#### Identifier

etd-12212004-191037

#### Degree

Doctor of Philosophy (PhD)

#### Department

Computer Science

#### Document Type

Dissertation

#### Abstract

Hidden Markov Models (HMMs) are probabilistic models that have been widely applied to a number of fields since their inception in the late 1960’s. Computational Biology, Image Processing, and Signal Processing, are but a few of the application areas of HMMs. In this dissertation, we develop several new efficient learning algorithms for learning HMM parameters. First, we propose a new polynomial-time algorithm for supervised learning of the parameters of a first order HMM from a state probability distribution (SD) oracle. The SD oracle provides the learner with the state distribution vector corresponding to a query string. We prove the correctness of the algorithm and establish the conditions under which it is guaranteed to construct a model that exactly matches the oracle’s target HMM. We also conduct a simulation experiment to test the viability of the algorithm. Furthermore, the SD oracle is proven to be necessary for polynomial-time learning in the sense that the consistency problem for HMMs, where a training set of state distribution vectors such as those provided by the SD oracle is used but without the ability to query on arbitrary strings, is NP-complete. Next, we define helpful distributions on an instance set of strings for which polynomial-time HMM learning from state distribution vectors is feasible in the absence of an SD oracle and propose a new PAC-learning algorithm under helpful distribution for HMM parameters. The PAC-learning algorithm ensures with high probability that HMM parameters can be learned from training examples without asking queries. Furthermore, we propose a hybrid learning algorithm for approximating HMM parameters from a dataset composed of strings and their corresponding state distribution vectors, and provide supporting experimental data, which indicates our hybrid algorithm produces more accurate approximations than the existing method.

#### Date

2005

#### Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

#### Recommended Citation

Moscovich, Luis G., "Learning discrete Hidden Markov Models from state distribution vectors" (2005). *LSU Doctoral Dissertations*. 4068.

https://digitalcommons.lsu.edu/gradschool_dissertations/4068

#### Committee Chair

Jianhua Chen

#### DOI

10.31390/gradschool_dissertations.4068