the second term is the prior or the regularizer so if you're using weight decay that corresponds to a Gaussian prior for example and if we factorize the likelihood if we assume independent and identically distributed data points then we get the familiar form shown here it's a sum over all of your data points of the log probability of the label Y I given the input X I and your parameters Phi so this is essentially supervised learning now of course there are some things that are a little bit problematic about this as Chelsea alluded to in the