Machine Learning Techniques 13 Sep 26 (Session 2) - 13 Sep 2026

Let be points in that are linearly separable by a hyperplane through the origin. Construct where is a constant. The perceptron algorithm (initialised at , learning rate ) is run on both and , using the same ordering of points in both runs. Which of the following statements are true?

Consider binary classification on input features . Define the decision boundary of a trained classifier as the set of points at which its predicted label changes. For which of the following method(s) can this decision boundary be non-linear in ?

Let be the sigmoid (logistic) function. Select all statements below that are true for every .

Identify the correct relationship(s) between bias, variance, and the hyperparameter in the - Nearest Neighbours algorithm.

Consider the effect of each operation below on a model's bias and variance. Which of the following statements are correct?

In logistic regression, a point is classified positive only if . What score threshold (with at the boundary of this rule) does this correspond to? (Round to 2 decimal places.)

You build a fully-connected feed-forward neural network for a classification task. The input is a - dimensional vector; the network has two hidden layers of neurons each, followed by an output layer of neurons. Every layer is densely (fully) connected to the next. Ignoring all bias terms, compute the total number of weight parameters in the network. (Enter if it cannot be determined.)

Let be the solution to the ordinary least-squares linear regression problem . Which of the following is always satisfied at ? Note that here is your feature matrix and is the label vector.

Consider a scenario where we use leave-one-out cross-validation (LOOCV) with a Support Vector Machine (SVM) for binary classification. Given a dataset , the cross- validation error for a sample is if and otherwise, where is the prediction for produced by the SVM trained on . The overall cross-validation error is . Let be the number of support vectors obtained by training on the full dataset . Which statement is true regarding the relationship between and ?

Consider one-dimensional ridge regression with no bias term. Given and , with , compute the optimal . Note that is th data point and is th label. (Round to 2 decimal places.)

For the covariance matrix , compute the variance captured along the first principal component.

Given a dataset with discrete attributes, each taking exactly 5 possible values (where ), for a three-class classification task, the number of parameters to be estimated for learning a naïve Bayes classifier is:

For an optimal soft-margin SVM solution (no bias term), a training point satisfies . Here denotes the slack variable for this point, and is the Lagrange multiplier on the constraint . Which statement is necessarily true?

Consider a binary classification dataset in which the two classes are perfectly linearly separable. You are considering a Perceptron, Logistic Regression, and a Decision Tree. If the objective is to learn a linear decision boundary and no probability estimates are required, which of the following classifiers are appropriate choices?

A Euclidean-distance-based -means clustering algorithm was run on a dataset of points with . If the points and are both part of cluster , then which ONE of the following points is necessarily also part of cluster ?

Note: coordinates of x1 vector are intentionally not provided.

Which of the following statements about entropy and information gain in decision-tree learning are correct?

Which of the following statements about bagging are correct?

Suppose we model data as with a single unknown parameter and known variance (each ). You perform maximum-likelihood estimation of . The MLE of must satisfy which of the following equations? Note that is a feature and is a label.