1. Consider a perceptron learning algorithm (PLA) used for a binary classification problem
(adaptive decision boundary).
Question:
What will be the algorithm’s output if the training data are not linearly separable?
Answer:
The perceptron learning algorithm does not terminate if the learning set is not linearly separable. To avoid infinite looping, specify finite number of iterations.
Question:
Would you call the PLA supervised or unsupervised learning?
Answer: Supervised learning
2. Obtain the linear regression of Y on X1, X2 (by hand-calculation or writing code, but do
not use an off-the-shelf linear regression function):
X1 X2 Y
0 0 2
0 1 2
1 0 10
1 1 10
Question1:
Write the regression equation.
Question2:
If we use the result of this regression as a classifier, what will be the equation of the classifier?
3. Exercises 3.6 and 3.7 from the textbook (page 92).
4. In least squares linear regression, we obtain the solution (the weights) analytically. In logistics regression, why don’t we analytically solve for the weights by setting the partial derivatives of the (log-)likelihood expression (or the negative of that expression) to zeros?
5. Explain the concepts of “training data,” “test data,” “training error,” and “test error.” Is it good to have as low a training error as possible?
6.Justify or refute: Gradient descent/ascent guarantees convergence to the global optimal solution.
7. Advice: Please read the textbook carefully. If you can devote further time, read the references.
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