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# Pattern Recognition and Machine Learning

CSCI 744 Pattern Recognition and Machine Learning

Part I Single Feature

1. Create a matlab script that will perform each of the steps required for this exercise.

2. Load βpartOneData.matβ into the matlab environment (included in blackboard as part of the assignment).

3. Create a histogram for each of the class distributions {classOne, classTwo}. Plot each of the histograms on the same figure (use 100 bins). The x and y axis should be labeled appropriately. There should be a title for the figure as well as a legend.

4. Report the prior probability for classOne? (Hint: Number of classOne samples divided by all samples)

5. Report the prior probability for classTwo? (Hint: see above hint, but for classTwo)

6. Create 5 random partitions of the data, splitting each of the classes into 60% training and 40% testing.

a. Using only the training data, find the maximum likelihood estimator for the following parameters:

i. πΆπππ π  πππ: π,π

ii. πΆπππ π  ππ€π: π,π

b. Classify each of the test samples using a Bayesian classifier (you must create a function that will do this). Report the prediction accuracy for each class.

7. Report the mean and standard deviation for the prediction accuracy from step 6.

Hint: You will need to create a method that, given the mean and standard deviation of a distribution, determines the probability of a value βxβ belonging to that distribution.

Matlab template below:

function probability = computeGaussianDensity(mean, stdDev, x)

end

Part II Multivariate

1. Create a matlab script that will perform each of the steps required for this exercise.

2. Load βpartTwoData.matβ into the matlab environment (included in blackboard as part of the assignment).

3. Report the prior probability for classOne?

4. Report the prior probability for classTwo?

5. Create 5 random partitions of the data, splitting each of the classes into 60% training and 40% testing.

a. Repeat the following process for each of the 5 random partitions:

i. Using only the training data, find the maximum likelihood estimator for the following parameters:

1. πΆπππ π  πππ: π,πππ£πππππππ πππ‘πππ₯

2. πΆπππ π  ππ€π: π,πππ£πππππππ πππ‘πππ₯

ii. Classify each of the test samples using a Bayesian classifier (you must create a function that will do this). Report the prediction accuracy for each class.

6. Report the mean and standard deviation for the prediction accuracy from step 5.

Hint: You will need to create a method that, given the mean and covariance matrix, determines the probability of a value βxβ belonging to the distribution.

Matlab template below:

function probability = computeGaussianDensityMultivariate(mean, covarianceMatrix, x)

end

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