📗 [4 points] Given two items $x_1$ = $8$ and $x_2$ = $-2$, suppose the feature map for a kernel SVM (Support Vector Machine) is $\phi \left(x\right)$ = $\left[\begin{array}{c}\exp \left(x\right)\\ x\\ x\end{array}\right]$, what is the kernel (Gram) matrix?

📗 Answer (matrix with multiple lines, each line is a comma separated vector): . Calculate

📗 [4 points] Given the counts, find the maximum likelihood estimate of $\mathbb{P}\{A=1|B+C=s\}$, for $s$ = $2$.

📗 Answer: . Calculate

📗 [4 points] Given the following training data, what is the $6$ fold cross validation accuracy if $1$NN (Nearest Neighbor) classifier with Manhattan distance is used. The first fold is the first $1$ instances, the second fold is the next $1$ instances, etc. Break the tie (in distance) by using the instance with the smaller index. Enter a number between 0 and 1.

📗 Answer: . Calculate

📗 [4 points] If $\mathbb{P}\left\{A|B\right\}$ is $6$ times the value of $\mathbb{P}\left\{B|A\right\}$, and $\mathbb{P}\left\{A\right\}$ = $0.4$. What is $\mathbb{P}\left\{B\right\}$?

📗 Answer: . Calculate

📗 [4 points] Consider a linear model $a_i=w^{\mathrm{\top }}{x}_i+b$, with the cross entropy cost function $C$ = $-y_i\cdot \ln \left(a_i\right)-(1-y_i)\cdot \ln (1-a_i)$. The initial weight is $\left[\begin{array}{c}w\\ b\end{array}\right]$ = $\left[\begin{array}{c}4\\ -1\end{array}\right]$. What is the updated weight and bias after one (stochastic) gradient descent step if the chosen training data is $x$ = $5$, $y$ = $0$? The learning rate is $3$.

📗 Answer (comma separated vector): . Calculate

📗 [4 points] What is the convolution between the image $\left[\begin{array}{ccc}9& 4& 10\\ 3& 3& 3\\ 5& 1& 7\end{array}\right]$ and the filter $\left[\begin{array}{ccc}0& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$ using zero padding? Remember to flip the filter first.

📗 Answer (matrix with multiple lines, each line is a comma separated vector): . Calculate

📗 [4 points] A convolutional neural network has input image of size $84$ x $84$ that is connected to a convolutional layer that uses a $7$ x $7$ filter, zero padding of the image, and a stride of 1. There are $2$ activation maps. (Here, zero-padding implies that these activation maps have the same size as the input images.) The convolutional layer is then connected to a pooling layer that uses $3$ x $3$ max pooling, a stride of $3$ (non-overlapping, no padding) of the convolutional layer. The pooling layer is then fully connected to an output layer that contains $4$ output units. There are no hidden layers between the pooling layer and the output layer. How many different weights must be learned in this whole network, not including any bias.

📗 Answer: . Calculate

📗 [4 points] In a convolutional neural network, suppose the activation map of a convolution layer is $\left[\begin{array}{cccc}8& -2& 10& -4\\ -3& -5& -1& -8\\ 5& -2& 0& 9\\ 9& -10& 6& 10\end{array}\right]$. What is the activation map after a non-overlapping (stride 2) 2 by 2 average-pooling layer?

📗 Answer (matrix with multiple lines, each line is a comma separated vector): . Calculate

📗 [4 points] Given the following transition matrix for a bigram model with words "I", "am" and "Groot": $\left[\begin{array}{ccc}0.38& 0.2& 0.42\\ 0.33& 0.37& 0.3\\ 0.35& 0.13& 0.52\end{array}\right]$. Row $i$ column $j$ is $\mathbb{P}\{w_t=j|w_{t-1}=i\}$. What is the probability that the third word is "am" given the first word is "am"?

📗 Answer: . Calculate

📗 [4 points] What is the gradient magnitude of the center element (pixel) of the image $\left[\begin{array}{ccc}8& -2& 10\\ -4& -3& -5\\ -1& -8& 5\end{array}\right]$. Use the x gradient filter: $\left[\begin{array}{ccc}-1& 0& 1\end{array}\right]$, and the y gradient filter: $\left[\begin{array}{c}-1\\ 0\\ 1\end{array}\right]$. Remember to flip the filters.

📗 Answer: . Calculate

📗 [4 points] In a problem where each example has $10$ real-valued attributes (i.e. features), where each attribute can be split at $3$ possible thresholds (i.e. binary splits), to select the best attribute for a decision tree node at depth $6$, where the root is at depth 0, how many conditional entropies must be calculated (at most)?

📗 Answer: . Calculate

📗 [3 points] Let a dataset consist of $n$ = $6$ points in $\mathbb{R}$, specifically, the first $n-1$ points are $\left[\begin{array}{ccccc}-4& -3& -2& 8& 10\end{array}\right]$ and the last point $x_n$ is unknown. What is the smallest value of $x_n$ above which $x_{n-1}$ is among $x_n$'s 3-nearest neighbors, but $x_n$ is NOT among $x_{n-1}$'s 3-nearest neighbor? Note that the 3-nearest neighbors of a point in the training set include the point itself.

📗 Answer: . Calculate

📗 [3 points] Assume the prior probability of having a female child (girl) is the same as having a male child (boy) and both are 0.5. The Smith family has $5$ kids. One day you saw one of the Smith children, and she is a girl. The Wood family has $5$ kids, too, and you heard that at least one of them is a girl. What is the chance that the Smith family has a boy? What is the chance that the Wood family has a boy?

📗 Answer (comma separated vector): . Calculate

📗 [5 points] Andy is a three-month old baby. He can be happy (state 0), hungry (state 1), or having a wet diaper (state 2). Initially when he wakes up from his nap at 1pm, he is happy. If he is happy, there is a $0.38$ chance that he will remain happy one hour later, a $0.2$ chance to be hungry by then, and a $0.42$ chance to have a wet diaper. Similarly, if he is hungry, one hour later he will be happy with $0.33$ chance, hungry with $0.37$ chance, and wet diaper with $0.3$ chance. If he has a wet diaper, one hour later he will be happy with $0.35$ chance, hungry with $0.13$ chance, and wet diaper with $0.52$ chance. He can smile (observation 0) or cry (observation 1). When he is happy, he smiles $0.47$ of the time and cries $0.53$ of the time; when he is hungry, he smiles $0.5$ of the time and cries $0.12$ of the time; when he has a wet diaper, he smiles of the time and cries of the time.

📗 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: .