CSED342 Assignment 3-Text Reconstruction Solution

General Instructions
This (and every) assignment has a written part and a programming part.
You should write both types of answers in submission.py between
# BEGIN_YOUR_ANSWER and
# END_YOUR_ANSWER
ÒThis icon means a written answer is expected. Some of these problems are multiple choice questions that impose negative scores if the answers are incorrect. So, don’t write answers unless you are confident.
¥This icon means you should write code. you can add other helper functions outside the answer block if you want. Do not make changes to files other than submission.py.
Your code will be evaluated on two types of test cases, basic and hidden, which you can see in grader.py. Basic tests, which are fully provided to you, do not stress your code with large inputs or tricky corner cases. Hidden tests are more complex and do stress your code. The inputs of hidden tests are provided in grader.py, but the correct outputs are not. To run all the tests, type
python grader.py
This will tell you only whether you passed the basic tests. On the hidden tests, the script will alert you if your code takes too long or crashes, but does not say whether you got the correct output. You can also run a single test (e.g., 3a-0-basic) by typing
python grader.py 3a-0-basic
We strongly encourage you to read and understand the test cases, create your own test cases, and not just blindly run grader.py.

Problems
In this homework, we consider two tasks: word segmentation and vowel insertion. Word segmentation often comes up in processing many non-English languages, in which words might not be flanked by spaces on either end, such as in written Chinese or in long compound German words.
Vowel insertion is relevant in languages such as Arabic or Hebrew, for example, where modern script eschews notations for vowel sounds and the human reader infers them from context. More generally, it is an instance of a reconstruction problem given lossy encoding and some context.
We already know how to optimally solve any particular search problem with graph search algorithms such as uniform cost search or A*. Our goal here is modeling — that is, converting real-world tasks into state-space search problems.
Setup: n-gram language models and uniform-cost search
Our algorithm will base segmentation and insertion decisions based on the cost of produced text according to a language model. A language model is some function of the processed text that captures its fluency by estimating the likelihood of text p(w1,w2,...,wN−1,wN) = A very common language model in NLP is an n-gram sequence model, which assumes p(wi|w1,...,wi−1) = p(wi|wi−(n−1),...,wi−1). We’ll use the n-gram model’s negative loglikelihood −logp(wi|wi−(n−1),...,wi−1) as a cost function c(wi−(n−1),wi−1,...,wi). The cost will always be positive, and lower costs indicate better fluency. As a simple example: in a case where n = 2 and c is our n-gram cost function, c(big, fish) would be low, but c(fish, fish) would be fairly high.
u(w1) + u(w2) + u(w3) + u(w4).
For a bigram model b (n = 2), the cost is
b(w0,w1) + b(w1,w2) + b(w2,w3) + b(w3,w4),
Problem 1. Word Segmentation
In word segmentation, you are given as input a string of alphabetical characters ([a-z]) without whitespace, and your goal is to insert spaces into this string such that the result is the most fluent according to the language model.
Problem 1a [6 points] ¥
Implement an algorithm that finds the optimal word segmentation of an input character sequence. Your algorithm will consider costs based simply on a unigram cost function.
Before jumping into code, you should think about how to frame this problem as a statespace search problem. How would you represent a state? What are the successors of a state? What are the state transition costs?
Uniform cost search (UCS) is implemented for you, and you should make use of it here.
Fill in the member functions of the SegmentationProblem class and the segmentWords function. The argument unigramCost is a function that takes in a single string representing a word and outputs its unigram cost. You can assume that all the inputs would be in lower case. The function segmentWords should return the segmented sentence with spaces as delimiters, i.e. ‘ ’.join(words).
For convenience, you can actually run python submission.py to enter a console in which you can type character sequences that will be segmented by your implementation of segmentWords. To request a segmentation, type seg mystring into the prompt. For example:
>> seg thisisnotmybeautifulhouse Query (seg): thisisnotmybeautifulhouse this is not my beautiful house
Console commands other than seg – namely ins and both – will be used for the upcoming parts of the assignment. Other commands that might help with debugging can be found by typing help at the prompt.
You are encouraged to refer to NumberLineSearchProblem and GridSearchProblem implemented in util.py for reference. They don’t contribute to testing your submitted code but only serve as a guideline to how your code should look like.
Problem 2. Vowel Insertion
Now you are given a sequence of English words with their vowels missing (A, E, I, O, and U; never Y). Your task is to place vowels back into these words in a way that maximizes sentence fluency (i.e., that minimizes sentence cost). For this task, you will use a bigram cost function.
You are also given a mapping possibleFills that maps any vowel-free word to a set of possible reconstructions (complete words). For example, possibleFills(‘fg’) returns set([‘fugue’, ‘fog’]).
Problem 2a [6 points] ¥
Implement an algorithm that finds optimal vowel insertions. Use the UCS subroutines.
When you’ve completed your implementation, the function insertVowels should return the reconstructed word sequence as a string with space delimiters, i.e. ‘ ’.join(filledWords). Assume that you have a list of strings as the input, i.e. the sentence has already been split into words for you. Note that empty string is a valid element of the list.
The argument queryWords is the input sequence of vowel-free words. Note well that the empty string is a valid such word. The argument bigramCost is a function that takes two strings representing two sequential words and provides their bigram score. The special out-ofvocabulary beginning-of-sentence word -BEGIN- is given by wordsegUtil.SENTENCE_BEGIN. The argument possibleFills is a function; it takes a word as string and returns a set of reconstructions.
Note: If some vowel-free word w has no reconstructions according to possibleFills, your implementation should consider w itself as the sole possible reconstruction.
Use the ins command in the program console to try your implementation. For example:
>> ins thts m n th crnr Query (ins): thts m n th crnr thats me in the corner
The console strips away any vowels you do insert, so you can actually type in plain English and the vowel-free query will be issued to your program. This also means that you can use a single vowel letter as a means to place an empty string in the sequence. For example:
>> ins its a beautiful day in the neighborhood Query (ins): ts btfl dy n th nghbrhd its a beautiful day in the neighborhood
Problem 3: Putting It Together
We’ll now see that it’s possible to solve both of these tasks at once. This time, you are given a whitespace- and vowel-free string of alphabetical characters. Your goal is to insert spaces and vowels into this string such that the result is the most fluent possible one. As in the previous task, costs are based on a bigram cost function.
Problem 3a [6 points] ¥
Implement an algorithm that finds the optimal space and vowel insertions. Use the UCS subroutines.
When you’ve completed your implementation, the function segmentAndInsert should return a segmented and reconstructed word sequence as a string with space delimiters, i.e.
’ ’.join(filledWords).
The argument query is the input string of space- and vowel-free words. The argument bigramCost is a function that takes two strings representing two sequential words and provides their bigram score. The special out-of-vocabulary beginning-of-sentence word -BEGINis given by wordsegUtil.SENTENCE_BEGIN. The argument possibleFills is a function; it takes a word as string and returns a set of reconstructions.
Note: Unlike in problem 2, where a vowel-free word could (under certain circumstances) be considered a valid reconstruction of itself, here you should only include in your output words that are the reconstruction of some vowel-free word according to possibleFills. Additionally, you should not include words containing only vowels such as “a” or “I”; all words should include at least one consonant from the input string.
Use the command both in the program console to try your implementation. For example:
>> both mgnllthppl Query (both): mgnllthppl imagine all the people
Problem 4: A* search
Now, we’ll apply A* search to accelerate search speed. First, you exercise by making a simple problem and a heuristic function to be familiar with A* search. Then, you make a heuristic function for the text reconstruction task.
Problem 4a [4 points] Ò
In this problem, you should define your own simple search problem SimpleProblem and

a heuristic function admissibleButInconsistentHeuristic. As the name suggests, the heuristic function should be admissible but not consistent, so A* cannot find the minimum

cost path with the heuristic function. Also, we assume the heuristic returns 0 when given

an end state. Before implementing them, check UniformCostSearch and its parameter heuristic to examine how A* works.
Problem 4b [4 points] ¥
We’re going to speed up joint space and vowel insertion with A*. Recall that having to score an output using a bigram model b(w0,w) is more expensive than using a unigram model u(w) because we have to remember the previous word w0 in the state. Now let’s tackle the task by following the below guideline:
Note: Don’t confuse ub defined here with the unigram cost function u used in Problem 1.
2. Implement RelaxedProblem which is a relaxed problem of JointSegmentationInsertionProblem. The relaxed problem calculate action’s cost based on wordCost.
3. Implement makeHeuristic which returns a consistent heuristic function for the given query. You can exploit RelaxedProblem and util.DynamicProgramming.
4. Finally implement fastSegmentAndInsert which should be faster than segmentAndInsert. You should use UniformCostSearch.solve with a proper heuristic argument.