Stable Mixing of Complete and Incomplete Information

An increasing number of parameter estimation tasks involve the use of at least two information sources, one complete but limited, the other abundant but incomplete. Standard algorithms such as EM (or em) used in this context are unfortunately not stable in the sense that they can lead to a dramatic loss of accuracy with the inclusion of incomplete observations. We provide a more controlled solution to this problem through differential equations that govern the evolution of locally optimal solutions (fixed points) as a function of the source weighting. This approach permits us to explicitly identify any critical (bifurcation) points leading to choices unsupported by the available complete data. The approach readily applies to any graphical model in O(n^3) time where n is the number of parameters. We use the naive Bayes model to illustrate these ideas and demonstrate the effectiveness of our approach in the context of text classification problems.

Multiclass Classification of SRBCTs

A novel approach to multiclass tumor classification using Artificial Neural Networks (ANNs) was introduced in a recent paper cite{Khan2001}. The method successfully classified and diagnosed small, round blue cell tumors (SRBCTs) of childhood into four distinct categories, neuroblastoma (NB), rhabdomyosarcoma (RMS), non-Hodgkin lymphoma (NHL) and the Ewing family of tumors (EWS), using cDNA gene expression profiles of samples that included both tumor biopsy material and cell lines. We report that using an approach similar to the one reported by Yeang et al cite{Yeang2001}, i.e. multiclass classification by combining outputs of binary classifiers, we achieved equal accuracy with much fewer features. We report the performances of 3 binary classifiers (k-nearest neighbors (kNN), weighted-voting (WV), and support vector machines (SVM)) with 3 feature selection techniques (Golub's Signal to Noise (SN) ratios cite{Golub99}, Fisher scores (FSc) and Mukherjee's SVM feature selection (SVMFS))cite{Sayan98}.