Machine Learning Techniques 13 Sep 26 - 13 Sep 2026

Which of the following statements correctly distinguishes the hard-margin SVM from the soft-margin SVM?

Given a linearly separable dataset with margin and radius , which of the following statements about the perceptron algorithm are true?

Assume that for a certain linear regression problem involving features, the following weight vectors all produce an equal mean squared error: Which of the weight vectors is likely to be chosen by ridge regression?

Consider the following dataset with two binary features and binary label : Consider the following three claims about this dataset: (i) Logistic regression (using the raw features , with or without a bias term) can achieve zero training error. (ii) A decision tree of depth at most , using axis-aligned splits on , can achieve zero training error. (iii) -nearest-neighbour, evaluated on this training set, achieves zero training error. Consider each point is its own nearest neighbour. Select the option that lists exactly the claims that are true.

Suppose the dataset is initially linearly separable. Later, the data-generating process changes and the class boundary becomes highly nonlinear, for example: for one class and for the other. Without manually creating nonlinear features, which classifier among the three is most naturally capable of representing this type of decision boundary?

Suppose the true data-generating process is a polynomial of degree . You fit three models to the data: linear regression, polynomial regression of degree , and polynomial regression of degree . Which option correctly characterizes the bias and variance of each fitted model relative to the true model?

Consider logistic regression on one-dimensional data, with (the model is ). The current weight is , the training set is a single example , and the step size is . Gradient ascent is performed directly on the log-likelihood of the data. Compute after one gradient-ascent step. (Round to decimal places; enter if it cannot be determined.)

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 decimal places.)

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

Consider one-dimensional linear regression with no bias term, . The squared-error objective over the training set is . The dataset is . Starting from with learning rate perform one gradient-descent step. What is the model's prediction at ?

Consider a soft-margin SVM in with and . Two of the training points strictly violate the margin constraint, these two points are with , and with . All other points lie strictly beyond the margin. Compute the perpendicular distance between the margin hyperplanes and . (Round to decimal places.)

A decision-tree node contains training examples: positive and negative. A candidate split divides them into two children: one child with positive and negative, the other with positive and negative. Using entropy (base- logarithms), compute the information gain of this split. (Round to decimal places.)

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

The figure below shows the training points of a soft-margin SVM in , together with its decision boundary and its two margin hyperplanes and (dashed). Each point is marked with its true label, or . For how many points is it possible that lie in the range ? (Enter if it cannot be determined from the figure.)

Consider a dataset with six datapoints , with labels and . A hard-margin linear SVM is trained on this dataset. Which ONE of the following sets is a possible set of support vectors?

Consider a binary classification problem in with positive examples and negative examples . Apply the feature map and a linear model . Which of the following weight vectors gives a maximum-margin decision surface separating the two classes?

In -nearest-neighbours, as the hyperparameter is increased from towards (the size of the training set), which of the following best describes the trend in the model's bias and variance?

Suppose are i.i.d. samples from the uniform distribution with unknown parameter . Which of the following is the maximum-likelihood estimate of ?