<SYSTEM_TASK:>
Given the following text description, write Python code to implement the functionality described below step by step
<END_TASK>
<USER_TASK:>
Description:
 Find duplicate questions on StackOverflow by their embeddings
In this assignment you will learn how to calculate a similarity for pieces of text. Using this approach you will know how to find duplicate questions from StackOverflow.
Libraries
In this task you will you will need the following libraries
Step1:  Grading
We will create a grader instace below and use it to collect your answers. Note that these outputs will be stored locally inside grader and will be uploaded to platform only after running submiting function in the last part of this assignment. If you want to make partial submission, you can run that cell any time you want.
Step2:  Word embedding
To solve the problem, you will use two different models of embeddings
Step3:  How to work with Google's word2vec embeddings?
Once you have loaded the representations, make sure you can access them. First, you can check if the loaded embeddings contain a word
Step5:  From word to text embeddings
Task 1 (Question2Vec). Usually, we have word-based embeddings, but for the task we need to create a representation for the whole question. It could be done in different ways. In our case we will use a mean of all word vectors in the question. Now you need to implement the function question_to_vec, which calculates the question representation described above.
Note that there could be words without the corresponding embeddings. In this case, you can just skip these words and don't take them into account during calculating the result. If the question doesn't contain any known word with embedding, the function should return a zero vector.
Step6:  To check the basic correctness of your implementation, run the function question_to_vec_tests.
Step7:  You can submit embeddings for the questions from file test_embeddings.tsv to earn the points. In this task you don't need to transform the text of a question somehow.
Step9:  Now we have a method to create a representation of any sentence and we are ready for the first evaluation. So, let's check how well our solution (Google's vectors + question_to_vec) will work.
Evaluation of text similarity
We can imagine that if we use good embeddings, the cosine similarity between the duplicate sentences should be less than for the random ones. Overall, for each pair of duplicate sentences we can generate R random negative examples and find out the position of the correct duplicate.  
For example, we have the question "Exceptions What really happens" and we are sure that another question "How does the catch keyword determine the type of exception that was thrown" is a duplicate. But our model doesn't know it and tries to find out the best option also among questions like "How Can I Make These Links Rotate in PHP", "NSLog array description not memory address" and "PECL_HTTP not recognised php ubuntu". The goal of the model is to rank all these 4 questions (1 positive and R = 3 negative) in the way that the correct one is in the first place.
However, it is unnatural to count on that the best candidate will be always in the first place. So let us consider the place of the best candidate in the sorted list of candidates and formulate a metric based on it. We can fix some K — a reasonalble number of top-ranked elements and N — a number of queries (size of the sample).
Hits@K
The first simple metric will be a number of correct hits for some K
Step11:  Test your code on the tiny examples
Step12:  Submit results of the functions hits_count and dcg_score for the following examples to earn the points.
Step13:  First solution
Step15:  We will use cosine distance to rank candidate questions which you need to implement in the function rank_questions. The function should return a sorted list of pairs (initial position in candidates list, question). Index of some pair corresponds to its rank (the first is the best). For example, if the list of candidates was [a, b, c] and the most similar is c, then a and b, the function should return a list [(2, c), (0, a), (1, b)].
Pay attention, if you use the function cosine_similarity from sklearn.metrics.pairwise to calculate similarity because it works in a different way
Step16:  Test your code on the tiny examples
Step17:  Now we can test the quality of the current approach. Run the next two cells to get the results. Pay attention that calculation of similarity between vectors takes time and this calculation is computed approximately in 10 minutes.
Step18:  If you did all the steps correctly, you should be frustrated by the received results. Let's try to understand why the quality is so low. First of all, when you work with some data it is necessary to have an idea how the data looks like. Print several questions from the data
Step19:  As you can see, we deal with the raw data. It means that we have many punctuation marks, special characters and unlowercased letters. In our case, it could lead to the situation where we can't find some embeddings, e.g. for the word "grid?". 
To solve this problem you should use the functions text_prepare from the previous assignments to prepare the data.
Step20:  Now transform all the questions from the validation set
Step21:  Let's evaluate the approach again after the preparation
Step22:  Now, prepare also train and test data, because you will need it in the future
Step23:  Task 4 (W2VTokenizedRanks). For each question from prepared test.tsv submit the ranks of the candidates to earn the points. It should take about 3-5 minutes. Pay attention that the function rank_candidates returns a ranking, while in this case you should find a position in this ranking. Ranks should start with 1.
Step24:  Advanced solution
Step25:  And now we can compare the new embeddings with the previous ones. You can find trained word vectors in the file [model_file_name].tsv. Upload the embeddings from StarSpace into a dict.
Step26:  Due to training for the particular task with the supervised data, you should expect to obtain a higher quality than for the previous approach. In additiion, despite the fact that StarSpace's trained vectors have a smaller dimension than word2vec's, it provides better results in this task.
Task 5 (StarSpaceRanks). For each question from prepared test.tsv submit the ranks of the candidates for trained representation.
Step27:  Authorization & Submission
To submit assignment parts to Cousera platform, please, enter your e-mail and token into variables below. You can generate token on this programming assignment page. <b>Note
Step28:  If you want to submit these answers, run cell below
<ASSISTANT_TASK:>
Python Code:
import sys
sys.path.append("..")
from common.download_utils import download_week3_resources
download_week3_resources()
Explanation: Find duplicate questions on StackOverflow by their embeddings
In this assignment you will learn how to calculate a similarity for pieces of text. Using this approach you will know how to find duplicate questions from StackOverflow.
Libraries
In this task you will you will need the following libraries:
- StarSpace — a general-purpose model for efficient learning of entity embeddings from Facebook
- Gensim — a tool for solving various NLP-related tasks (topic modeling, text representation, ...)
- Numpy — a package for scientific computing.
- scikit-learn — a tool for data mining and data analysis.
- Nltk — a platform to work with human language data.
Data
The following cell will download all data required for this assignment into the folder week3/data.
End of explanation
from grader import Grader
grader = Grader()
Explanation: Grading
We will create a grader instace below and use it to collect your answers. Note that these outputs will be stored locally inside grader and will be uploaded to platform only after running submiting function in the last part of this assignment. If you want to make partial submission, you can run that cell any time you want.
End of explanation
import gensim
wv_embeddings = ######### YOUR CODE HERE #############
Explanation: Word embedding
To solve the problem, you will use two different models of embeddings:
Pre-trained word vectors from Google which were trained on a part of Google News dataset (about 100 billion words). The model contains 300-dimensional vectors for 3 million words and phrases. You need to download it by following this link.
Representations using StarSpace on StackOverflow data sample. You will need to train them from scratch.
It's always easier to start with pre-trained embeddings. Unpack the pre-trained Goggle's vectors and upload them using the function KeyedVectors.load_word2vec_format from gensim library with the parameter binary=True. If the size of the embeddings is larger than the avaliable memory, you could load only a part of the embeddings by defining the parameter limit (recommended: 500000).
End of explanation
def check_embeddings(embeddings):
    error_text = "Something wrong with your embeddings ('%s test isn't correct)."
    most_similar = embeddings.most_similar(positive=['woman', 'king'], negative=['man'])
    if len(most_similar) < 1 or most_similar[0][0] != 'queen':
        return error_text % "Most similar"
    doesnt_match = embeddings.doesnt_match(['breakfast', 'cereal', 'dinner', 'lunch'])
    if doesnt_match != 'cereal':
        return error_text % "Doesn't match"
    
    most_similar_to_given = embeddings.most_similar_to_given('music', ['water', 'sound', 'backpack', 'mouse'])
    if most_similar_to_given != 'sound':
        return error_text % "Most similar to given"
    
    return "These embeddings look good."
print(check_embeddings(wv_embeddings))
Explanation: How to work with Google's word2vec embeddings?
Once you have loaded the representations, make sure you can access them. First, you can check if the loaded embeddings contain a word:
'word' in wv_embeddings
Second, to get the corresponding embedding you can use the square brackets:
wv_embeddings['word']
Checking that the embeddings are correct
To prevent any errors during the first stage, we can check that the loaded embeddings are correct. You can call the function check_embeddings, implemented below, which runs 3 tests:
1. Find the most similar word for provided "positive" and "negative" words.
2. Find which word from the given list doesn’t go with the others.
3. Find the most similar word for the provided one.
In the right case the function will return the string These embeddings look good. Othervise, you need to validate the previous steps.
End of explanation
import numpy as np
def question_to_vec(question, embeddings, dim=300):
    
        question: a string
        embeddings: dict where the key is a word and a value is its' embedding
        dim: size of the representation
        result: vector representation for the question
    
    ######################################
    ######### YOUR CODE HERE #############
    ######################################
Explanation: From word to text embeddings
Task 1 (Question2Vec). Usually, we have word-based embeddings, but for the task we need to create a representation for the whole question. It could be done in different ways. In our case we will use a mean of all word vectors in the question. Now you need to implement the function question_to_vec, which calculates the question representation described above.
Note that there could be words without the corresponding embeddings. In this case, you can just skip these words and don't take them into account during calculating the result. If the question doesn't contain any known word with embedding, the function should return a zero vector.
End of explanation
def question_to_vec_tests():
    if (np.zeros(300) != question_to_vec('', wv_embeddings)).any():
        return "You need to return zero vector for empty question."
    if (np.zeros(300) != question_to_vec('thereisnosuchword', wv_embeddings)).any():
        return "You need to return zero vector for the question, which consists only unknown words."
    if (wv_embeddings['word'] != question_to_vec('word', wv_embeddings)).any():
        return "You need to check the corectness of your function."
    if ((wv_embeddings['I'] + wv_embeddings['am']) / 2 != question_to_vec('I am', wv_embeddings)).any():
        return "Your function should calculate a mean of word vectors."
    return "Basic tests are passed."
print(question_to_vec_tests())
Explanation: To check the basic correctness of your implementation, run the function question_to_vec_tests.
End of explanation
from util import array_to_string
question2vec_result = []
for question in open('data/test_embeddings.tsv'):
    question = question.strip()
    answer = question_to_vec(question, wv_embeddings)
    question2vec_result = np.append(question2vec_result, answer)
grader.submit_tag('Question2Vec', array_to_string(question2vec_result))
Explanation: You can submit embeddings for the questions from file test_embeddings.tsv to earn the points. In this task you don't need to transform the text of a question somehow.
End of explanation
def hits_count(best_ranks, k):
    
        best_ranks: list with ranks for each element (the best rank is 1, the worst — len(best_ranks))
        k: number of top-ranked elements
        result: float number
    
    ######################################
    ######### YOUR CODE HERE #############
    ######################################
Explanation: Now we have a method to create a representation of any sentence and we are ready for the first evaluation. So, let's check how well our solution (Google's vectors + question_to_vec) will work.
Evaluation of text similarity
We can imagine that if we use good embeddings, the cosine similarity between the duplicate sentences should be less than for the random ones. Overall, for each pair of duplicate sentences we can generate R random negative examples and find out the position of the correct duplicate.  
For example, we have the question "Exceptions What really happens" and we are sure that another question "How does the catch keyword determine the type of exception that was thrown" is a duplicate. But our model doesn't know it and tries to find out the best option also among questions like "How Can I Make These Links Rotate in PHP", "NSLog array description not memory address" and "PECL_HTTP not recognised php ubuntu". The goal of the model is to rank all these 4 questions (1 positive and R = 3 negative) in the way that the correct one is in the first place.
However, it is unnatural to count on that the best candidate will be always in the first place. So let us consider the place of the best candidate in the sorted list of candidates and formulate a metric based on it. We can fix some K — a reasonalble number of top-ranked elements and N — a number of queries (size of the sample).
Hits@K
The first simple metric will be a number of correct hits for some K:
$$ \text{Hits@K} = \frac{1}{N}\sum_{i=1}^N \, [dup_i \in topK(q_i)]$$
where $q_i$ is the i-th query, $dup_i$ is its duplicate, and topK($q_i$) is the top of the ranked sentences provided by our model.
DCG@K
The second one is a simplified DCG metric:
$$ DCG = \frac{1}{N} \sum_{i=1}^N\frac{1}{\log_2(1+rank_{dup_i})}\cdot[rank_{dup_i} \le K] $$
where $rank_{dup_i}$ is a position of the duplicate in the sorted list of the nearest sentences for the query $q_i$. According to this metric, the model gets a higher reward for a higher position of the correct answer. If the answer does not appear in topK at all, the reward is zero. 
Evaluation examples
Let's calculate the described metrics for the toy example introduced above. Consider the following ranking of the candidates:
1. "How Can I Make These Links Rotate in PHP"
2. "How does the catch keyword determine the type of exception that was thrown"
3. "NSLog array description not memory address"
4. "PECL_HTTP not recognised php ubuntu"
Using the ranking above, calculate Hits@K metric for K = 1, 2, 4: 
[K = 1] We consider only the first place and Hits@1 = 0
[K = 2] We consider the first and the second places and Hits@1 = 1
[K = 4] We consider the whole list and Hits@1 = 1
Using the ranking above, calculate DCG@K metric for K = 1, 2, 4:
[K = 1] DCG = 0 because the correct answer doesn't appear in the top1 list.
[K = 2] DCG = $\frac{1}{\log_2{3}}$, because $rank_{dup}$ = 2.
[K = 4] DCG = $\frac{1}{\log_2{3}}$.
Tasks 2 and 3 (HitsCount and DCGScore). Implement the functions hits_count and dcg_score as described above.
End of explanation
def test_hits():
    answers = ['woman', 'man']
    candidates_ranking = [['woman', 'queen'], ['man', 'king']]
    best_ranks = [1, 1]
    correct_answers = [1, 1]
    for k in range(1, 3):
        if not np.isclose(hits_count(best_ranks, k), correct_answers[k - 1]):
            return "Check the function."
    candidates_ranking = [['woman', 'queen'], ['king', 'man']]
    best_ranks = [1, 2]
    correct_answers = [0.5, 1]
    for k in range(1, 3):
        if not np.isclose(hits_count(best_ranks, k), correct_answers[k - 1]):
            return "Check the function."
    return "Basic tests are passed."
print(test_hits())
def dcg_score(best_ranks, k):
    
        best_ranks: list with ranks for each element (the best rank is 1, the worst — len(best_ranks))
        k: number of top-ranked elements
        result: float number
    
    ######################################
    ######### YOUR CODE HERE #############
    ######################################
def test_dcg():
    answers = ['woman', 'man']
    candidates_ranking = [['woman', 'queen'], ['man', 'king']]
    best_ranks = [1, 1]
    correct_answers = [1.0, 1.0]
    for k in range(1, 3):
        if not np.isclose(dcg_score(best_ranks, k), correct_answers[k - 1]):
            return "Check the function."
    candidates_ranking = [['woman', 'queen'], ['king', 'man']]
    best_ranks = [1, 2]
    correct_answers = [0.5, 0.8154]
    for k in range(1, 3):
        if not np.isclose(dcg_score(best_ranks, k), correct_answers[k - 1], atol=1e-03):
            return "Check the function."
    return "Basic tests are passed."
print(test_dcg())
Explanation: Test your code on the tiny examples:
End of explanation
test_examples = [
    [1],
    [1, 2],
    [2, 1],
    [1, 2, 3],
    [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
    [9, 5, 4, 2, 8, 10, 7, 6, 1, 3],
    [4, 3, 5, 1, 9, 10, 7, 8, 2, 6],
    [5, 1, 7, 6, 2, 3, 8, 9, 10, 4],
    [6, 3, 1, 4, 7, 2, 9, 8, 10, 5],
    [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],
]
hits_results = []
for example in test_examples:
    for k in range(len(example)):
        hits_results.append(hits_count(example, k + 1))
grader.submit_tag('HitsCount', array_to_string(hits_results))
dcg_results = []
for example in test_examples:
    for k in range(len(example)):
        dcg_results.append(dcg_score(example, k + 1))
grader.submit_tag('DCGScore', array_to_string(dcg_results))
Explanation: Submit results of the functions hits_count and dcg_score for the following examples to earn the points.
End of explanation
def read_corpus(filename):
    data = []
    for line in open(filename, encoding='utf-8'):
        data.append(line.strip().split('\t'))
    return data
validation = ######### YOUR CODE HERE #############
from sklearn.metrics.pairwise import cosine_similarity
Explanation: First solution: pre-trained embeddings
We will work with predefined train, validation and test corpora. All the files are tab-separated, but have a different format:
 - train corpus contains similar sentences at the same row.
 - validation corpus contains the following columns: question, similar question, negative example 1, negative example 2, ... 
 - test corpus contains the following columns: question, example 1, example 2, ...
Validation corpus will be used for the intermediate validation of models. The test data will be necessary for submitting the quality of your model in the system.
Now you should upload validation corpus to evaluate current solution.
End of explanation
def rank_candidates(question, candidates, embeddings, dim=300):
    
        question: a string
        candidates: a list of strings (candidates) which we want to rank
        embeddings: some embeddings
        dim: dimension of the current embeddings
        
        result: a list of pairs (initial position in the list, question)
    
    
    ######################################
    ######### YOUR CODE HERE #############
    ######################################
Explanation: We will use cosine distance to rank candidate questions which you need to implement in the function rank_questions. The function should return a sorted list of pairs (initial position in candidates list, question). Index of some pair corresponds to its rank (the first is the best). For example, if the list of candidates was [a, b, c] and the most similar is c, then a and b, the function should return a list [(2, c), (0, a), (1, b)].
Pay attention, if you use the function cosine_similarity from sklearn.metrics.pairwise to calculate similarity because it works in a different way: most similar objects has greatest similarity.
End of explanation
def test_rank_candidates():
    questions = ['converting string to list', 'Sending array via Ajax fails']
    candidates = [['Convert Google results object (pure js) to Python object', 
                   'C# create cookie from string and send it',
                   'How to use jQuery AJAX for an outside domain?'], 
                  ['Getting all list items of an unordered list in PHP', 
                   'WPF- How to update the changes in list item of a list', 
                   'select2 not displaying search results']]
    results = [[(1, 'C# create cookie from string and send it'), 
                (0, 'Convert Google results object (pure js) to Python object'), 
                (2, 'How to use jQuery AJAX for an outside domain?')],
               [(0, 'Getting all list items of an unordered list in PHP'), 
                (2, 'select2 not displaying search results'), 
                (1, 'WPF- How to update the changes in list item of a list')]]
    for question, q_candidates, result in zip(questions, candidates, results):
        ranks = rank_candidates(question, q_candidates, wv_embeddings, 300)
        if not np.all(ranks == result):
            return "Check the function."
    return "Basic tests are passed."
print(test_rank_candidates())
Explanation: Test your code on the tiny examples:
End of explanation
wv_ranking = []
for line in validation:
    q, *ex = line
    ranks = rank_candidates(q, ex, wv_embeddings)
    wv_ranking.append([r[0] for r in ranks].index(0) + 1)
for k in [1, 5, 10, 100, 500, 1000]:
    print("DCG@%4d: %.3f | Hits@%4d: %.3f" % (k, dcg_score(wv_ranking, k), k, hits_count(wv_ranking, k)))
Explanation: Now we can test the quality of the current approach. Run the next two cells to get the results. Pay attention that calculation of similarity between vectors takes time and this calculation is computed approximately in 10 minutes.
End of explanation
for line in validation[:3]:
    q, *examples = line
    print(q, *examples[:3])
Explanation: If you did all the steps correctly, you should be frustrated by the received results. Let's try to understand why the quality is so low. First of all, when you work with some data it is necessary to have an idea how the data looks like. Print several questions from the data:
End of explanation
from util import text_prepare
Explanation: As you can see, we deal with the raw data. It means that we have many punctuation marks, special characters and unlowercased letters. In our case, it could lead to the situation where we can't find some embeddings, e.g. for the word "grid?". 
To solve this problem you should use the functions text_prepare from the previous assignments to prepare the data.
End of explanation
prepared_validation = []
for line in validation:
    ######### YOUR CODE HERE #############
Explanation: Now transform all the questions from the validation set:
End of explanation
wv_prepared_ranking = []
for line in prepared_validation:
    q, *ex = line
    ranks = rank_candidates(q, ex, wv_embeddings)
    wv_prepared_ranking.append([r[0] for r in ranks].index(0) + 1)
for k in [1, 5, 10, 100, 500, 1000]:
    print("DCG@%4d: %.3f | Hits@%4d: %.3f" % (k, dcg_score(wv_prepared_ranking, k), 
                                              k, hits_count(wv_prepared_ranking, k)))
Explanation: Let's evaluate the approach again after the preparation:
End of explanation
def prepare_file(in_, out_):
    out = open(out_, 'w')
    for line in open(in_, encoding='utf8'):
        line = line.strip().split('\t')
        new_line = [text_prepare(q) for q in line]
        print(*new_line, sep='\t', file=out)
    out.close()
######################################
######### YOUR CODE HERE #############
######################################
Explanation: Now, prepare also train and test data, because you will need it in the future:
End of explanation
from util import matrix_to_string
w2v_ranks_results = []
prepared_test_data = ######### YOUR CODE HERE #############
for line in open(prepared_test_data):
    q, *ex = line.strip().split('\t')
    ranks = rank_candidates(q, ex, wv_embeddings, 300)
    ranked_candidates = [r[0] for r in ranks]
    w2v_ranks_results.append([ranked_candidates.index(i) + 1 for i in range(len(ranked_candidates))])
    
grader.submit_tag('W2VTokenizedRanks', matrix_to_string(w2v_ranks_results))
Explanation: Task 4 (W2VTokenizedRanks). For each question from prepared test.tsv submit the ranks of the candidates to earn the points. It should take about 3-5 minutes. Pay attention that the function rank_candidates returns a ranking, while in this case you should find a position in this ranking. Ranks should start with 1.
End of explanation
######### TRAINING HAPPENING HERE #############
Explanation: Advanced solution: StarSpace embeddings
Now you are ready to train your own word embeddings! In particular, you need to train embeddings specially for our task of duplicates detection. Unfortunately, StarSpace could not be run on Windows and we recommend to use provided
docker container or other alternatives.
How it works and what's the main difference with word2vec?
The main point in this section is that StarSpace can be trained specifically for some tasks. In contrast to word2vec model, which tries to train similar embeddings for words in similar contexts, StarSpace uses embeddings for the whole sentence (just as a sum of embeddings of words and phrases). Despite the fact that in both cases we get word embeddings as a result of the training, StarSpace embeddings are trained using some supervised data, e.g. a set of similar sentence pairs, and thus they can better suit the task.
In our case, StarSpace should use two types of sentence pairs for training: "positive" and "negative". "Positive" examples are extracted from the train sample (duplicates, high similarity) and the "negative" examples are generated randomly (low similarity assumed). 
How to choose the best params for the model?
Normally, you would start with some default choice and then run extensive experiments to compare different strategies. However, we have some recommendations ready for you to save your time:
- Be careful with choosing the suitable training mode. In this task we want to explore texts similarity which corresponds to trainMode = 3.
- Use adagrad optimization (parameter adagrad = true).
- Set the length of phrase equal to 1 (parameter ngrams), because we need embeddings only for words.
- Don't use a large number of epochs (we think that 5 should be enough).
- Try dimension dim equal to 100.
- To compare embeddings usually cosine similarity is used.
- Set minCount greater than 1 (for example, 2) if you don't want to get embeddings for extremely rare words.
- Parameter verbose = true could show you the progress of the training process.
- Set parameter fileFormat equals labelDoc.
- Parameter negSearchLimit is responsible for a nuber of negative examples which is used during the training. We think that 10 will be enought for this task.
- To increase a speed of training we recommend to set learning rate to 0.05.
Train StarSpace embeddings for unigrams on the train dataset. You don't need to change the format of the input data. Just don't forget to use prepared version of the training data. 
If you follow the instruction, the training process will take about 1 hour.
End of explanation
starspace_embeddings = ######### YOUR CODE HERE #############
ss_prepared_ranking = []
for line in prepared_validation:
    q, *ex = line
    ranks = rank_candidates(q, ex, starspace_embeddings, 100)
    ss_prepared_ranking.append([r[0] for r in ranks].index(0) + 1)
for k in [1, 5, 10, 100, 500, 1000]:
    print("DCG@%4d: %.3f | Hits@%4d: %.3f" % (k, dcg_score(ss_prepared_ranking, k), 
                                               k, hits_count(ss_prepared_ranking, k)))
Explanation: And now we can compare the new embeddings with the previous ones. You can find trained word vectors in the file [model_file_name].tsv. Upload the embeddings from StarSpace into a dict.
End of explanation
starspace_ranks_results = []
prepared_test_data = ######### YOUR CODE HERE #############
for line in open(prepared_test_data):
    q, *ex = line.strip().split('\t')
    ranks = rank_candidates(q, ex, starspace_embeddings, 100)
    ranked_candidates = [r[0] for r in ranks]
    starspace_ranks_results.append([ranked_candidates.index(i) + 1 for i in range(len(ranked_candidates))])
    
grader.submit_tag('StarSpaceRanks', matrix_to_string(starspace_ranks_results))
Explanation: Due to training for the particular task with the supervised data, you should expect to obtain a higher quality than for the previous approach. In additiion, despite the fact that StarSpace's trained vectors have a smaller dimension than word2vec's, it provides better results in this task.
Task 5 (StarSpaceRanks). For each question from prepared test.tsv submit the ranks of the candidates for trained representation.
End of explanation
STUDENT_EMAIL = # EMAIL 
STUDENT_TOKEN = # TOKEN 
grader.status()
Explanation: Authorization & Submission
To submit assignment parts to Cousera platform, please, enter your e-mail and token into variables below. You can generate token on this programming assignment page. <b>Note:</b> Token expires 30 minutes after generation.
End of explanation
grader.submit(STUDENT_EMAIL, STUDENT_TOKEN)
Explanation: If you want to submit these answers, run cell below
End of explanation
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