Inverting the Viterbi Algorithm: an Abstract Framework for Structure Design
published: Aug. 29, 2008, recorded: July 2008, views: 706
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Probabilistic grammatical formalisms such as hidden Markov models (HMMs) and stochastic context-free grammars (SCFGs) have been extensively studied and widely applied in a number of fields. Here, we introduce a new algorithmic problem on HMMs and SCFGs that arises naturally from protein and RNA design, and which has not been previously studied. The problem can be viewed as an inverse to the one solved by the Viterbi algorithm on HMMs or by the CKY algorithm on SCFGs. We study this problem theoretically and obtain the first algorithmic results. We prove that the problem is NP-complete, even for a 3-letter emission alphabet, via a reduction from 3-SAT, a result that has implications for the hardness of RNA secondary structure design. We then develop a number of approaches for making the problem tractable. In particular, for HMMs we develop a branch-and-bound algorithm, which can be shown to have fixed-parameter tractable worst-case running time, exponential in the number of states of the HMM but linear in the length of the structure. We also show how to cast the problem as a Mixed Integer Linear Program.
Download slides: icml08_schnall_levin_iva_01.pdf (728.8 KB)
Download slides: icml08_schnall_levin_iva_01.ppt (2.0 MB)
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !