Tutorial Questions Flashcards
What is the Bayes predictor of a 0-1 cost of a binary prediction problem?
f*: x -> 1 {η(X) > 0.5}
What is the Bayes risk of a 0-1 cost binary prediction problem?
R*_P = E[min{η(X), 1 - η(X)}]
When is a predictor Bayes predictor?
(in a 0-1 cost learning problem)
Any predictor f s.t. {f(x) = f*(x) or η(X) = 0.5} is a Bayes predictor a.s.
How to derive the Bayes risk explicitly? (given η(x) and f*)
- Extract the Bayes formula for the possible X as follows: P(X = 1)E[… | X = 1] + … etc.
- Solve.
What is (usually) the definition of η(x)?
E[Y|X]
What is the Cauchy-Swartz inequality?
E[XY] ≤ sqrt(|XY|^2) ≤ sqrt(E[X^2]E[Y^2])
What is the formula for excess risk in a binary framework?
𝓁(f, f*) = E[|2η(x) - 1|1{f(D_n;x)} != f*(x)}]
What is the plug-in classifier of η^hat?
In a binary classification model
f^hat_{n^hat}(D_n; x) = 1{n^hat(D_n; x) > 0.5}
What is a trick that can be used in a binary classification learning problem when finding a simplfication of η(X) > 0.5?
If η(X) > 0.5, then P(A) > P(B)
What is a trick that can be used in a binary classification learning algorithm when splitting a formula?
If P(A) +P(B) = 1, then
X1{A} + X1{B} = X
What is the definition of the ERM predictor?
