1 Section 6.4 noted that the output of the logistic function could be interpreted as a probability p assigned by the model to the proposition that f (x)=1; the probability that f(x)=0 is therefore 1 − p. Write down the probability p as a function of x and calculate the derivative of log p with respect to each weight w . Repeat the process for log (1−p).

These calculations give a learning rule for minimizing the negative-log-likelihood loss function for a probabilistic hypothesis. Comment on any resemblance to other learning rules in the chapter.