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CS5012 algorithms
创建日期：2024-08-07 16:20:35
标签： CS5012
algorithms

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CS5012 algorithms


This practical is worth 50% of the coursework component of this module. Its due

date is Wednesday 6th of March 2024, at 21:00. Note that MMS is the definitive source

for deadlines and weights.

The purpose of this assignment is to gain understanding of the Viterbi algorithm,

and its application to part-of-speech (POS) tagging. The Viterbi algorithm will be

related to two other algorithms.

You will also get to see the Universal Dependencies treebanks. The main purpose

of these treebanks is dependency parsing (to be discussed later in the module), but

here we only use their part-of-speech tags.

Getting started

We will be using Python3. On the lab (Linux) machines, you need the full path

/usr/local/python/bin/python3, which is set up to work with NLTK. (Plain

python3 won’t be able to find NLTK.)

If you run Python on your personal laptop, then next to NLTK , 

you will also need to install the conllu package .

To help you get started, download gettingstarted.py and the other Python

files, and the zip file with treebanks from this directory. After unzipping, run

/usr/local/python/bin/python3 gettingstarted.py. You may, but need not, use

parts of the provided code in your submission.

The three treebanks come from Universal Dependencies. 

1

Parameter estimation

First, we write code to estimate the transition probabilities and the emission probabilities of an HMM (Hidden Markov Model), on the basis of (tagged) sentences from

a training corpus from Universal Dependencies. Do not forget to involve the start-ofsentence marker ?s? and the end-of-sentence marker ?/s? in the estimation.

The code in this part is concerned with:

? counting occurrences of one part of speech following another in a training corpus,

? counting occurrences of words together with parts of speech in a training corpus,

? relative frequency estimation with smoothing.

As discussed in the lectures, smoothing is necessary to avoid zero probabilities for

events that were not witnessed in the training corpus. Rather than implementing a

form of smoothing yourself, you can for this assignment take the implementation of

Witten-Bell smoothing in NLTK (among the implementations of smoothing in NLTK,

this seems to be the most robust one). An example of use for emission probabilities is

in file smoothing.py; one can similarly apply smoothing to transition probabilities.

Three algorithms for POS tagging

Algorithm 1: eager algorithm

First, we implement a naive algorithm that chooses the POS tag for the i-th token

on the basis of the chosen (i ? 1)-th tag and the i-th token. To be more precise, we

determine for each i = 1, . . . , n, in this order:

t?i = argmax

ti

P(ti

| t?i?1) · P(wi

| ti)

assuming t?0 is the start-of-sentence marker ?s?. Note that the end-of-sentence marker

?/s? is not even used here.

Algorithm 2: Viterbi algorithm

Now we implement the Viterbi algorithm, which determines the sequence of tags for a

given sentence that has the highest probability. As discussed in the lectures, this is:

t?1 · · ·t?n = argmax

t1···tn

Yn

i=1

P(ti

| ti?1) · P(wi

| ti)

!

· P(tn+1 | tn)

2

where the tokens of the input sentence are w1 · · ·wn, and t0 = ?s? and tn+1 = ?/s? are

the start-of-sentence and end-of-sentence markers, respectively.

To avoid underflow for long sentences, we need to use log probabilities.

Algorithm 3: individually most probable tags

We now write code that determines the most probable part of speech for each token

individually. That is, for each i, computed is:

t?i = argmax

ti

X

t1···ti?1ti+1···tn

Yn

i=1

P(ti

| ti?1) · P(wi

| ti)

!

· P(tn+1 | tn)

To compute this effectively, we need to use forward and backward values, as discussed

in the lectures on the Baum-Welch algorithm, making use of the fact that the above is

equivalent to:

t?i = argmax

ti

P

t1···ti?1

Qi

k=1 P(tk | tk?1) · P(wk | tk)



·

P

ti+1···tn

Qn

k=i+1 P(tk | tk?1) · P(wk | tk)



· P(tn+1 | tn)

The computation of forward values is very similar to the Viterbi algorithm, so you

may want to copy and change the code you already had, replacing statements that

maximise by corresponding statements that sum values together. Computation of

backward values is similar to computation of forward values.

See logsumexptrick.py for a demonstration of the use of log probabilities when

probabilities are summed, without getting underflow in the conversion from log probabilities to probabilities and back.

Evaluation

Next, we write code to determine the percentages of tags in a test corpus that are

guessed correctly by the above three algorithms. Run experiments for the training

and test corpora of the three included treebanks, and possibly for treebanks of more

languages (but not for more than 5; aim for quality rather than quantity). Compare

the performance of the three algorithms.

You get the best experience out of this practical if you also consider the languages of

the treebanks. What do you know (or what can you find out) about the morphological

and syntactic properties of these languages? Can you explain why POS tagging is more

difficult for some languages than for others?

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