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FIT5217 (S1 2022) - Assignment 1
Marks Worth 80 marks, and 20% of all marks for the unit
Due Date Friday, 15 April 2022, 11:55 PM
Extension An extension could be granted under some circumstances. A special consideration
application form must be submitted. Please refer to the university webpage on
special consideration.
Lateness For all assessment items handed in after the official due date, and without an agreed
extension, a 10% penalty applies to the student’s mark for each day after the due
date (including weekends) for up to 7 days. Assessment items handed in after 7
days without special consideration will not be considered.
Authorship This is an individual assessment. All work must be your own. All submissions will
be placed through Turnitin. This makes plagiarism remarkably easy to identify for
us.
Submission All answers should be typed. A single pdf file needs to be submitted. The name
of the file must be Assignment 1 FIT5217 012345678.pdf where “012345678” is
replaced by your own student ID. The pages should be A4 size with standard
margins and 11 point font or similar.
Table 1: Instructions for FIT5217 (S1 2022) - Assignment 1
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Part 1 - Language Model (Total 20 Marks)
Take the corpus which contains the following three sentences:
YI READ BALL LIGHTNING
JINMING READ A DIFFERENT BOOK
SHE READ A BOOK BY LIU
Question 1.1. List all the unigrams, bigrams and trigrams. (4 Marks)
Question 1.2. Using a bigram language model and maximum likelihood estimation (from the above
corpus), calculate the probability of each of the following 2 sentences. List all the bigram probabilities
as well as the final probabilities of the sentences. (8 Marks)
YI READ A BOOK
LIU READ A BOOK
Question 1.3. Similar to the above question, using a bigram language model and add-1 Smoothing,
calculate the probability of each of the following 2 sentences. List all the bigram probabilities as
well as the final probabilities of the sentences. (8 Marks)
YI READ A BOOK
LIU READ A BOOK
Part 2 - POS Tagging (Total 15 Marks)
Consider the following HMM with three possible observations “snow”, “fell”, “storm” and three
possible Part-of-Speech (POS) tags (“N”, V”, “J”):
State transition probabilities (A) – e.g., aN,J = P(si+1 = J|si = N) = 0.1
A N V J
(noun) (verb) (adj)
N 0.4 0.5 0.1
V 0.5 0.1 0.4
J 0.5 0.1 0.4
Emission probabilities (B) – e.g., bN (snow) = P(oi = snow|si = N) = 0.4
B snow fell storm
N 0.4 0.2 0.4
V 0.3 0.5 0.2
J 0.2 0.4 0.4
Initial state distributions (π) – e.g., π[J] = P(s1 = J|s0 =< S >) = 0.3
N V J
π 0.4 0.3 0.3
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Question 2.1. Explain how to obtain the values in the matrices A, B and π given above in a supervised
manner. (3 marks)
Question 2.2. Draw the forward trellis diagram of the sentence “snow fell” using the given HMM.
Clearly show the forward arrows to illustrate the computation of the forward algorithm. (4 marks)
Question 2.3. Find the most likely state sequence for the sentence “snow fell” using the Viterbi
algorithm (show your steps clearly). What is the joint probability of the sentence “snow fell” and
its most likely state sequence? (4 marks)
Question 2.4. What are the two main assumptions that are built into an HMM? What is the
major downside if we construct an HMM without (or relaxing) these assumptions? You may need
to read the text book for this. (4 marks)
Part 3 - Syntactic Parsing (Total 10 Marks)
Question 3.1. Answer with True or False (you need to do a bit of research for some of these questions):
a. A lexicalized PCFG is the PCFG which does not have any non-terminals on the right-hand-side
of the grammar rules.
b. The Inside-Outside algorithm is a version of Expectation-Maximisation.
c. The Inside-Outside algorithm is used for unsupervised learning of a PCFG.
d. CKY algorithm has a complexity of O(n
3
) where n is the length of the input sentence.
e. Tree Adjoining Grammars (TAGs) are more expensive to parse compared to Context Free
Grammars (CFGs).
Part 4 - Chomsky Normal Form (Total 5 Marks)
Consider the following parse tree:
Question 4.1. Write down all the grammar rules extracted from the parse tree. Then convert the
rules into Chomsky Normal Form (CNF).
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Part 5 - PCFG (Total 15 Marks)
Consider the following parse trees:
Question 5.1. List all the grammar rules and estimate their corresponding probabilities (based on
all trees) using Maximum Likelihood estimation. (8 Marks)
Note. Structure you response as one rule per line:
[0.2] A → B C
[0.1] D → E
...
where A → B C is the grammar rule, and [0.2] is its probability.
Question 5.2. Using the estimated probabilities, calculate the probability of the following sentence:
(8 Marks)
The dog chased my silver cat .
Hint. First parse the sentence (no need to include this in your response), then use the grammar
rules and their probabilities to calculate the probability of the tree.
Part 6 - Short Essay (Total 15 Marks)
Read the following paper, then write a short essay, no more than 2 paragraphs, summarising:
• Problem Statement
• Motivation and Novelty
• Method
• Key Results
Paper: Pauls, Adam, and Dan Klein. Large-scale syntactic language modeling with treelets.
In Proceedings of the 50th Annual Meeting of the Association for Computational Linguistics.
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