2. Consider a Bayesian classification problem where we wish to determine if a contact on a social network is a friend, relative, or co-worker. We use four features - x1 (MessageFrequency), x2 (MainMessageType), x3 (Proximity), X4 Age. Each feature takes on one of up to five values, shown below: MessageFrequency | Annually Monthly Daily MainMessageType VideoCall DirectMessage | StatusUpdate Proximity SameCity SameCountry SameState SameBuilding Age Child SeniorCitizen MiddleAge Teen We classify each user as one of four classes: y'=Friend, y'=Relative, y'=Co-worker, or y'=Acquaintance. Based on a large training set, we wish to estimate all joint probability likelihoods, e.g., P(x1=Monthly,x2=StatusUpdate,x3=SameBuilding,x4=Teen | y=Co-Worker), P(x1=Daily,x2=StatusUpdate,x3=SameState,x4=SeniorCitizen | y=Co-Worker). a) Assuming the features are independent, how many total parameters need to be estimated, accounting for classifying friends, relatives, and co-workers? b) Assuming the features are not independent, how many total parameters need to be estimated, accounting for classifying friends, relatives, and co-workers? Now assume we only classify subjects using the first two features, and we replace the discrete feature values with numbers: MessageFrequency| 0 (Annually) 1 (Monthly) 2 (Daily) Age 0 (Child) 1 (Teen) 2 (MiddleAge) 3 (SeniorCitizen) We use a joint Gaussian likelihood for the probability of the two features for each class y: P(x1,*2 |y) , and we also will estimate a prior probability for each of the three contact classes. c) Assuming x1 and x2 are not independent, how many parameters need to be learned to compute the posterior probabilities X2) d) Assuming x1 and x2 are independent, how many parameters need to be learned to compute the posterior probabilities Xz)