**Practice Test 3**

**Task 1** 
Write the pseudocode for the perceptron algorithm. Include the
formulas for updating the weight vector and the classification rule.

**Task 2**
What is the difference, in terms of margin, between the linear
separator found by the perceptron algorithm and that found by SVM?

**Task 3**
Define the optimization criterion for SVM such that it is robust to
noise and to some outlying data (meaning that the data is linearly
separable, excepting a few points).

**Task 4**
Suppose $\mathbf{w},b$ are the parameters of a line where $\mathbf{w}$
is the unit normal to the line. Let $y_i\in\{-1,1\}$ and $\mathbf{x}
\in R^2$. Plot the areas defined by $y_i(\mathbf{w}\mathbf{x}+b)-1
\leq 0$ and the area defined by $y_i(\mathbf{w}\mathbf{x}+b)-1 > 0$
and mark them as "A" and "B" respectively.

**Task 5**
Explain the difference between expected risk and empirical risk. In
what setting would you prefer expected risk over empirical risk?
Rigorously define both quantities.