Gene Expression Networks
I was involved in some of the earlier work toward learning stochastic circuit models (a kind of temporal graphical model) of gene regulation from microarray expression data. This method was a statistical physics-based (deterministic annealing) clustering model and algorithm in which a datum could truly belong to multiple clusters simultaneously. (Mjolsness, Castano, and Gray, Multi-Parent Clustering Algorithms for Large-Scale Gene Expression, JPL Report 1999. Mjolsness at al. Clustering Methods for the Analysis of C. elegans Gene Expression Array Data, PSB 1999.)
Computational Chemistry,
Drug Discovery, Biology
Along with many other people today, I believe that applied mathematical approaches (computational, statistical, engineering) to chemical and biological problems represent one of the most fruitful scientific goldmines for the next few decades at least. I would say, however, that this is really a special case of a more general opportunity -- all of the natural sciences should and will be transformed by such approaches in the near future. We have a large collaboration with a major pharmaceutical company.

Molecule Ranking for Virtual Screening
??? Automated high-throughput drug screening constitutes a critical emerging approach in modern pharmaceutical research. The statistical task of interest is that of discriminating active versus inactive molecules given a target molecule, in order to rank potential drug candidates for further testing. Because the core problem is one of ranking, our approach concentrates on accurate estimation of unknown class probabilities, in contrast to popular non-probabilistic methods which simply estimate decision boundaries. While this motivates nonparametric density estimation, we are faced with the fact that the molecular descriptors used in practice typically contain thousands of binary features. In this paper we attempt to improve the extent to which kernel density estimation can work well in high-dimensional classification settings. We present a synthesis of techniques (SLAMDUNK: Sphere, Learn A Metric, Discriminate Using Nonisotropic Kernels) which yields favorable performance in comparison to previous published approaches to drug screening such as support vector machines, as tested on a large high-dimensional proprietary pharmaceutical dataset. (Gray, Komarek, Liu, and Moore, High-Dimensional Probabilistic Classification for Drug Discovery [pdf], [ps] Computational Statistics 2004.) I consider this to just be a first dip into the sea of this problem. Whether we use this method as a component of the eventual system depends on the next step.

??? Next step: The ultimate goal is to automatically choose which molecules to test, in a running system. I am working right now on a new formulation of active learning which is not based on the traditional least-squares approach to experimental design. Another huge sub-problem in this enterprise is the effective representation of molecules.