[SOLVED] python network theory Assignment 3 MLP and Probability

Assignment 3 MLP and Probability
Assignment overview. This assignment is designed to practice one more time the principle ideas behind neural networks and to move to a probabilistic framework. The second part includes some practice with probability theory. You are asked to write a program to plot a histogram for a specific probabilistic process that we can model by drawing samples from a specific distribution. Graduate students will also be asked to provide some analytic solutions.
Submission. Submit a Jupyder file and a pdf file for question 4 called MLAssignment3 Questions:
1. 20 marks MLP for 3class problem: This assignment is once more an opportunity to implementing an MLP for multiclass classification. The data for this assignment can be loaded with
Xnp.loadtxtFeaturesX.csv
Ynp.loadtxtLabelsY.csv
Convert the labels of these data set to a one hot representation and implement a neural network by adapting the MLPxor program from the manuscript. Estimate and state the best classification performance for this classification problem.
2. 20 marks; CSCI 4155 only Implement the MLP of question 1 with Keras.
3. 20 marks Working with random numbers:
3.1. Write a program that rolls two dice randomly selects a number between 1 and 6 inclusive for each die.
Repeat rolling dice 20 times. For each trial, you should add the two numbers that appear on each die and save it in a vector. Plot a histogram of the values you have gathered in the vector. Based on this histogram, what are the estimates for the probabilities of each number?
3.2. Run your code for 1000 times. What is your estimation now?
3.3. Change your program and assume that you have one altered die and one correct die. The altered die has
the number 0 instead of the number 2 on one face. This means that when you roll this defect die, a random number should be chosen among 1,0,3,4,5, and 6. Plot histogram of the values you have gathered in the vector. Calculate analytically the probability of getting the number 7 as the sum of the numbers of the two dice. What is the probability of getting 3?

4. 20 marks This Assignment requires you to write a Python script to calculate some inference of a simplified version of the car repair example from the manuscript.
Given are the following probabilities: The marginal probability that the alternator is broken is 11000 and the marginal probability that the fan belt is broken is 2100. The probability that the battery is charging when either the alternator or the fan belt is broken is zero. However, even if both are working there is a 51000 probability that the battery is not charging. When the battery is not charging then there is a 90 chance that the battery is flat, though even if the battery is charging then there is a 10 chance that the battery is flat. Finally, the car does not start if either the battery is flat, or there is no gas, or the starter is broken. However, even if these three conditions dont hold there is a 5 chance that the car wont start.
a. Draw the causal model of this system submit picture.
b. What is the probability that the alternator is broken given that the car wont start?
c. What is the probability that the fan belt is broken given that the car wont start?
d. What is the probability that the fan belt is broken given that the car wont start and the alternatoris broken?
e. What is the probability that the alternator and the fan belt is broken given that the car wont start?
Hint: You might use lea.Lea methods from the Lea 2 distribution as in the manuscript or implement it with Lea 3.