MADS BAGGESEN - 20042326

Abstract
In this master’s thesis I implement and evaluate an alternative representation
of hidden Markov models (HMMs), focusing on sparse HMMs. The
reason for working with sparse HMMs is that the classic algorithms all
assume that the model is completely connected, and have the running
time of O(TN 2 ), where T is the length of the observed sequence and N
is the number of states. The representation that I use give another bound
namely O(TK) where K is the number of transitions with a positive
transition probability. This bound is no different from the N 2 bound for
completely connected HMMs, but when the model is sparse the O(TK)
will be better – and for some models even linear in the size of the model.
These very sparse models, with only a linear number of transitions, do
occur in practise and are among others used for sequence alignment. Durbin
et al. (2006) uses a family of models called profile HMMs, where each
state is only connected to three other states. These profile models are used
as a generel example throughout the thesis.
The structure of the thesis follows the working process so I will first
present the generel theory of the main algorithms for working with HMMs
and based on that I present different implementations of the forward algorithm.
I first produce a naive implementation which I use as a base
line when comparing my other implementations. Having the naive implementation
running I change the memory layout to get more sequencial
reads and by that I make significant improvements in the running time,
without changing the memory usage. Based on the improved memory
layout I then discuss and evaluate different strategies for splitting the
problem up into smaller chunks suitable for working in different threads.
My final implementation is a threaded implementation using pthreads
and the improved memory layout. This turns out to work very well, but
the increase in efficiency decreases fast when I use four threads or more.
The conclusion is that the new algorithm gives a large performance
boost on sparse models and can even compete on complete models. I
suggest continuing with this strategy, especially for sparse models.
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