Lecture 3 Flashcards
What is the equation for absolute loss?
L_abs(y_i, H(x_i)) = |y_i - H(x_i)|
What is the simplified absolute loss function for the constant model?
L_abs(y_i, h) = |y_i - h|
When we use absolute loss, what is h*?
the point at which the average absolute loss is minimized
What is another name for average absolute loss?
mean absolute error or MAE
What is the equation for MAE?
R_abs(h) = 1/n En i=1 |y_i - h|
What kind of function is |x|?
a piecewise function
What is the equation for the slope of R_abs at h?
1/n [(# of y_i < h) - (# of y_i > h)]
What is h* for R_abs(h)?
the median
What is the best constant prediction in terms of mean absolute error?
the median
What happens to the best constant prediction for the MAE when n is odd?
the answer is unique
What happens to the best constant prediction for the MAE when n is even?
any number between the middle two data points (when sorted) also minimizes the mean absolute error
What is the formal name for the process of minimizing average loss?
empirical risk minimization
What is another name for “average loss”?
empirical risk
If L(y_i, h) is any loss function, what is the corresponding empirical risk?
R(h) = 1/n En i=1 L(y_i, h)
