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?

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?

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?

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?

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?

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

What is the shape of the decision boundary in LDA?

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)?

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?