-diagonal case. We apply both new algorithms, called the Matrix Exponentiated Gradient (MEG) update and DefiniteBoost, to learn a kernel matrix from distance measurements.

We present a competitive analysis of Bayesian learning algorithms in the online learning setting and show that many simple Bayesian algorithms (such as Gaussian linear regression and Bayesian logistic regression) perform favorably when compared, in retrospect, to the single best model in the model class. The analysis does not assume that the Bayesian algorithms' modeling assumptions are "correct," and our bounds hold even if the data is adversarially chosen. For Gaussian linear regression (using logloss), our error bounds are comparable to the best bounds in the online learning literature, and we also provide a lower bound showing that Gaussian linear regression is optimal in a certain worst case sense. We also give bounds for some widely used maximum a posteriori (MAP) estimation algorithms, including regularized logistic regression.

Learning algorithms have enjoyed numerous successes in robotic control tasks. In problems with time-varying dynamics, online learning methods have also proved to be a powerful tool for automatically tracking and/or adapting to the changing circumstances. However, for safety-critical applications suchas airplane flight, the adoption of these algorithms has been significantly hampered by their lack of safety, such as "stability," guarantees. Rather than trying to show difficult, a priori, stability guarantees forspecific learning methods, in this paper we propose a method for "monitoring" the controllers suggested by the learning algorithm online, andrejecting controllers leading to instability. We prove that even if an arbitrary online learning method is used with our algorithm to control a linear dynamical system, the resulting system is stable.

Schema learning is a way to discover probabilistic, constructivist, predictive actionmodels (schemas) from experience. It includes methods for finding and using hidden state to make predictions more accurate. Weextend the original schema mechanism [1] to handle arbitrary discrete-valued sensors, improve the original learning criteria to handle POMDP domains, and better maintain hidden state by using schema predictions. Theseextensions show large improvement over the original schema mechanism in several rewardless POMDPs, and achieve very low prediction error in a difficult speech modeling task. Further, we compare extended schema learning to the recently introduced predictive state representations [2],and find their predictions of next-step action effects to be approximately equal in accuracy. This work lays the foundation for a schema-based system of integrated learning and planning.

We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Ratherthan treating the most general case, we focus on two key applications that exemplify our methods: Online learning with a simple square loss and finding a symmetric positive definite matrix subject to symmetric linear constraints. The updates generalize the Exponentiated Gradient (EG) update and AdaBoost, respectively: the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector (which in this context is a diagonal positive definite matrix with trace one). The generalized updates use matrix logarithms and exponentials topreserve positive definiteness. Most importantly, we show how the analysis of each algorithm generalizes to the non-diagonal case. We apply both new algorithms, called the Matrix Exponentiated Gradient (MEG) update and DefiniteBoost, to learn a kernel matrix from distance measurements.

We present a competitive analysis of Bayesian learning algorithms in the online learning setting and show that many simple Bayesian algorithms (such as Gaussian linear regression and Bayesian logistic regression) perform favorablywhen compared, in retrospect, to the single best model in the model class. The analysis does not assume that the Bayesian algorithms' modelingassumptions are "correct," and our bounds hold even if the data is adversarially chosen. For Gaussian linear regression (using logloss),our error bounds are comparable to the best bounds in the online learning literature, and we also provide a lower bound showing that Gaussian linear regression is optimal in a certain worst case sense. We also give bounds for some widely used maximum a posteriori (MAP) estimation algorithms, including regularized logistic regression.

For more information on the BS in CS program, see Philip Flora, 1981 Rina Dechter, 2002 http://www.csd.cs.cmu.edu/education/bscs/index.html.

I claim that achieving real human-level artificial intelligence would necessarily imply that most of the tasks that humans perform for pay could be automated. Rather than work toward this goal of automation by building special-purpose systems, I argue for the development of general-purpose, educable systems that can learn and be taught to perform any of the thousands of jobs that humans can perform. Joining others who have made similar proposals, I advocate beginning with a system that has minimal, although extensive, built-in capabilities. These would have to include the ability to improve through learning along with many other abilities.

By the early 1960s there were several active research groups in AI, including those at Carnegie Mellon University (CMU), the Massachusetts Institute of Technology (MIT), Stanford University, Stanford Research Institute (later SRI International), and a little later the University of Southern California Information Sciences Institute (USC-ISI). My own involvement in AI began in 1963, when I joined Stanford as a graduate student working with John McCarthy. After completing my Ph.D. in 1966, I joined the faculty at Stanford as an assistant professor and stayed there until 1969 when I left to join Allen Newell and Herb Simon at Carnegie Mellon University

The AAAI-06 workshops will be held rather than a regular AAAI paper.