Implement a Naive Bayes classifier from scratch with fit and predict, estimating priors and likelihoods and working in log space.

Multinomial Naive Bayes over count features, with Laplace smoothing.

import numpy as np

class MultinomialNB:
    def __init__(self, alpha=1.0):
        self.alpha = alpha

    def fit(self, X, y):
        # X (N, V) counts, y (N,) labels
        self.classes = np.unique(y)
        n, V = len(self.classes), X.shape[1]
        self.log_prior = np.empty(n)
        self.log_lik = np.empty((n, V))
        for i, c in enumerate(self.classes):
            Xc = X[y == c]
            self.log_prior[i] = np.log(len(Xc) / len(X))
            cnt = Xc.sum(0) + self.alpha
            self.log_lik[i] = np.log(cnt / cnt.sum())
        return self

    def predict(self, X):
        s = X @ self.log_lik.T + self.log_prior
        return self.classes[s.argmax(1)]

Interviewers check you sum log-probabilities instead of multiplying, which underflows; that smoothing stops one unseen feature zeroing a class; and that you can name the variant to swap in: Gaussian for continuous features, Bernoulli for binary. For probabilities, normalize the scores with log-sum-exp.