📗 [4 points] There are parrots. They have either a red beak or a black beak. They can either talk or not. Complete the two cells in the following table so that the mutual information (i.e. information gain) between "Beak" and "Talk" is :

📗 Answer (comma separated vector): . Calculate

📗 [4 points] You have a data set with positive items and negative items. You perform a "leave-one-out" procedure: for each item i, learn a separate kNN (k Nearest Neighbor) classifier on all items except item i, and compute that kNN's accuracy in predicting item i. The leave-one-out accuracy is defined to be the average of the accuracy for each item. What is the leave-one-out accuracy when k = ?
📗 Answer: . Calculate

📗 [4 points] Some Na'vi's don't wear underwear, but they are too embarrassed to admit that. A surveyor wants to estimate that fraction and comes up with the following less-embarrassing scheme: Upon being asked "do you wear your underwear", a Na'vi would flip a fair coin outside the sight of the surveyor. If the coin ends up head, the Na'vi agrees to say "Yes"; otherwise the Na'vi agrees to answer the question truthfully. On a very large population, the surveyor hears the answer "Yes" for fraction of the population. What is the estimated fraction of Na'vi's that don't wear underwear? Enter a fraction like 0.01 instead of a percentage 1%.
📗 Answer: . Calculate

📗 [4 points] Consider a linear model \(a_{i} = w^\top x_{i} + b\), with the hinge cost function . The initial weight is \(\begin{bmatrix} w \\ b \end{bmatrix}\) = . What is the updated weight and bias after one stochastic (sub)gradient descent step if the chosen training data is \(x\) = , \(y\) = ? The learning rate is .
📗 Answer (comma separated vector): . Calculate

📗 [4 points] Consider a kernel \(K\left(x, y\right)\) = + + , where both \(x\) and \(y\) are positive real numbers. What is the feature vector \(\varphi\left(x\right)\) induced by this kernel evaluated at \(x\) = ?
📗 Answer (comma separated vector): . Calculate

📗 [4 points] Fill in the missing values in the following joint probability table so that A and B are independent.

📗 Answer (comma separated vector): . Calculate

📗 [4 points] In a convolutional neural network, suppose the activation map of a convolution layer is . What is the activation map after a non-overlapping (stride 2) 2 by 2 max-pooling layer?
📗 Answer (matrix with multiple lines, each line is a comma separated vector): . Calculate

📗 [4 points] John tells his professor that he forgot to submit his homework assignment. From experience, the professor knows that students who finish their homework on time forget to turn it in with probability . She also knows that of the students who have not finished their homework will tell her they forgot to turn it in. She thinks that of the students in this class completed their homework on time. What is the probability that John is telling the truth (i.e. he finished it given that he forgot to submit it)?
📗 Answer: . Calculate

📗 [4 points] Say we use Naive Bayes in an application where there are features represented by variables, each having possible values, and there are classes. How many probabilities must be stored in the CPTs (Conditional Probability Table) in the Bayesian network for this problem? Do not include probabilities that can be computed from other probabilities.
📗 Answer: . Calculate

📗 [4 points] Say we have a training set consisting of positive examples and negative examples where each example is a point in a two-dimensional, real-valued feature space. What will the classification accuracy be on the training set with NN (Nearest Neighbor).
📗 Answer: . Calculate

📗 [4 points] What is the conditional entropy \(H\left(B|A\right)\) for the following set of training examples.

📗 Answer: . Calculate

📗 [4 points] Given the number of instances in each class summarized in the following table, how many instances are used to train an one-vs-one SVM (Support Vector Machine) for class vs ?

📗 Answer: . Calculate

📗 [4 points] Given the following transition matrix for a bigram model with words "I" (label 0), "am" (label 1) and "Groot" (label 2): . Row \(i\) column \(j\) is \(\mathbb{P}\left\{w_{t} = j | w_{t-1} = i\right\}\). Two uniform random numbers between 0 and 1 are generated to simulate the words after "I", say \(u_{1}\) = and \(u_{2}\) = . Using the CDF (Cumulativ Distribution Function) inversion method (inverse transform method), which two words are generated? Enter two integer labels (0, 1, or 2), not strings.
📗 Answer (comma separated vector): . Calculate

📗 [4 points] What is the gradient magnitude of the center element (pixel) of the image . Use the x gradient filter: \(\begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}\), and the y gradient filter: \(\begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix}\). Remember to flip the filters.
📗 Answer: . Calculate

📗 [1 points] Please enter any comments including possible mistakes and bugs with the questions or your answers. If you have no comments, please enter "None": do not leave it blank.
📗 Answer: .