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📗 [3 points] What is the minimum number of training items that needs to be removed so that a Perceptron can learn the remaining training set (with accuracy 100 percent)?
\(x_{1}\)
\(x_{2}\)
\(x_{3}\)
\(y\)
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📗 Answer: .
📗 [3 points] In one iteration of the Perceptron Algorithm, \(x\) = , \(y\) = , and predicted label \(\hat{y} = a\) = . The learning rate \(\alpha = 1\). After the iteration, how many of the weights (include bias \(b\)) are increased (the change is strictly larger than 0). If it is impossible to figure out given the information, enter -1.
📗 Answer: .
📗 [3 points] In one iteration of the Perceptron Algorithm, the initial weights are \(w\) = and \(b\) = , with \(x\) = , \(y \in \left\{0, 1\right\}\), and learning rate \(\alpha = 1\). After the iteration, the weights remain unchanged. What is the correct label \(y\)? The LTU perceptron classifier is \(1_{\left\{w x + b \geq 0\right\}}\).
📗 Answer: .
📗 [2 points] The Perceptron algorithm does not terminate (cannot converge) for any learning rate on the following training set. Give an example of \(x_{1}\). If there are multiple possible answers, enter only one, and if no such \(x\) exists, enter \(-1\).
\(i\)
\(x_{i}\)
\(y_{i}\)
1
\(x_{1}\)
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📗 Answer: .
📗 [2 points] The Perceptron algorithm does not terminate (cannot converge) for any learning rate on the following training set. Give an example of \(y_{1}\) (either 0 or 1). If there are multiple possible answers, enter only one, and if no such \(y_{1}\) exists, enter \(-1\).
\(i\)
\(x_{i}\)
\(y_{i}\)
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\(y_{1}\)
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📗 Answer: .
📗 [3 points] Let \(g\left(z\right) = \dfrac{1}{1 + \exp\left(-z\right)}, z = w^\top x = w_{1} x_{1} + w_{2} x_{2} + ... + w_{d} x_{d}\), \(d\) = be a sigmoid perceptron with inputs \(x_{1} = ... = x_{d}\) = and weights \(w_{1} = ... = w_{d}\) = . There is no bias term. If the desired output is \(y\) = , and the sigmoid perceptron update rule has a learning rate of \(\alpha\) = , what will happen after one step of update? Each \(w_{i}\) will change by (enter a number, positive for increase and negative for decrease).
📗 Answer: .
📗 [4 points] Consider a Linear Threshold Unit (LTU) perceptron with initial weights \(w\) = and bias \(b\) = trained using the Perceptron Algorithm. Given a new input \(x\) = and \(y\) = . Let the learning rate be \(\alpha\) = , compute the updated weights, \(w', b'\) = :
📗 Answer (comma separated vector): .
📗 [4 points] Which one of the following LTUs (Linear Threshold Unit) represent the following binary operators?
\(x_{1}\)
\(x_{2}\)
(A)
(B)
(C)
(D)
(E)
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1.
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📗 For example, if you think 1 is matched with A, D, 2 is matched with B and C, 4 is matched with E ..., enter (1, 2, 2, 1, 4).
📗 Answer (comma separated vector): .
📗 [6 points] With a linear threshold unit perceptron, implement the following function. That is, you should write down the weights \(w_{0}, w_{A}, w_{B}\). Enter the bias first, then the weights on A and B.
A
B
function
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📗 Answer (comma separated vector): .
📗 [6 points] With a linear threshold unit perceptron, implement the following function. That is, you should write down the weights \(w_{0}, w_{A}, w_{B}\). Enter the bias first, then the weights on A and B.
A
B
function
0
0
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1
📗 You can plot your line given by \(w_{0}, w_{A}, w_{B}\) to see if it separates the dataset correctly: . If no green line shows up, it means the entire line is outside of the range [0, 1].
📗 Answer (comma separated vector): .
📗 [2 points] Consider a rectified linear unit (ReLU) with input \(x\) and a bias term. The output can be written as \(y\) = . Here, the weight is and the bias is . Write down the input value \(x\) that produces a specific output \(y\) = .
📗 The red curve is a plot of the activation function, given the y-value of the green point, the question is asking for its x-value.
📗 Answer: .
📗 [3 points] What is the minimum zero-one cost of a binary (y is either 0 or 1) linear (threshold) classifier (for example, an LTU (Linear Threshold Unit) perceptron) on the following data set?
\(x_{i}\)
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\(y_{i}\)
📗 Answer: .
📗 [3 points] What is the minimum zero-one cost of a binary (y is either 0 or 1) linear (threshold) classifier (for example, LTU perceptron) on the following data set?
\(x_{i}\)
1
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\(y_{i}\)
📗 A linear classifier is a vertical line that separates the two classes: you want to draw the line such that the least number of mistakes (i.e. zero-one cost) are made.
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📗 You can find videos going through the questions on Link.