
Type: New Feature

Status: Closed

Priority: Minor

Resolution: Fixed

Affects Version/s: 0.4

Fix Version/s: 0.4

Component/s: None

Labels:None
Overview
This is a project proposal for a summerterm university project to write a (sequential) HMM implementation for Mahout. Five students will work on this project as part of a course mentored by Isabel Drost.
Abstract:
Hidden Markov Models are used in multiple areas of Machine Learning, such as speech recognition, handwritten letter recognition or natural language processing. A Hidden Markov Model (HMM) is a statistical model of a process consisting of two (in our case discrete) random variables O and Y, which change their state sequentially. The variable Y with states
{y_1, ... , y_n}is called the "hidden variable", since its state is not directly observable. The state of Y changes sequentially with a so called  in our case firstorder  Markov Property. This means, that the state change probability of Y only depends on its current state and does not change in time. Formally we write: P(Y(t+1)=y_iY(0)...Y(t)) = P(Y(t+1)=y_iY(t)) = P(Y(2)=y_iY(1)). The variable O with states
{o_1, ... , o_m}is called the "observable variable", since its state can be directly observed. O does not have a Markov Property, but its state propability depends statically on the current state of Y.
Formally, an HMM is defined as a tuple M=(n,m,P,A,B), where n is the number of hidden states, m is the number of observable states, P is an ndimensional vector containing initial hidden state probabilities, A is the nxndimensional "transition matrix" containing the transition probabilities such that A[i,j]=P(Y(t)=y_iY(t1)=y_j) and B is the mxndimensional "observation matrix" containing the observation probabilties such that B[i,j]= P(O=o_iY=y_j).
Rabiner [1 defined three main problems for HMM models:
 Evaluation: Given a sequence O of observations and a model M, what is the probability P(OM) that sequence O was generated by model M. The Evaluation problem can be efficiently solved using the Forward algorithm
 Decoding: Given a sequence O of observations and a model M, what is the most likely sequence Y*=argmax(Y) P(OM,Y) of hidden variables to generate this sequence. The Decoding problem can be efficiently sovled using the Viterbi algorithm.
 Learning: Given a sequence O of observations, what is the most likely model M*=argmax(M)P(OM) to generate this sequence. The Learning problem can be efficiently solved using the BaumWelch algorithm.
The target of each milestone is defined as the implementation for the given goals, the respective documentation and unit tests for the implementation.
Timeline
Mid of May 2010  Mid of July 2010
Milestones
I) Define an HMM class based on Apache Mahout Math package offering interfaces to set model parameters, perform consistency checks, perform output prediction.
1 week from May 18th till May 25th.
II) Write sequential implementations of forward (cf. problem 1 [1) and backward algorithm.
2 weeks from May 25th till June 8th.
III) Write a sequential implementation of Viterbi algorithm (cf. problem 2 [1), based on existing forward algorithm implementation.
2 weeks from June 8th till June 22nd
IV) Have a running sequential implementation of BaumWelch algorithm for model parameter learning (application II [ref]), based on existing forward/backward algorithm implementation.
2 weeks from June 8th till June 22nd
V) Provide a usage example of HMM implementation, demonstrating all three problems.
2 weeks from June 22nd till July 6th
VI) Finalize documentation and implemenation, clean up open ends.
1 week from July 6th till July 13th
References:
[1 Lawrence R. Rabiner (February 1989). "A tutorial on Hidden Markov Models and selected applications in speech recognition". Proceedings of the IEEE 77 (2): 257286. doi:10.1109/5.18626.
Potential test data sets:
http://www.cnts.ua.ac.be/conll2000/chunking/
http://archive.ics.uci.edu/ml/datasets/Character+Trajectories