Where we have define
Denominator =
Where we have defined
Q3
The likelihood functio
By using logarithm lik
d:
n is
elihood:
Since there is a constr expression, which bec
aint on , so we need to add a Lagrange Multiplier to the omes:
, we have and , for ∀ . Together with and
(∗), we know that And if we calculate from the perspective of following the same procedure, we can obtain . Hence contradictory occurs. In other words, they are not linearly separable if their convex hulls intersect.
We have already proved the first statement, i.e., "convex hulls intersect" gives "not linearly separable", and what the second part wants us to prove is that "linearly separable" gives "convex hulls do not intersect". This can be done simply by contrapositive.
The true converse of the first statement should be if their convex hulls do not intersect, the data sets should be linearly separable. This is exactly what Hyperplane Separation Theorem shows us.
