8 - Naïve Bayes Classification

Question 1

What is the basis of Naïve Bayes classification methods?

Answer 1

Bayes Theorem

Developed by Reverend Thomas Bayes, it updates knowledge about data parameters by combining prior knowledge with new information.

Question 2

What does the prior distribution represent in Bayes Theorem?

Answer 2

Previous knowledge about the data parameters

It is denoted as p(Y = y*).

Question 3

What is the posterior distribution in the context of Bayes Theorem?

Answer 3

Updated parameter knowledge after observing data

Denoted as p(Y = y* | X*).

Question 4

In a dataset with predictors X and response variable Y, how many class values can Y take in the given example?

Answer 4

Three possible class values: y1, y2, and y3

Question 5

What is the objective of using Bayes Theorem in classification?

Answer 5

Identify the most likely class for a combination of predictor variable values

Specifically, find which of y1, y2, or y3 is most likely for the combination X*.

Question 6

What does p(Y = y* | X*) represent?

Answer 6

The likelihood of class value y* given observed predictor values X*

Question 7

How can you classify a record using the maximum a posteriori hypothesis?

Answer 7

Classify as the value of Y with the highest posterior probability

Question 8

What is the class conditional independence assumption?

Answer 8

It allows writing p(X* | Y = y*) as the product of independent events

For example, p(X* | Y = y) = p(X1 | Y = y) × p(X2 | Y = y*).

Question 9

What are the two predictor variables used in the wine classification example?

Answer 9

Alcohol content and sugar content

Question 10

What is the prior probability of a wine being Red if there are 500 red wines out of 1000 total?

Answer 10

0.5

Question 11

What is the marginal probability of Alcohol_flag being High in the wine dataset?

Answer 11

0.486

Question 12

What is the marginal probability of Sugar_flag being Low in the wine dataset?

Answer 12

0.584

Question 13

What is p(Alcohol_flag High | Type Red)?

Answer 13

0.436

Question 14

What is the conditional probability p(Sugar_flag Low | Type White)?

Answer 14

0.4

Question 15

How does the Naïve Bayes algorithm classify a wine with low alcohol and low sugar content?

Answer 15

It classifies it as Red based on higher posterior probability

Question 16

What is the posterior probability of a low alcohol, low sugar wine being Red?

Answer 16

72.15%

Question 17

What is the prior probability of a wine being White?

Answer 17

0.5

Question 18

What is the probability of a low alcohol, low sugar wine being White?

Answer 18

30.92%

Question 19

What happens to the classification when comparing prior and posterior probabilities?

Answer 19

Posterior probabilities can significantly change based on new data

Question 20

What is the posterior probability of a wine being Red given high alcohol and high sugar content?

Answer 20

25.02%

Question 21

Fill in the blank: The denominator in Bayes Theorem, p(X*), is known as the _______.

Answer 21

Marginal probability of the data

Question 22

What is the posterior probability of a wine being red given high alcohol and high sugar?

Answer 22

25.02%

This is calculated using the Naïve Bayes algorithm.

Question 23

What is the posterior probability of a wine being white given high alcohol and high sugar?

Answer 23

79.53%

This indicates the Naïve Bayes algorithm classifies the wine as white.

Question 24

What is the Naïve Bayes classification for low alcohol and high sugar wine?

Answer 24

White

This classification is based on the alcohol and sugar content.

Question 25

What is the Naïve Bayes classification for high alcohol and low sugar wine?

Answer 25

Red ## Footnote This classification is based on the alcohol and sugar content.

Question 26

What is the accuracy of the Naïve Bayes model when predicting wine types?

Answer 26

65.93% ## Footnote This is calculated from the model's predictions on a test data set.

Question 27

What is the accuracy of the Naïve Bayes model for classifying red wines?

Answer 27

79.32% ## Footnote This is the proportion of correctly classified red wines from the test data.

Question 28

What is the accuracy of the Naïve Bayes model for classifying white wines?

Answer 28

61.48% ## Footnote This is the proportion of correctly classified white wines from the test data.

Question 29

What is the baseline accuracy for the wine types if half are red and half are white?

Answer 29

50% ## Footnote This serves as a comparison to evaluate the performance of the Naïve Bayes model.

Question 30

What are the predictor variables used in the Naïve Bayes classification model?

Answer 30

* Alcohol_flag * Sugar_flag ## Footnote These variables are used to classify the type of wine.

Question 31

What Python library is used to implement the Naïve Bayes algorithm?

Answer 31

sklearn ## Footnote Specifically, the MultinomialNB class is used for the implementation.

Question 32

What is the first step in using the Naïve Bayes algorithm in Python?

Answer 32

Import required libraries ## Footnote Including pandas, numpy, and sklearn.

Question 33

Fill in the blank: The contingency table helps to obtain the _______ needed for Naïve Bayes calculations.

Answer 33

marginal and conditional probabilities ## Footnote These probabilities are essential for the calculations.

Question 34

What R package is used for Naïve Bayes classification?

Answer 34

e1071 ## Footnote This package contains the naiveBayes function for classification.

Question 35

What command in R is used to run the Naïve Bayes estimator?

Answer 35

naiveBayes() ## Footnote This function builds the model using the specified formula and data.

Question 36

What do A-priori probabilities represent in the Naïve Bayes model?

Answer 36

Values of p(Y) ## Footnote These probabilities indicate the likelihood of each class before any evidence is considered.

Question 37

What do conditional probabilities represent in the Naïve Bayes model?

Answer 37

Values of p(Y | X) ## Footnote These probabilities indicate the likelihood of each class given the predictor variables.

Question 38

What is the purpose of the predict() command in R for Naïve Bayes?

Answer 38

To classify each record in the test data set ## Footnote This generates predictions based on the trained model.

Question 39

Fill in the blank: The contingency table of actual versus predicted wine types in R is created using the _______ command.

Answer 39

table() ## Footnote This command creates a cross-tabulation of the actual and predicted values.

Question 40

What information does Bayes Theorem update about the data parameters?

Answer 40

Bayes Theorem updates our previous knowledge about the data parameters based on new evidence.

Question 41

What does the prior probability represent?

Answer 41

The prior probability represents our initial belief about the probability of a parameter before observing any evidence.

Question 42

What formula represents how the data behave within the target variable’s class values?

Answer 42

The formula representing how the data behave within the target variable’s class values is p(X | Y).

Question 43

What formula represents how the data behave without reference to the class values?

Answer 43

The formula is p(X).

Question 44

What is the formula from the previous exercise called?

Answer 44

The formula is called the likelihood.

Question 45

What does the posterior probability represent?

Answer 45

The posterior probability represents the updated probability of a hypothesis after considering new evidence.

Question 46

What do we use for a prior probability if we have no prior knowledge about the parameters?

Answer 46

We use a uniform distribution for the prior probability.

Question 47

How does the maximum a posteriori hypothesis help us to classify a record?

Answer 47

It helps classify a record by selecting the class that maximizes the posterior probability.

Question 48

What is the class conditional independence assumption?

Answer 48

The assumption that the features are independent given the class label.

Question 49

How do we write p(X* ∣ Y = y*) if we have two predictor variables X* = {X1 = x1, X2 = x2}?

Answer 49

We write it as p(X1 = x1, X2 = x2 | Y = y*).

Question 50

Create two contingency tables for which variables?

Answer 50

One with Type and Alcohol_flag, and another with Type and Sugar_flag.

Question 51

What is the prior probability of Type = Red and Type = White?

Answer 51

Calculated from the contingency tables.

Question 52

What can we calculate regarding alcohol content from the contingency tables?

Answer 52

The probability of high and low alcohol content.

Question 53

What can we calculate regarding sugar content from the contingency tables?

Answer 53

The probability of high and low sugar content.

Question 54

What are the conditional probabilities for Alcohol_flag given Type = Red?

Answer 54

p(Alcohol_flag = High | Type = Red) and p(Alcohol_flag = Low | Type = Red).

Question 55

What are the conditional probabilities for Alcohol_flag given Type = White?

Answer 55

p(Alcohol_flag = High | Type = White) and p(Alcohol_flag = Low | Type = White).

Question 56

What are the conditional probabilities for Sugar_flag given Type = Red?

Answer 56

p(Sugar_flag = High | Type = Red) and p(Sugar_flag = Low | Type = Red).

Question 57

What are the conditional probabilities for Sugar_flag given Type = White?

Answer 57

p(Sugar_flag = High | Type = White) and p(Sugar_flag = Low | Type = White).

Question 58

How likely is it that a randomly selected wine is red?

Answer 58

Discussed based on prior probabilities.

Question 59

How likely is it that a randomly selected wine has high alcohol content?

Answer 59

Discussed based on prior probabilities.

Question 60

How likely is it that a randomly selected wine has low sugar content?

Answer 60

Discussed based on prior probabilities.

Question 61

What might a typical white wine have as its alcohol and sugar content?

Answer 61

Discussed based on conditional probabilities.

Question 62

What might a typical red wine have as its alcohol and sugar content?

Answer 62

Discussed based on conditional probabilities.

Question 63

What do side-by-side bar graphs for Type compare?

Answer 63

They compare Alcohol_flag and Sugar_flag.

Question 64

What is the posterior probability of Type = Red for a wine that is low in alcohol and high in sugar?

Answer 64

Calculated based on the relevant probabilities.

Question 65

What is the posterior probability of Type = White for the same wine?

Answer 65

Calculated based on the relevant probabilities.

Question 66

Which type is more probable for a wine with low alcohol and high sugar content?

Answer 66

Determined from posterior probabilities.

Question 67

What is the posterior probability of Type = Red for a wine that is high in alcohol and low in sugar?

Answer 67

Calculated based on the relevant probabilities.

Question 68

Which type is more probable for a wine with high alcohol and low sugar content?

Answer 68

Determined from posterior probabilities.

Question 69

What does the Naïve Bayes classifier classify wines based on?

Answer 69

Alcohol and sugar content.

Question 70

How do we evaluate the Naïve Bayes model on the wines_test data set?

Answer 70

Display results in a contingency table.

Question 71

What values do we find for the Naïve Bayes model in the contingency table?

Answer 71

Accuracy and error rate.

Question 72

How often does the Naïve Bayes model correctly classify red wines?

Answer 72

Determined from the contingency table.

Question 73

How often does the Naïve Bayes model correctly classify white wines?

Answer 73

Determined from the contingency table.

Question 74

What should be done with the variables Death, Sex, and Educ?

Answer 74

Convert all variables to factors.

Question 75

What two contingency tables should be created for the framingham_nb data sets?

Answer 75

One with Death and Sex, and another with Death and Educ.

Question 76

What is the probability a randomly selected person is alive or dead?

Answer 76

Calculated from the contingency tables.

Question 77

What is the probability a randomly selected person is male?

Answer 77

Calculated from the contingency tables.

Question 78

What is the probability a randomly selected person has an Educ value of 3?

Answer 78

Calculated from the contingency tables.

Question 79

What are the probabilities that a dead person is male with education level 1?

Answer 79

Calculated from the contingency tables.

Question 80

What are the probabilities that a living person is male with education level 1?

Answer 80

Calculated from the contingency tables.

Question 81

What are the probabilities that a living person is female with education level 2?

Answer 81

Calculated from the contingency tables.

Question 82

What are the probabilities that a dead person is female with education level 2?

Answer 82

Calculated from the contingency tables.

Question 83

What do side-by-side bar graphs for Death compare?

Answer 83

One with an overlay of Sex and the other with an overlay of Educ.

Question 84

If we know a person is dead, are they more likely to be male or female?

Answer 84

Determined from the bar graphs.

Question 85

If we know a person is alive, are they more likely to be male or female?

Answer 85

Determined from the bar graphs.

Question 86

If we know a person is dead, what education level are they most likely to have?

Answer 86

Determined from the bar graphs.

Question 87

If we know a person is alive, what education level are they most likely to have?

Answer 87

Determined from the bar graphs.

Question 88

Which education levels are more prevalent for dead persons?

Answer 88

Determined from the graphs.

Question 89

Which education levels are more prevalent for living persons?

Answer 89

Determined from the graphs.

Question 90

What is the posterior probability of Death = 0 for a male with education level 1?

Answer 90

Calculated based on the relevant probabilities.

Question 91

What is the posterior probability of Death = 1 for a male with education level 1?

Answer 91

Calculated based on the relevant probabilities.

Question 92

What is the posterior probability of Death = 0 for a female with education level 2?

Answer 92

Calculated based on the relevant probabilities.

Question 93

What is the posterior probability of Death = 1 for a female with education level 2?

Answer 93

Calculated based on the relevant probabilities.

Question 94

What does the Naïve Bayes classifier classify persons based on?

Answer 94

Sex and education.

Question 95

How do we evaluate the Naïve Bayes model on the framingham_nb_test data set?

Answer 95

Display results in a contingency table.

Question 96

How often does the Naïve Bayes model correctly classify dead persons?

Answer 96

Determined from the contingency table.

Question 97

How often does the Naïve Bayes model correctly classify living persons?

Answer 97

Determined from the contingency table.