a typical bayes net has the following representation:
Graphical Model Notation

Nodes: variables (with domains)

Can be assigned (observed) or unassigned
(unobserved)

Arcs: interactions

Similar to CSP constraints

Indicate “direct influence” between variables

Formally: encode conditional independence
(more later)

For now: imagine that arrows mean
direct causation (in general, they don’t!)

with reference to this representation, tell if the following code follows it (used to solve the problem given as: Consider the dataset available here. Refer to the train and test files.
This is a multi-label dataset with sparse features. In both train and test files, the first line
contains three numbers that denote the number of data points, feature dimensionality, and
number of labels in the dataset respectively.
Each line from line-2 onwards corresponds to a data point. At the beginning of each line, the
comma-separated indices denote the label indices of that data point, followed by a space,
followed by the indices of the feature vector with non-zero feature values and the corresponding
values (separated by a ‘:’).
Task: Learn a Bayes net on the features and use it for predicting the label with the maximum
confidence score. Use average “Precision@1” on the test set as the evaluation metric. Note that
there may be one or more labels in the ground-truth label-set of a given test data point.
Your program should take the train and test files as input, and display average precision@1.)

code:
import sys
import math
from collections import defaultdict

def parse_file(filename):
    """
    Parses the given dataset file.
    Returns:
        num_data: int
        num_features: int
        num_labels: int
        data: list of tuples (set of labels, dict of features)
    """
    data = []
    with open(filename, 'r') as f:
        first_line = f.readline()
        num_data, num_features, num_labels = map(int, first_line.strip().split())
        for line in f:
            line = line.strip()
            if not line:
                continue
            labels_part, features_part = line.split(' ', 1)
            labels = set(map(int, labels_part.split(',')))
            features = {}
            for item in features_part.split(' '):
                if ':' in item:
                    idx, val = item.split(':', 1)
                    features[int(idx)] = float(val)
            data.append((labels, features))
    return num_data, num_features, num_labels, data

def train_naive_bayes(train_data, num_features, num_labels, alpha=1.0):
    """
    Trains a multi-label Naive Bayes classifier.
    Returns:
        log_prior: list of log P(label)
        log_likelihood: list of dicts containing log P(feature|label)
    """
    label_counts = [0] * num_labels
    feature_counts = [defaultdict(float) for _ in range(num_labels)]
    
    for labels, features in train_data:
        for label in labels:
            label_counts[label] += 1
            for f in features:
                feature_counts[label][f] += 1.0
    
    total_labels = sum(label_counts)
    log_prior = []
    log_likelihood = []
    
    for l in range(num_labels):
        # Prior with Laplace smoothing
        prior = (label_counts[l] + alpha) / (total_labels + alpha * num_labels)
        log_prior.append(math.log(prior))
        
        # Likelihood with Laplace smoothing
        feature_likelihood = {}
        denominator = label_counts[l] + alpha * num_features
        for f in range(num_features):
            count = feature_counts[l].get(f, 0.0)
            prob = (count + alpha) / denominator
            feature_likelihood[f] = math.log(prob)
        log_likelihood.append(feature_likelihood)
        print(len(log_likelihood))
    
    return log_prior, log_likelihood

def predict(test_data, log_prior, log_likelihood, num_features, num_labels):
    """
    Predicts the label with maximum confidence score for each test instance.
    Returns:
        predictions: list of predicted label indices
    """
    predictions = []
    for _, features in test_data:
        scores = []
        for l in range(num_labels):
            score = log_prior[l]
            for f in features:
                if f < num_features:
                    score += log_likelihood[l].get(f, math.log(1e-10))  # Handle unseen features
            scores.append(score)
        # Get the label with the highest score
        best_label = scores.index(max(scores))
        predictions.append(best_label)
    return predictions

def evaluate(test_data, predictions):
    """
    Evaluates the average Precision@1.
    """
    correct = 0
    total = len(test_data)
    for i, (labels, _) in enumerate(test_data):
        if predictions[i] in labels:
            correct += 1
    average_precision_at_1 = correct / total
    return average_precision_at_1

def main():
    if len(sys.argv) != 3:
        print("Usage: python3 bayesnet.py <train_file> <test_file>")
        sys.exit(1)
    
    train_file = sys.argv[1]
    test_file = sys.argv[2]
    
    # Parse training and test data
    _, num_features_train, num_labels_train, train_data = parse_file(train_file)
    _, num_features_test, num_labels_test, test_data = parse_file(test_file)
    
    # Check consistency
    if num_features_train != num_features_test or num_labels_train != num_labels_test:
        print("Train and test files have different feature or label dimensions.")
        sys.exit(1)
    
    num_features = num_features_train
    num_labels = num_labels_train
    
    # Train Naive Bayes model
    log_prior, log_likelihood = train_naive_bayes(train_data, num_features, num_labels, alpha=1.0)
    
    # Predict on test data
    predictions = predict(test_data, log_prior, log_likelihood, num_features, num_labels)
    
    # Evaluate Precision@1
    average_precision_at_1 = evaluate(test_data, predictions)
    
    # Print the result with 4 decimal places
    print("{0:.4f}".format(average_precision_at_1))

if __name__ == "__main__":
    main()

does this code follow the bayes net representation I provided earlier