 # Proposal for Implementing Hidden Markov Model

XMLWordPrintableJSON

#### Details

• Type: New Feature
• Status: Closed
• Priority: Minor
• Resolution: Fixed
• Affects Version/s: 0.4
• Fix Version/s:
• Component/s: None
• Labels:
None

#### Overview

This is a project proposal for a summer-term 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 first-order - 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_i|Y(0)...Y(t)) = P(Y(t+1)=y_i|Y(t)) = P(Y(2)=y_i|Y(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 n-dimensional vector containing initial hidden state probabilities, A is the nxn-dimensional "transition matrix" containing the transition probabilities such that A[i,j]=P(Y(t)=y_i|Y(t-1)=y_j) and B is the mxn-dimensional "observation matrix" containing the observation probabilties such that B[i,j]= P(O=o_i|Y=y_j).

Rabiner [1 defined three main problems for HMM models:

1. Evaluation: Given a sequence O of observations and a model M, what is the probability P(O|M) that sequence O was generated by model M. The Evaluation problem can be efficiently solved using the Forward algorithm
2. Decoding: Given a sequence O of observations and a model M, what is the most likely sequence Y*=argmax(Y) P(O|M,Y) of hidden variables to generate this sequence. The Decoding problem can be efficiently sovled using the Viterbi algorithm.
3. Learning: Given a sequence O of observations, what is the most likely model M*=argmax(M)P(O|M) to generate this sequence. The Learning problem can be efficiently solved using the Baum-Welch 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 Baum-Welch 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): 257-286. doi:10.1109/5.18626.

#### Attachments

1. MAHOUT-396.diff
112 kB
Isabel Drost-Fromm
2. MAHOUT-396.diff
106 kB
Max Heimel
3. MAHOUT-396.diff
46 kB
Max Heimel
4. MAHOUT-396.diff
43 kB
Max Heimel
5. MAHOUT-396.diff
28 kB
Max Heimel
6. MAHOUT-396.diff
22 kB
Max Heimel
7. MAHOUT-396.patch
108 kB
Max Heimel

#### People

• Assignee: Max Heimel
Reporter: Max Heimel
• Votes:
0 Vote for this issue
Watchers:
0 Start watching this issue

#### Dates

• Created:
Updated:
Resolved: