ml02450

This is a library which extends the toolbox provided in the 02450-course at The Technical University of Denmark and contains a series of functions that will speed up a lot of exercises found in exam sets, that normally are calculated by hand.

Tip: The functions can also be used as a result-checking mechanism if you still prefer to do the questions by hand.

Install

Install this package with pip:

!pip install --ignore-installed ml02450

Disclaimer: The author of most of this package is Tue Herlau

Usage

Import library in python with:

import toolbox_extended as te
import toolbox_02450 as tb
import numpy as np

Most library functions require numpy vectors as inputs, so numpy needs to be imported as well.

Usage of the main toolbox

Whenever you would normally use toolbox functions such as

density, log_density = gausKernelDensity(X,w)

Instead, simply use the tb. as the module prefix:

density, log_density = tb.gausKernelDensity(X,w)

This accomplishes two things:

• No namespace pollution
• The toolbox being much easier to use in Jupyter Notebooks

Usage of the extended toolbox

AdaBoost

Given a classification problem with 25 observations in total, with 5 of them being misclassified in round 1, the weights can be calculated as:

miss = np.zeros(25)
miss[:5] = 1
te.adaboost(miss, rounds=1)

The weights are as follows:

w[0]: 0.100000
w[1]: 0.100000
w[2]: 0.100000
w[3]: 0.100000
w[4]: 0.100000
w[5]: 0.025000
w[6]: 0.025000
w[7]: 0.025000
w[8]: 0.025000
w[9]: 0.025000
w[10]: 0.025000
w[11]: 0.025000
w[12]: 0.025000
w[13]: 0.025000
w[14]: 0.025000
w[15]: 0.025000
w[16]: 0.025000
w[17]: 0.025000
w[18]: 0.025000
w[19]: 0.025000
w[20]: 0.025000
w[21]: 0.025000
w[22]: 0.025000
w[23]: 0.025000
w[24]: 0.025000

Naive Bayes

Example from exam, fall 2018.

Given the following transaction matrix, where the rows correspond to a feature , and the classes being given by the vector , what is ?

X = np.array([
    [1,1,0,0,0,1,0,0,0,1],
    [1,0,0,0,0,0,0,0,0,0],
    [1,1,0,0,0,1,0,0,0,1],
    [0,1,1,1,0,0,0,1,1,0],
    [1,1,0,0,0,1,0,0,0,1],
    [0,1,1,1,0,0,1,1,1,0],
    [1,1,1,0,0,1,1,1,1,0],
    [0,1,1,1,0,1,1,0,0,1],
    [0,0,0,0,1,1,1,0,1,1],
    [1,0,0,0,0,1,1,1,1,0],
])

labels = ['f%i' %i for i in range(1,11)]
f1,f2,f3,f4,f5,f6,f7,f8,f9,f10 = X.T

y = [1,1,1,2,2,2,2,2,3,3]
x = [1,1,0]

te.naive_bayes(y, x, f1, f2, f6)

The probabilities for is given by the following vector:

array([0.45454545, 0.54545455, 0.        ])

The answer is therefore .

Support

Given the transaction matrix, the support of the item-set can be calculated using the supp(I) function:

te.supp([f1,f3,f8,f9,f2,f6,f7])

Output:

0.1

Confidence

Given the transaction matrix, what is the confidence of the rule

a = [f1,f3,f8,f9]
b = [f2,f6,f7]
te.conf(a,b)

Output:

1.0

Confusion Matrix

Given a 2x2 confusion matrix with:

• TP: 18
• FN: 12
• TN: 15
• FP: 9

Calculating the accuracy, error rate, recall, and much more, is done as follows:

M = [[18,12],[9,15]]
te.confusion_matrix(M)

Alternatively, by providing the attributes directly:

te.confusion_matrix(tp=18, fn=12, tn=15, fp=9)

Output:

TP: 18 FN: 12 TN: 15 FP: 9
Accuracy: 0.6111111111111112
Error rate: 0.38888888888888884
Recall: 0.6
Precision: 0.6666666666666666
FPR: 0.375
TPR: 0.6

ARD

Using K=2 nearest neighbours given the following distances, the avergae relative density becomes:

o1 = np.array([68.1, 165.4])
o3 = np.array([68.1, 111.1])
o4 = np.array([44.74, 32.5])

te.density(o1) / np.mean([te.density(o3), te.density(o4)])

Output:

0.46231460448232553