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https://issues.apache.org/jira/browse/MAHOUT-396?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12898285#action_12898285
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Isabel Drost commented on MAHOUT-396:
-------------------------------------
Hmpf - please add a "good" between: "Rest of the code looks" and "to me
otherwise".
> Proposal for Implementing Hidden Markov Model
> ---------------------------------------------
>
> Key: MAHOUT-396
> URL: https://issues.apache.org/jira/browse/MAHOUT-396
> Project: Mahout
> Issue Type: New Feature
> Affects Versions: 0.4
> Reporter: Max Heimel
> Assignee: Max Heimel
> Priority: Minor
> Fix For: 0.4
>
> Attachments: MAHOUT-396.diff, MAHOUT-396.diff, MAHOUT-396.diff,
> MAHOUT-396.diff, MAHOUT-396.diff
>
>
> h4. 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.
> h4. 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|My Page#reference1]] defined three main problems for HMM models:
> # 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
> # 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.
> # 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.
> h4.Timeline
> Mid of May 2010 - Mid of July 2010
> h4.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|My
> Page#reference1]]) and backward algorithm.
> 2 weeks from May 25th till June 8th.
> III) Write a sequential implementation of Viterbi algorithm (cf. problem 2
> [[1|My Page#reference1]]), 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
> h4.References:
> {anchor:reference1}[[1|http://www.cs.ubc.ca/~murphyk/Bayes/rabiner.pdf]]
> 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.
> Potential test data sets:
> [http://www.cnts.ua.ac.be/conll2000/chunking/]
> [http://archive.ics.uci.edu/ml/datasets/Character+Trajectories]
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