A. Pac Learning

• Let X=R with orthonormal basis (e1, e2) and consider the set of concepts defined by the area inside a right triangle ABC with two sides parallel to the axes, with −−→ AB/AB = e1 and −→ AC/AC = e2, and AB/AC = α for some positive real α ∈ R+. Show, using similar methods to those used in the lecture slides for the axis-aligned rectangles, that this class can be (ǫ, δ)PAC-learned from training data of size m ≥ (3/ǫ) log(3/δ). As in the case of axis-aligned rectangles, consider three regions r1, r2, r3, along the sides of the target concept as indicated in Figure 1. Note that the triangle formed by the points A”, B”, C” is similar to ABC (same angles) since A”B” must be parallel to AB, and similarly for the other sides.