MOTIVATION: Epistasis or gene-gene interaction has gained increasing attention in studies of complex diseases. Its presence as an ubiquitous component of genetic architecture of common human diseases has been contemplated. However, the detection of gene-gene interaction is difficult due to combinatorial explosion. RESULTS: We present a novel feature selection method incorporating variable interaction. Three gene expression datasets are analyzed to illustrate our method, although it can also be applied to other types of high-dimensional data. The quality of variables selected is evaluated in two ways: first by classification error rates, then by functional relevance assessed using biological knowledge. We show that the classification error rates can be significantly reduced by considering interactions. Secondly, a sizable portion of genes identified by our method for breast cancer metastasis overlaps with those reported in gene-to-system breast cancer (G2SBC) database as disease associated and some of them have interesting biological implication. In summary, interaction-based methods may lead to substantial gain in biological insights as well as more accurate prediction.

The following coin tossing game is analyzed: a store of N fair coins is given and it is desired to achieve M heads in a round of tosses of the coins. To allow for unfavorable sequences of tails, restarts are permitted at any epoch in the game where, in any restart, all coins are returned to store and tosses are begun anew from tabula rasa. A restart strategy is a prescription that specifies when a restart should be made. It is desired to estimate the minimum expected duration of the game over all restart strategies, and to find an optimal strategy that minimizes the expected duration of the game. This simple coin tossing game, proposed by R.L. Rivest, has cryptographic roots and is linked to issues in the factoring of integers.>