Category Archives: Masters of Science

Data Mining: Unit 9

Ensemble Models:

Basics
Boosting
Ranmdom Forests

Support Vector Machines
Basics
Linear Classification
Nonlinear Classification
Properties of SVMs

Discriminant Analysis
Basics

 

Exercise:

We are going to create some data mining models for classification and compare their performance. The goal with our models is still.

 

Data Mining: Exercise 8

Design of network topology

Determine:

Number of input nodes
Too few nodes => misclassification
Too many nodes=> overfitting

 

Problems with dollar sign:

https://stackoverflow.com/questions/42560090/what-is-the-meaning-of-the-dollar-sign-in-r-function

Problem with tilde sign:

https://stackoverflow.com/questions/14976331/use-of-tilde-in-r-programming-language?noredirect=1&lq=1

 

 

Unit 5- Multiple Linear Regression

iT IS HAPPEN WHEN MORE THAN ONE POSSIBLE PREDICTOR VARIABLE.

including more than one independent variable in the regression model, makes us extend the simple linerar regression model to a multiple linear regression model.

Advantages:
Relationship between response variables and several predictors simultaneously.

Disadvantages:
Model building , interpration difficulties due to complexity.

Multiple linear regression with two predictors:

Y=beta0+beta1X1+beta2X2+epsylon
where, Y is the dependent variable.
X1,X2…Xk are predictors(independent variables)
Epsylon is the random error
beta1, beta2, beta0 are unknown regression coefficients

Example=> oil consumption:

Y=oil consumption(per month)
X1=outdoor temperature

X2=size of house(in meter square)

Model:

Y=beta0+beta1X1+beta2X2+epsylon

now beta1 is expected change in Y(oil consiumption) at one unit increase in X1(outdoor temperature), when all other predictors are kept constant, i.e. in this case the size of the house is not changed.

beta1 is estimated with beta1=-27.2 degree C

 

Assumptions:

The random error term epsylon is normally distributed and has mean zero. i.e. E(epsylon)=0

Epsylon has (unknown) variance sigma epsylon^2. i.e. all random errors have the same variance.

Adjusted R^2
R^2adj=1- SSE/(n-k-1)/SST/(n-1)

 

 

As for simple linear regression:

plots of residual against y prime
plots of residuals against xi
normal probability plot of residuals
plots of residuals in observation order
Cook’s distance
Studentized residuals
Standardized residuals
Dffits

Collinearity:
Can only occur for multiple regression.
Predictors explaining the same variation of the response variabl.

Oil consumption continued:
One predictor measuring house size in cm^2 and another predictor in m^2
Variance inflation factor

VIFi=1/1-Ri^2

Condition Index for collinearity:
between 10 and 30=>weak collinearity
between 30 and 100=>moderate
collinearity>100=>strong collinearity

Example of Oil consumption continued:
Assume that we would like to use outdoor temperature X1 and house size X2 as predictors. Additionally, we want to use a third predictor:

X3={1 if extra-thick walls, 0 otherwise

Model:
Y=beta0+beta1X1+beta2X2+beta3X3+epsylon

Model Selection Strategies:
Mldel ranked using R^2, adjusted R^2 or mallow’s Cp
Stepwise selection methods:
Backward, forward, stepwise selection

r^2 Selection
In a data set with 7 possible predictors, there would be 2^7-1=127 possible regression models.
For every model size(k=1,2,…..,p) look at, let say, m models, chosen

Mallow’s Cp:
Large Cp=>biased model
it’s a formula.
where MSEp=mean squared error for a model with p parametes
mean squared error for the full model
n=number of observations

Beta Error

https://www.khanacademy.org/math/ap-statistics/tests-significance-ap/error-probabilities-power/v/introduction-to-type-i-and-type-ii-errors

https://www.google.com/search?q=%CE%B2+error&rlz=1C1CHBF_enBD864BD864&oq=%CE%B2+error&aqs=chrome..69i57j0l7.10568j0j8&sourceid=chrome&ie=UTF-8

 

Some quick excel tips

Exercise Sheet 5

1d theke clear na , eta clear korte hobe , In Sha Allah.

 

Lagle onno kono tutorial ba example dekhte hobe.

IDA Old Question Solve

Winter 2019/20:

Normal distribution: meu=152
sigma=4.0

The Normal Distribution has:
Mean=Median=Mode
Symmetry about the center
50% of value less than the mean and 50% greater than the mean

 

1(b) Weibull

1(c)
https://www.statisticshowto.com/triangular-distribution/

(but I need to clear it up about Professor Orth solution)

2a

chi squaRE TEST

DEGREES of freedom

 

STATISTICS what it is?

 

 

Winter 2018/19:

 

Exercise Sheet 4

Data Mining Methods: Unit 4
Correlation and Simple Linear Regression

Interpretation of the correlation coefficient
Possible range: [-1, 1]
-1: perfect negative linear relationship
0: no linear relationship,
1: perfect positive linear relationship.

Regression: Objective

To predict one variable from other variables.
To explain the variability of one variable using the other variables.

Predicts scores on one variable from the scores on a second variable.

Response variable: predicting variable (Y )
Predictor variable: predictions based on this variable (X)

Simple regression:
Only one predictor variable; otherwise multiple regression

Linear regression:

Predictions of the response variable (Y ) is a linear function of  the predictor variable (X)

Data Preprocessing/Exercise Sheet 2

Theory:
Data Preprocessing in the Data Mining Process:

The data mining/KDD process
Why data preprocessing?

Issues in Data Preprocessing:

Data Cleaning
Data Transformation
Variable Construction
Data Reduction and Discretization
Data Integration

The data mining/KDD Process:
Understanding customer: 10%-20%
Understanding data:20-30
Prepare data: 40-70%
Build Models: 10-20%
Evaluate models: 10%-20%
Take action:10%20%

Why data mining?

Real – world data is dirty
Low data quality anyway a huge problem in data mining
Garbage in,garbage out
Different methods, different requirements

R Working Codes for data mining:

R code is case sensitive:
I am doing it from professors sheet.

dim means dimension

 

This line i could not make work:

hist(Ozone,breaks=25,ylim=(c(0,45)),main=”Original data”)

And another question how the imputation works

 

Exercise 2 (K)= I have to find the answers

 

Exercise 3: Answer:

 

 

R programming

R:

Manipulation of Vectors and Numbers
Vectors and Assignment
Extraction of Elements from VectorsMatrices
Basic Manipulations
The Data Frame
Table
Frames
Cumulative Distribution Function
Measures of Central Tendency
Measures of Spread
Correlation[Ektu dekhte hobe]

 

 

Standard Deviation

What we learnt:
ctrl+d

ctrl+r

$ sign to lock before column and row

Related to F-test

https://support.office.com/en-us/article/f-inv-rt-function-d371aa8f-b0b1-40ef-9cc2-496f0693ac00

https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/f-statistic-value-test/#FandP

 

https://support.office.com/de-de/article/fvert-funktion-ecf76fba-b3f1-4e7d-a57e-6a5b7460b786

 

Programming language confusion for AI

Machine Learning Algorithm Solutions