ml案例 Inclass we covered the derivation of basic learning algorithms to derive a model

ml案例 案例CSE 6363 – Machine Learning

Homework 1- Spring 2019

Due Date: Feb. 8 2019, 11:59 pm

MLE and MAP

Inclass we covered the derivation of basic learning algorithms to derive a model for a coin flip  Consider a similar problems where we monitor the time of the occurrence of a severe computer failure (which requires a system reboot) and which occurs according to a Poisson process (i.e. it is equally likely to happen at any point in time with an arrival rate of λ ). For a Poisson process the probability of the first event to occur at time x after a restart is described by an exponential distribution:
ml案例ml案例
−

pλ(x) = λe


ml案例 项目介绍We are assuming here that the different data points we measured are independent, i.e. nothing changes between reboots.

Derivethe performance function and the optimization result for analytic MLE optimization for a model learning algorithm that returns the MLE for the parameter λ of the model given a data set D = {k1, …kn}. Make sure you show your
Apply the learning algorithm from a) to the followingdataset:


D = {1.5, 3, 2.5, 2.75, 2.9, 3} .



Derive the optimization for a MAP approach using the conjugate prior, the Gamma


The Gamma distribution is:

pα,β

(λ) =

βα




Γ(α)

λα−1

−βλ



ml案例 Note that α and β are constants and that there still is only one parameter, λ, to be learned. Show your derivation and the result for the data in part b) and values for α and β of 5 and 10, respectively.



K Nearest Neighbor
Consider the problem where we want to predict the gender of a person from a set of input parameters, namely height, weight, and age. Assume our training data is given asfollows:




D = { ((170, 57, 32), W ),
((192, 95, 28), M ),
((150, 45, 30), W ),
((170, 65, 29), M ),
((175, 78, 35), M ),
((185, 90, 32), M ),
((170, 65, 28), W ),
((155, 48, 31), W ),
((160, 55, 30), W ),
((182, 80, 30), M ),
((175, 69, 28), W ),
((180, 80, 27), M ),
((160, 50, 31), W ),
((175, 72, 30), M ), }
Using Cartesian distance as the similarity ml案例 measurements show the results of the gender prediction forthe following data items for values of K of 1, 3, and 5. Include the intermedia steps (i.e. distance calculation, neighbor selection, prediction).


(155, 40, 35), (170, 70, 32), (175, 70, 35), (180, 90, 20)





Implement the KNN algorithm for this problem. ml案例  Your implementation should work with different training data sets and allow to input a data point for the
Repeat the prediction using KNN when the age data is removed. Try to determine (using multiple target values) which data gives you better predictions. Show your intermediate


Gaussian Na¨ıve Bayes Classification
Using the data from Problem 2, build a Gaussian Na¨ıve  Bayes classifier for this problem.  For this you  haveto learn Gaussian distribution parameters for each input data feature, e. for p(height|W ), p(height|M ), p(weight|W ), p(weight|M ), p(age|W ), p(age|M ).


Learn/derive the parameters for the Gaussian Na¨ıve Bayes Classifier and apply them to the same target as in problem 2b). Show your intermediate
Implement the Gaussian Na¨ıve Bayes Classifier for this
Repeat the experiment in part 2c) with the Gaussian Na¨ıve Bayes
Compare the results of the two classifiers and discuss reasons why one might perform better than the