Assignment 2 Solution

This assignment will use the Linnerrud dataset: https://scikit-learn.org/stable/datasets/index.html




import using: from sklearn.datasets import load_linnerud




Objective 1: familiarize with vector operations for manipulating multi-dimensional arrays in numpy




Objective 2: learn basic data visualization (scatter plots and line charts)




Objective 3: understand how to code basic machine-learning algorithms from scratch




N.B: there will be no usage of sklearn or any other machine learning libraries in this assignment, the ONLY imports permitted are numpy and matplotlib (you can use sklearn to load the Linnerrud dataset only).




you must submit your scripts, any assignment submitted without python scripts attached, or with python scripts that use the sklearn libraries for question 2,3 will be penalized







Question 1: (question 1 does not use the Linnerrud dataset)




set up a working version of numpy/matplotlib in your IDE of choice (spyder, pycharm, etc.)




using numpy, initialize an array of random numbers each number ranging between 0 and 1 -array should have shape=[1000,50] (1000 rows, 50 columns)



create the correlation matrix of pearson correlations between all pairs of rows from (1A)



correlation matrix should have shape=[1000,1000])



using matplotlib, plot a 100-bin histogram, using values from lower triangle of 1000x1000 correlation coe cient (r-values) matrix obtained in 1B (omit the diagonal and all cells above the diagonal)



*hint - the histogram will be shaped like a gaussian




using the histogram, estimate the probability of obtaining an r-value 0.75 or <-0.75 from correlating two random vectors of size 50. repeat A-C with only 10 columns in (A), how does the smaller sample a ect the histogram in (C)?




QUESTION 1 OUTPUT: a gure with two histograms, hist1 based on correlations of vectors of size 50,




hist2 based on correlations of vectors of size 10. display the probability from (C) as the title of the histograms







Question 2:




A) get the Linnerrud data using: data = load_linnerrud()




-weight, waist, and heartrate are attributes, chinups, situps, and jumps are outcomes




using numpy’s matrix functions (np.dot, np.transpose, etc.), compute the linear-least-squares solution, nding the intercept and slope of best t line for each [attribute, outcome] pair (attribute on x-axis, outcome on y-axis)
*hint - be sure to augment the attribute vectors with a column of 1’s (so LLS can nd the intercept)




QUESTION 2 OUTPUT: a gure with a 3x3 grid of nine (9) subplots, each showing a scatter plot and best t line:




i) x=weight, y=chinups.
ii) x=weight, y=situps.
iii) x=weight, y=jumps.
iv) x=waist, y=chinups.
v) x=waist, y=situps.
vi) x=waist, y=jumps.
vii) x=heartrate,y=chinups.
viii)x=heartrate, y=situps.
ix) x=heartrate,y=jumps
display the slope and intercept of each scatter plot’ as the title of each scatter plot, as well as the attribute/outcome name on the x/y axis respectively







Question 3:




Implement the following two algorithms, from scratch, in python (using only the numpy import)




Gaussian Naive Bayes (probabilistic modeling)



Perceptron learning rule (Linear modeling) if perceptron does not converge run for 1000 iterations



do NOT copy-paste the sklearn code, or any other code from the internet (i will check this)




test your algorithms on the Linnerrud dataset using all 3 attributes, and only the chinups outcome, rst de ne new vector assigning binary classe to the outcome of chinups as follows:




if(chinupsmedian(chinups)) then chinups=0 else chinups=1




use these classes (0/1) to train the perceptron and build the probability table




QUESTION 3 OUTPUT: two .txt les:




gnb_results.txt = 20 probability values output by Gaussian Naive Bayes,




each value is P(chinups=1 | instance_i), where instance_i are the attributes of ith instance perceptron_results.txt = 20 prediction values output by perceptron




each value is a weighted sum (dot product of perceptron’s weights with attribute values)