Introduction to Machine Learning Quiz-3

For a two-class problem using discriminant functions (δk - discriminant function for class k), where is the separating hyperplane located?

• Whereδ1 > δ2

• Whereδ1 < δ2

• Whereδ1 =δ2

• Whereδ1 +δ2 = 1

Given the following dataset consisting of two classes, A and B, calculate the prior probability of each class. Feature 1 Class 2.3A 1.8A 3.2A 2.7B 3.0A 2.1A 1.9B 2.4B What are the prior probabilities of class A and class B?

• P(A) = 0.5, P(B) = 0.5

• P(A) = 0.625, P(B) = 0.375

• P(A) = 0.375, P(B) = 0.625

• P(A) = 0.6, P(B) = 0.4

In a 3-class classification problem using linear regression, the output vectors for three data points are [0.8, 0.3, -0.1], [0.2, 0.6, 0.2], and [-0.1, 0.4, 0.7]. To which classes would these points be assigned?

• 1, 2, 1

• 1, 2, 2

• 1, 3, 2

• 1, 2, 3

If you have a 5-class classification problem and want to avoid masking using polynomial regression, what is the minimum degree of the polynomial you should use?

• 3

• 4

• 5

• 6

Consider a logistic regression model where the predicted probability for a given data point is 0.4. If the actual label for this data point is 1, what is the contribution of this data point to the log-likelihood?

• -1.3219

• -0.9163

• +1.3219

• +0.9163

What additional assumption does LDA make about the covariance matrix in comparison to the basic assumption of Gaussian class conditional density?

• The covariance matrix is diagonal

• The covariance matrix is identity

• The covariance matrix is the same for all classes

• The covariance matrix is different for each class

What is the shape of the decision boundary in LDA?

• Quadratic

• Linear

• Circular

• Can not be determined

For two classes C1 and C2 with within-class variances σ2w1 = 1 and σ2w2 = 4 respectively, if the projected means are μ′1 = 1 and μ′2 = 3, what is the Fisher criterion J(w)?

• 0.5

• 0.8

• 1.25

• 1.5

Given two classes C1 and C2 with means μ1 = [2, 3] and μ2 = [5, 7] respectively, what is the direction vector w for LDA when the within-class covariance matrix Sw is the identity matrix I?

• [4, 3]

• [5, 7]

• [0.7, 0.7]

• [0.6, 0.8]