MLT week 9 - real exam questions

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

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?

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.)

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 .

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.)

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?

Two loss functions are plotted in this graph. What are the two?

Consider a logistic regression classifier trained on a dataset for a binary classification problem with features in and labels in . The weight vector learnt by the classifier is . Given a test data-point , the probability , where is the base of the natural logarithm. Find the value of and enter the nearest integer as your answer.

Consider a dataset with two data-points for a binary classification problem with features in . is a data-point from the positive class while is from the negative class. We now consider three linear classifiers: perceptron, logistic regression and SVM. If is the weight vector with the largest margin, which of the following is true?

Consider a binary classification dataset in that is linearly separable. Suppose there exist two distinct weight vectors and that both correctly classify all training points with a positive margin. The Perceptron algorithm is applied to this dataset. Which of the following statements are correct? (Select all that apply.)

Consider a binary classification problem using logistic regression. The model predicts the probability of class as: A threshold of is used for classification. The predicted class label is given by: The values of for the following datapoints are: How many datapoints will be classified as class ?

Consider two datasets and where and such that and , where and . The maximum number of mistakes made by the perceptron algorithm is higher on dataset than on dataset .

Given a two-dimensional data set where points from class 1 are: {(−2, 3), (−1, 1)} and points from class 0 are: {(1, 3), (1, 4)}. Which of the following statements are true?

Consider a logistic regression model trained to detect spam emails. Emails containing harmful phishing links are labeled as spam (1), while regular emails are labeled as not spam (0). A good spam detector should correctly identify almost all emails with phishing links. Even a single phishing email incorrectly classified as not spam could expose users to significant risks. However, the detector may classify some regular emails as spam. This trade-off is acceptable to ensure safety. To ensure user safety, if the threshold is set to a low value to prioritize the detection of phishing emails, type 1. If the threshold is set to a high value to minimize false positives (misclassifying regular emails as spam), type 0.

The weight vector output by the perceptron algorithm on this dataset can be expressed as a linear combination of the data-points where the coefficients of the linear combination are integers.

What is the most appropriate choice of activation function for the output layer if the binary cross-entropy loss is used?

The weight vector output by the perceptron algorithm can be expressed as a linear combination of the data-points where the coefficients of the linear combination are integers.

Enter the number corresponding to the logistic loss.

Enter the number corresponding to the perceptron loss.

Consider a simple neural network with one hidden layer. The network has the following architecture: Input layer with 3 neurons. Hidden layer with 2 neurons, using the sigmoid activation function. Output layer with 1 neuron, using the linear activation function. The weights and biases for the network are as follows: Hidden Layer: Neuron 1: Weights: [0.5, -0.2, 0.8] Bias: 0.1 Neuron 2: Weights: [0.4, 0, 0.2] Bias: -0.4 Output Layer: Neuron 1: Weights: [0.2, 0.4] Bias: -0.3 Assume that the input values are [0.6, 0.3, 0.8]. Calculate output of Neuron 1 in hidden layer

Which of the following statements is/are true regarding logistic regression and perceptron algorithm?

What is the maximum number of mistakes that the Perceptron algorithm can make in this data set?

During classification of linearly separable data-set using perceptron algorithm, as the value of learning rate α is decreased,

The following is the activation vector output by some hidden layer in a neural network when some input vector is given to it: The following is the activation vector output by some hidden layer in a neural network when some input vector is given to it: Which of the following could be the activation function used in this layer?

You are given a linearly separable dataset with feature matrix X, for which a perceptron has been trained until it converges (perfectly separates the data). The weight vector corresponding to it is w. This dataset has 60 points from the positive class and 40 from the negative class. What is the output of the following snippet of code? You are given a linearly separable dataset with feature matrix X, for which a perceptron has been trained until it converges (perfectly separates the data). The weight vector corresponding to it is w. This dataset has 60 points from the positive class and 40 from the negative class. What is the output of the following snippet of code?

During classification of linearly separable data-set using perceptron algorithm, as the value of learning rate α is increased,

Consider a logistic regression model that is trained on videos to detect objectionable content. Videos with objectionable content belong to the positive class (label 1). Harmless videos belong to the negative class (label 0). A good detector should be able to correctly identify almost all videos that are objectionable. If it incorrectly classifies even a single video that has inappropriate content in it, that could have serious consequences, as millions of people might end up watching it. In this process the detector may classify some harmless videos as belonging to the positive class. But that is a price we are willing to pay. How should we choose the threshold (for inference) of this logistic regression model?