Naive Bayes and probability models quiz

Question 1

What does the 'naive' assumption in the Naive Bayes classifier refer to?

Accepted Answer

Features are conditionally independent given the class

Answer

The model uses no prior probabilities

Answer

All classes are equally likely

Answer

The dataset must be very small

Question 2

State Bayes' theorem in the form used by a Naive Bayes classifier.

Accepted Answer

P(class|features) = P(features|class)·P(class)/P(features)

Answer

P(class|features) = P(features)·P(class)

Answer

P(class|features) = P(features|class) + P(class)

Answer

P(class|features) = P(class)/P(features|class)

Question 3

In Bayes' theorem, what is the 'prior' probability?

Accepted Answer

The probability of a class before seeing the features

Answer

The probability after seeing all features

Answer

The probability that the model is correct

Answer

The probability of an error

Question 4

Why can the denominator P(features) be ignored when classifying with Naive Bayes?

Accepted Answer

It is the same for all classes, so it doesn't affect the argmax

Answer

It is always equal to 1

Answer

It is unknown and cannot be computed

Answer

It equals the prior probability

Question 5

Given the conditional independence assumption, how is P(x1, x2, ..., xn | class) computed?

Accepted Answer

As the product of P(xi | class) over all features

Answer

As the sum of P(xi | class) over all features

Answer

As the average of P(xi | class)

Answer

As P(x1 | class) only

Question 6

What is Laplace (additive) smoothing and why is it used in Naive Bayes?

Accepted Answer

Adding a constant to counts to avoid zero probabilities

Answer

Removing rare features from the data

Answer

Scaling all features to unit variance

Answer

Choosing the prior randomly

Question 7

Which Naive Bayes variant is most appropriate for word-count features in text classification?

Accepted Answer

Multinomial Naive Bayes

Answer

Gaussian Naive Bayes

Answer

Linear Regression

Answer

K-Means

Question 8

Which Naive Bayes variant assumes features follow a normal (Gaussian) distribution?

Accepted Answer

Gaussian Naive Bayes

Answer

Multinomial Naive Bayes

Answer

Bernoulli Naive Bayes

Answer

Categorical Naive Bayes

Question 9

What type of features does Bernoulli Naive Bayes work with?

Accepted Answer

Binary presence/absence features

Answer

Real-valued continuous features

Answer

Word frequency counts

Answer

Image pixel intensities only

Question 10

Why are log probabilities often used when implementing Naive Bayes?

Accepted Answer

To avoid numerical underflow by turning products into sums

Answer

To make probabilities larger than 1

Answer

To remove the need for a prior

Answer

To force all features to be independent

Question 11

A spam filter has prior P(spam)=0.4 and P(ham)=0.6. For an email, P(words|spam)=0.02 and P(words|ham)=0.005. Which class does Naive Bayes predict?

Accepted Answer

Spam

Answer

Ham

Answer

Both equally likely

Answer

Cannot be determined

Question 12

What is the difference between a generative model and a discriminative model, and which type is Naive Bayes?

Accepted Answer

Naive Bayes is generative; it models the joint distribution

Answer

Naive Bayes is discriminative; it models the boundary directly

Answer

Naive Bayes models neither distribution

Answer

Naive Bayes only works without probabilities

Question 13

What is the zero-frequency problem in Naive Bayes?

Accepted Answer

An unseen feature value gives zero probability, zeroing the product

Answer

The model has no features to learn from

Answer

The prior probability is always zero

Answer

Two classes have identical probabilities

Question 14

What does P(A and B) = P(A) * P(B) tell us about events A and B?

Accepted Answer

A and B are independent events

Answer

A and B are mutually exclusive

Answer

A causes B

Answer

A and B are the same event

Question 15

What is conditional probability P(A | B), and how is it defined?

Accepted Answer

P(A and B) / P(B)

Answer

P(A) + P(B)

Answer

P(A) * P(B)

Answer

P(B) / P(A and B)

Question 16

A disease affects 1% of people. A test is 99% accurate (true positive and true negative rates). If a random person tests positive, roughly what is the probability they have the disease? Choose the closest value.

Accepted Answer

About 50%

Answer

About 99%

Answer

About 1%

Answer

About 90%

Question 17

Which scikit-learn class implements Multinomial Naive Bayes?

Accepted Answer

MultinomialNB

Answer

GaussianMixture

Answer

LinearSVC

Answer

KNeighborsClassifier

Question 18

Why does Naive Bayes often perform well even when its independence assumption is violated?

Accepted Answer

It only needs correct class ranking, not exact probabilities

Answer

Its assumption is always true in practice

Answer

It ignores the features entirely

Answer

It corrects correlations automatically

Question 19

What is the difference between the likelihood and the posterior in Bayesian classification?

Accepted Answer

Likelihood is P(features|class); posterior is P(class|features)

Answer

They are identical

Answer

Likelihood is P(class|features); posterior is the prior

Answer

Posterior ignores the features

Question 20

In a bag-of-words spam filter, how is P(word | spam) typically estimated from training data?

Accepted Answer

(count of word in spam + 1) / (total words in spam + vocab size)

Answer

Number of spam emails / total emails

Answer

Random value between 0 and 1

Answer

Count of word in ham / total ham words

Question 21

What kind of decision boundary does Gaussian Naive Bayes produce when classes share the same variance for each feature?

Accepted Answer

A linear boundary

Answer

Always a circular boundary

Answer

A random boundary

Answer

No boundary at all

Question 22

What is the law of total probability, as used to compute the evidence P(features)?

Accepted Answer

Sum over classes of P(features|class)·P(class)

Answer

P(features|class) for one class only

Answer

Product of all priors

Answer

P(class) divided by P(features|class)

Question 23

If two features are perfectly correlated (duplicated), what undesirable effect can this have on Naive Bayes?

Accepted Answer

The correlated evidence gets double-counted and overweighted

Answer

The model becomes more accurate automatically

Answer

The duplicate is ignored automatically

Answer

The prior becomes zero

Question 24

What does the MAP (maximum a posteriori) decision rule choose in a Naive Bayes classifier?

Accepted Answer

The class maximizing P(features|class)·P(class)

Answer

The class with the smallest prior

Answer

The class with the most features

Answer

A randomly chosen class

Question 25

How does the maximum likelihood (ML) decision rule differ from the MAP rule in Naive Bayes?

Accepted Answer

ML ignores the prior; MAP includes it

Answer

ML uses two priors; MAP uses none

Answer

They are always identical

Answer

MAP ignores the likelihood

Question 26

For a continuous feature in Gaussian Naive Bayes, which formula gives the likelihood of a value x for a class?

Accepted Answer

The Gaussian (normal) probability density function

Answer

A uniform distribution

Answer

The factorial function

Answer

A linear function of x

Question 27

A bag has 3 red and 2 blue balls. Two are drawn without replacement. What is the probability both are red?

Accepted Answer

0.3

Answer

0.36

Answer

0.5

Answer

0.6

Question 28

Why is Naive Bayes especially well-suited to high-dimensional data such as text?

Accepted Answer

It estimates each feature independently, scaling well with many features

Answer

It requires more data as features grow exponentially

Answer

It cannot handle more than ten features

Answer

It needs features to be removed first

Question 29

What are the mutually exclusive and exhaustive requirements for the classes when applying Bayes' theorem for classification?

Accepted Answer

Each example belongs to exactly one class and priors sum to 1

Answer

Classes can overlap freely

Answer

There must be exactly two classes

Answer

Priors can sum to any value

Question 30

In text classification, what is a 'bag-of-words' representation?

Accepted Answer

A word-count vector that ignores word order

Answer

A list of sentences in order

Answer

A grammar tree of the document

Answer

An image of the text

Test yourself