Independence & Conditional Independence

Independence & Conditional Independence Two random variables, \(X\) and \( Y \) are independent if the occurance of one does not give any information on the likelihood of the other event occuring. In other words, their probability distribution can be expressed as a product of two factors, one only involving \(X\), and one only involving \(Y\): \[\forall x \in X, y \in Y, \, p(X = x, Y= y) = p(X = x)p(Y = y)\] Two random variables, x and y are conditionally independentif, given knowledge of the occurance of \(Z\), knowledge of the occurance of \(X\) provides no information on the likeihood of the occurance of \(Y\). Read more...

Machine Learning Definition (Mitchell, 1997)

Machine Learning Definition (Mitchell, 1997) A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.