New Expectation-Maximization Algorithms
AutoBayes can already derive fairly sophisticated EM (Expectation-Maximization) algorithms for new user-specified statistical models. In addition to standard textbook examples such as the EM algorithm for mixtures of Gaussians, AutoBayes was able to reproduce four research-level EM algorithms, i.e. EM algorithms appearing in research papers in recent years, such as a nested EM algorithm where the M-step itself is solved with an EM algorithm. (Gray, Fischer, Schumann and Buntine, Automatic Derivation of Statistical Algorithms: The EM Family and Beyond [pdf], [ps] NIPS 2002.)

Next steps. I started to extend the capabilities of the system with several other algorithmic schemas, including particle filter-like algorithms, k-means-like algorithms, and basic kd-tree-based algorithms. However, most of these are in a partial state of completion for the moment. Wray has done at least one variational method and had been thinking about expectation-propagation, last I heard.
An impending collaboration with Ashish Agarwal may provide a basis for this system in category theory.

Automatic Derivation of Algorithms
Q: "Okay, I want to use state-of-the-art, computationally-efficient algorithms for my statistical model (either for learning/estimating it or using it to predict) -- but do I have to become an expert in the latest algorithms or numerical methods to do that? No one has published a paper or released software applying the most advanced existing computational methods for exactly my statistical model." A: It is possible to automatically apply an algorithmic principle to a new statistical model to derive an algorithm for it. The resulting specialized algorithm may or may not have existed before.

In recent years, research in parametric learning methods has seen the emergence of a handful of general algorithmic principles, such as the EM algorithm, which can be applied in many different model contexts and combined with other algorithmic patterns, or 'schemas', to obtain a rich family of parametric learning methods. Many current or recent research-level learning methods are in fact applications of such known algorithm recipes to different model distributions and model structures. The process of deriving such algorithms can in fact be automated. The AutoBayes system takes a high-level statistical model specification given by the user, represents it internally as a graphical model, then uses symbolic transformation techniques based on computer algebra and schema-based theorem proving to derive an efficient specialized algorithm for learning that model, and finally generates executable C or Matlab code implementing that algorithm. AutoBayes is the only existing system with these capabilities, to my knowledge, for deriving novel algorithms in machine learning or in any domain.

The AutoBayes Project was begun by Wray Buntine in 1995 and is led by Bernd Fischer and Johann Schumann of NASA Ames. I joined the project in 2001 with the goal of pushing AutoBayes to the point of becoming a serious tool for the machine learning research community. We made a push of progress in 2001 but currently things are stalled.