Discriminative motif elicitation via maximization of statistical overpresentation

Abstract

The Fisher Exact Test score (FETS) and its variants are based on the hypergeometric distribution. It’s very natural to describe the enrichment level of TF binding site (TFBS) by it. And several widely used methods that discriminant motif discovery have choose them as the objective functions, for example, HOMER and DERME. Although the method is highly efficient and universal, FETS is a non-smooth and non-differentiable function. So it can not be optimized numerically. In order to solve the problem, the current methods that learn to optimize FETS either reduce the search set to discrete domain or introduce some external variables which will definitely hurt the precision, not to mention that to use the complete potential of input sequences for generate motifs. In this paper, we propose an approach that allows direct learning the motifs parameters in the continuous space use the FETS as the objective function. We find that when the loss function is optimized in a coordinate-wise mode, the cost function can be a piece-wise constant function in each resultant sub-problem. The process of finding optimal value is exactly and efficiently. Furthermore one key step in every iteration of optimize the FETS requires finding the most statistically significant scores among the tens of thousands of Fisher’s exact test scores, which is solved efficiently by a ‘lookahead’ technique. Experiments on ENCODE ChIP-seq data testify the performance of the proposed method.