In this question, you will learn to build a Naive Bayes Classifier for the binary classification

task.

$1.$ Dataset: "Financial Phrasebank" dataset from HuggingFace$\mathrm{.}1$ To load the data, you

need to install library "datasets" $($pip install datasets$)$ and then use load$\_$datset$()$

method to load the dataset. You can find the code on the link provided above.

$2.$ The dataset contains $3$ class labels, neutral $(1),$ positive $(2),$ and negative $(0).$ Consider

only positive and negative samples and ignore the neutral samples. Use $80\%$ of the

samples selected randomly to train the model and the remaining $20\%$ for the test.

$3.$ Clean the dataset with the steps from the previous assignment and build a vocabulary of

all the words.

$4.$ Compute the prior probability of each class

$()=()$

$$

Here, $()$ is the number of samples with class $$ and $$ is the total number of

samples in the dataset.

$5.$ Compute the likelihood $($

$|)$ for a all words $$ and all classes$$ with following equation:

$($

$|)=($

$,)+1$

$||+(,)$

Here, the $($

$,)$ is the frequency of the word $$

in class c while $(,)$ is

the frequency of all the words in the class c$.$ Laplace smoothing is used to avoid zero

probability in the case of a new word.

$6.$ For each sample in the test set, predict class $$ which is the class with the highest

posterior probability. To avoid underflow and increase speed, use log space to predict

the class as follows:

$=$ argmax

$$

$($log $()+$

$$

log $($

$|))(3\mathrm{.}1)$

$7.$ Using the metrics from scikit$-$learn library$2$

$,$ calculate the accuracy and macro$-$average

precision, recall, and F$1$ score, and also provide the confusion matrix on the test set.

Q$2.$ Logistic Regression: Code $[25]$

In this task, you will learn to build a Logistic Regression Classifier for the same "Financial

Phrasebank" dataset. Bag of Words model will be used for this task.

$1.$ Use $60\%$ of the data selected randomly for training, $20\%$ selected randomly for testing and

the remaining $20\%$ for validation set. Use classes $$positive$$ and $$negative$$ only. Perform

the same cleaning tasks on the text data and build a vocabulary of the words.

$1$Link to the dataset.

$2$Link to the scikit$-$learn documentation for metrics.

$2$

$2.$ Using CountVectorizer$3$

$,$ fit the cleaned train data. This will create the bag$-$of$-$words

model for the train data. Transform test and validation sets using same CountVectorizer.

$3.$ To implement the logistic regression using following equations,

$=.$

$=()$

we need the weight vector W$.$ Create an array of dimension equal to those of each $$

from the CountVectorizer.

$4.$ Apply above equations over whole training dataset and calculate $$ and cross$-$entropy

loss $$ which can be calculated as

$=$ log $+(1)$ log$(1)$

$5.$ Now, update the weights as follows:

$+1=().$

Here, $().$

is the gradient of sigmoid function and $=0\mathrm{.}01$ is the learning rate.

$6.$ Repeat step $4$ and step $5$ for $500$ iterations or epochs. For each iteration, calculate the

cross$-$entropy loss on validation set.

$7.$ Calculate the accuracy and macro$-$average precision, recall, and F$1$ score and provide

the confusion matrix on the test set.

$8.$ Experiment with varying values of $$ in $(0\mathrm{.}0001,0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1).$ Report your observations

with respect to the performance of the model. You can vary the number of iterations to

enhance the performance if necessary