Probabilistic logical inference using quantities of DNA strands

We overview a series of our research on DNA-based supervised learning of Boolean formulae and its application to gene expression analyses. In our previous work, we have presented methods for encoding and evaluating Boolean formulae on DNA strands and supervised learning of Boolean formulae on DNA computers which is known as NP-hard problem in computational learning theory [Kearns and Vazirani 94]. We have also applied those methods to executing logical operations of gene expression profiles in test tube [Sakakibara and Suyama 00]. These proposed methods are discrete (qualitative) algorithms and do not deal with quantitative analysis and are not robust for noise and errors. Recently, we have proposed several methods to execute quantitative inferences using large quantities of DNA strands in test tube and extend the previous algorithms to robust ones for noise and errors in the data. These methods include probabilistic inference and randomized prediction, and weighted majority prediction and learning by am plification in the test tube based on the weighted majority algorithm [Littlestone and Warmuth 94].