Machine Learning Foundations Quiz 1: 7 July 2024 (May 2024 term)

Let $A = \begin{pmatrix} 2 & 1 & 1 \\ a & 3 & 2 \\ 3 & b & c \end{pmatrix}$ be a $3 \times 3$ matrix. Let $\alpha$ be the eigenvalue corresponding to the eigenvector $v_1 = \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}$ and $\beta$ is the eigenvalue corresponding to the eigenvector $v_2 = \begin{pmatrix} 0 \\ 1 \\ -1 \end{pmatrix}$ of matrix $A$. Based on this information, answer the given sub-questions.

Find the value of α + 2β.

Let $A = \begin{pmatrix} 2 & 1 & 1 \\ a & 3 & 2 \\ 3 & b & c \end{pmatrix}$ be a $3 \times 3$ matrix. Let $\alpha$ be the eigenvalue corresponding to the eigenvector $v_1 = \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix}$ and $\beta$ is the eigenvalue corresponding to the eigenvector $v_2 = \begin{pmatrix} 0 \\ 1 \\ -1 \end{pmatrix}$ of matrix $A$. Based on this information, answer the given sub-questions.

Which of the following options is/are true ?

Which of the following options is/are true?

Which of the following statements is true for a function f(x, y) that is differentiable at a point (a, b)?

Which of the following functions cannot be approximated linearly around x = 0?

In a sports analytics company, the team is interested in predicting whether a basketball player will score above 20 points in a game using classification models. They collected data on various factors $x = [x_1, x_2, x_3]$ from past games of different players. The factors include minutes played, shots attempted, and free throw percentage. The data and corresponding labels are shown in the table below: Compute the misclassification

rate if they use the following step function:

$u(z) = \begin{cases} 1, & \text{if } z \ge 3 \\ 0, & \text{otherwise} \end{cases}$

and the linear combination $z$ is given by: $0.6x_1 + 0.3x_2 + 0.1x_3$. Enter the answer correct to one decimal place.

Note: Here, $x_1$ represents whether the player is a starter (1) or not (0), $x_2$ is the number of shots attempted, and $x_3$ is the free throw percentage. The label $y$ indicates whether the player scored more than 20 points (1) or not (0). The misclassification rate is the number of labels misclassified.e.g. if 3 out of 5 players are mislabeled then the misclassification rate is 3/5.

Consider a dataset from an e-commerce company such as Flipkart that has details of customer behavior, which of the following problems can be best approached using clustering?