4. Write a function called labelBayes that takes in posting times for multiple birds as well as the learned parameters for the likelihoods and prior, and return the most probable class for each bird. Specifically, the function will be called as:

labelsOut = labelBayes(birdFeats,params,priors)

where birdFeats is a numpy array of shape (K,2) containing the 2 features for K birds, params is a numpy array with shape (M,2) matching the description of the output for 'learnParams' and priors is a numpy array with shape (M) matching the description of the output for 'learnPriors' ;

labelsOut is a numpy array with shape (K) containing the most probable label for each bird, where labelsOut[j] corresponds to birdFeats[j] .

Labels are computed using the Exponential Bayes classifier!

labelBayes(np.array([[0.5,5],[0.5,2],[2,8]]), np.array([[0.7,0.2],[0.4,0.1]]), np.array([0.4,0.6]))

would return np.array([0,0,1])

{ Note 1: function called 'learnPriors' that takes in a data set and returns the prior probability of each class. Specifically, the function will be called as:

priors=learnPriors(Data)

where Data is a numpy array with shape (N,3) where N is the number of data points and priors is a numpy array with shape (M) where there are M classes, priors[i] is the estimated prior probability for class i .

Note 2:

function called 'learnParams' that takes in a data set and returns the learned lambda parameter mean and standard deviation for each class for the two features. Specifically, the function will be called as:

params =learnParams(Data) where Data is a numpy array with shape (N,3) where N is the number of data points and params is a both paramsSpeed and paramsChirpDelay are numpy array with shape (M,2) where there are M classes, params[i,0] is the lambda for the speed for class i and params[i,1] is the lambda for the chirp delay of class i.}