Practical Machine Learning with R and Python – Part 1


Introduction

This is the 1st part of a series of posts I intend to write on some common Machine Learning Algorithms in R and Python. In this first part I cover the following Machine Learning Algorithms

  • Univariate Regression
  • Multivariate Regression
  • Polynomial Regression
  • K Nearest Neighbors Regression

The code includes the implementation in both R and Python. This series of posts are based on the following 2 MOOC courses I did at Stanford Online and at Coursera

  1. Statistical Learning, Prof Trevor Hastie & Prof Robert Tibesherani, Online Stanford
  2. Applied Machine Learning in Python Prof Kevyn-Collin Thomson, University Of Michigan, Coursera

I have used the data sets from UCI Machine Learning repository(Communities and Crime and Auto MPG). I also use the Boston data set from MASS package

While coding in R and Python I found that there were some aspects that were more convenient in one language and some in the other. For example, plotting the fit in R is straightforward in R, while computing the R squared, splitting as Train & Test sets etc. are already available in Python. In any case, these minor inconveniences can be easily be implemented in either language.

R squared computation in R is computed as follows
RSS=\sum (y-yhat)^{2}
TSS= \sum(y-mean(y))^{2}
Rsquared- 1-\frac{RSS}{TSS}

Note: You can download this R Markdown file and the associated data sets from Github at MachineLearning-RandPython
Note 1: This post was created as an R Markdown file in RStudio which has a cool feature of including R and Python snippets. The plot of matplotlib needs a workaround but otherwise this is a real cool feature of RStudio!

1.1a Univariate Regression – R code

Here a simple linear regression line is fitted between a single input feature and the target variable

# Source in the R function library
source("RFunctions.R")
# Read the Boston data file
df=read.csv("Boston.csv",stringsAsFactors = FALSE) # Data from MASS - Statistical Learning

# Split the data into training and test sets (75:25)
train_idx <- trainTestSplit(df,trainPercent=75,seed=5)
train <- df[train_idx, ]
test <- df[-train_idx, ]

# Fit a linear regression line between 'Median value of owner occupied homes' vs 'lower status of 
# population'
fit=lm(medv~lstat,data=df)
# Display details of fir
summary(fit)
## 
## Call:
## lm(formula = medv ~ lstat, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.168  -3.990  -1.318   2.034  24.500 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 34.55384    0.56263   61.41   <2e-16 ***
## lstat       -0.95005    0.03873  -24.53   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.216 on 504 degrees of freedom
## Multiple R-squared:  0.5441, Adjusted R-squared:  0.5432 
## F-statistic: 601.6 on 1 and 504 DF,  p-value: < 2.2e-16
# Display the confidence intervals
confint(fit)
##                 2.5 %     97.5 %
## (Intercept) 33.448457 35.6592247
## lstat       -1.026148 -0.8739505
plot(df$lstat,df$medv, xlab="Lower status (%)",ylab="Median value of owned homes ($1000)", main="Median value of homes ($1000) vs Lowe status (%)")
abline(fit)
abline(fit,lwd=3)
abline(fit,lwd=3,col="red")

rsquared=Rsquared(fit,test,test$medv)
sprintf("R-squared for uni-variate regression (Boston.csv)  is : %f", rsquared)
## [1] "R-squared for uni-variate regression (Boston.csv)  is : 0.556964"

1.1b Univariate Regression – Python code

import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
#os.chdir("C:\\software\\machine-learning\\RandPython")

# Read the CSV file
df = pd.read_csv("Boston.csv",encoding = "ISO-8859-1")
# Select the feature variable
X=df['lstat']

# Select the target 
y=df['medv']

# Split into train and test sets (75:25)
X_train, X_test, y_train, y_test = train_test_split(X, y,random_state = 0)
X_train=X_train.values.reshape(-1,1)
X_test=X_test.values.reshape(-1,1)

# Fit a linear model
linreg = LinearRegression().fit(X_train, y_train)

# Print the training and test R squared score
print('R-squared score (training): {:.3f}'.format(linreg.score(X_train, y_train)))
print('R-squared score (test): {:.3f}'.format(linreg.score(X_test, y_test)))
     
# Plot the linear regression line
fig=plt.scatter(X_train,y_train)

# Create a range of points. Compute yhat=coeff1*x + intercept and plot
x=np.linspace(0,40,20)
fig1=plt.plot(x, linreg.coef_ * x + linreg.intercept_, color='red')
fig1=plt.title("Median value of homes ($1000) vs Lowe status (%)")
fig1=plt.xlabel("Lower status (%)")
fig1=plt.ylabel("Median value of owned homes ($1000)")
fig.figure.savefig('foo.png', bbox_inches='tight')
fig1.figure.savefig('foo1.png', bbox_inches='tight')
print "Finished"
## R-squared score (training): 0.571
## R-squared score (test): 0.458
## Finished

1.2a Multivariate Regression – R code

# Read crimes data
crimesDF <- read.csv("crimes.csv",stringsAsFactors = FALSE)

# Remove the 1st 7 columns which do not impact output
crimesDF1 <- crimesDF[,7:length(crimesDF)]

# Convert all to numeric
crimesDF2 <- sapply(crimesDF1,as.numeric)

# Check for NAs
a <- is.na(crimesDF2)
# Set to 0 as an imputation
crimesDF2[a] <-0
#Create as a dataframe
crimesDF2 <- as.data.frame(crimesDF2)
#Create a train/test split
train_idx <- trainTestSplit(crimesDF2,trainPercent=75,seed=5)
train <- crimesDF2[train_idx, ]
test <- crimesDF2[-train_idx, ]

# Fit a multivariate regression model between crimesPerPop and all other features
fit <- lm(ViolentCrimesPerPop~.,data=train)

# Compute and print R Squared
rsquared=Rsquared(fit,test,test$ViolentCrimesPerPop)
sprintf("R-squared for multi-variate regression (crimes.csv)  is : %f", rsquared)
## [1] "R-squared for multi-variate regression (crimes.csv)  is : 0.653940"

1.2b Multivariate Regression – Python code

import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
# Read the data
crimesDF =pd.read_csv("crimes.csv",encoding="ISO-8859-1")
#Remove the 1st 7 columns
crimesDF1=crimesDF.iloc[:,7:crimesDF.shape[1]]
# Convert to numeric
crimesDF2 = crimesDF1.apply(pd.to_numeric, errors='coerce')
# Impute NA to 0s
crimesDF2.fillna(0, inplace=True)

# Select the X (feature vatiables - all)
X=crimesDF2.iloc[:,0:120]

# Set the target
y=crimesDF2.iloc[:,121]

X_train, X_test, y_train, y_test = train_test_split(X, y,random_state = 0)
# Fit a multivariate regression model
linreg = LinearRegression().fit(X_train, y_train)

# compute and print the R Square
print('R-squared score (training): {:.3f}'.format(linreg.score(X_train, y_train)))
print('R-squared score (test): {:.3f}'.format(linreg.score(X_test, y_test)))
## R-squared score (training): 0.699
## R-squared score (test): 0.677

1.3a Polynomial Regression – R

For Polynomial regression , polynomials of degree 1,2 & 3 are used and R squared is computed. It can be seen that the quadaratic model provides the best R squared score and hence the best fit

 # Polynomial degree 1
df=read.csv("auto_mpg.csv",stringsAsFactors = FALSE) # Data from UCI
df1 <- as.data.frame(sapply(df,as.numeric))

# Select key columns
df2 <- df1 %>% select(cylinder,displacement, horsepower,weight, acceleration, year,mpg)
df3 <- df2[complete.cases(df2),]

# Split as train and test sets
train_idx <- trainTestSplit(df3,trainPercent=75,seed=5)
train <- df3[train_idx, ]
test <- df3[-train_idx, ]

# Fit a model of degree 1
fit <- lm(mpg~. ,data=train)
rsquared1 <-Rsquared(fit,test,test$mpg)
sprintf("R-squared for Polynomial regression of degree 1 (auto_mpg.csv)  is : %f", rsquared1)
## [1] "R-squared for Polynomial regression of degree 1 (auto_mpg.csv)  is : 0.763607"
# Polynomial degree 2 - Quadratic
x = as.matrix(df3[1:6])
# Make a  polynomial  of degree 2 for feature variables before split
df4=as.data.frame(poly(x,2,raw=TRUE))
df5 <- cbind(df4,df3[7])

# Split into train and test set
train_idx <- trainTestSplit(df5,trainPercent=75,seed=5)
train <- df5[train_idx, ]
test <- df5[-train_idx, ]

# Fit the quadratic model
fit <- lm(mpg~. ,data=train)
# Compute R squared
rsquared2=Rsquared(fit,test,test$mpg)
sprintf("R-squared for Polynomial regression of degree 2 (auto_mpg.csv)  is : %f", rsquared2)
## [1] "R-squared for Polynomial regression of degree 2 (auto_mpg.csv)  is : 0.831372"
#Polynomial degree 3
x = as.matrix(df3[1:6])
# Make polynomial of degree 4  of feature variables before split
df4=as.data.frame(poly(x,3,raw=TRUE))
df5 <- cbind(df4,df3[7])
train_idx <- trainTestSplit(df5,trainPercent=75,seed=5)

train <- df5[train_idx, ]
test <- df5[-train_idx, ]
# Fit a model of degree 3
fit <- lm(mpg~. ,data=train)
# Compute R squared
rsquared3=Rsquared(fit,test,test$mpg)
sprintf("R-squared for Polynomial regression of degree 2 (auto_mpg.csv)  is : %f", rsquared3)
## [1] "R-squared for Polynomial regression of degree 2 (auto_mpg.csv)  is : 0.773225"
df=data.frame(degree=c(1,2,3),Rsquared=c(rsquared1,rsquared2,rsquared3))
# Make a plot of Rsquared and degree
ggplot(df,aes(x=degree,y=Rsquared)) +geom_point() + geom_line(color="blue") +
    ggtitle("Polynomial regression - R squared vs Degree of polynomial") +
    xlab("Degree") + ylab("R squared")

1.3a Polynomial Regression – Python

For Polynomial regression , polynomials of degree 1,2 & 3 are used and R squared is computed. It can be seen that the quadaratic model provides the best R squared score and hence the best fit

import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
autoDF =pd.read_csv("auto_mpg.csv",encoding="ISO-8859-1")
autoDF.shape
autoDF.columns
# Select key columns
autoDF1=autoDF[['mpg','cylinder','displacement','horsepower','weight','acceleration','year']]
# Convert columns to numeric
autoDF2 = autoDF1.apply(pd.to_numeric, errors='coerce')
# Drop NAs
autoDF3=autoDF2.dropna()
autoDF3.shape
X=autoDF3[['cylinder','displacement','horsepower','weight','acceleration','year']]
y=autoDF3['mpg']

# Polynomial degree 1
X_train, X_test, y_train, y_test = train_test_split(X, y,random_state = 0)
linreg = LinearRegression().fit(X_train, y_train)
print('R-squared score - Polynomial degree 1 (training): {:.3f}'.format(linreg.score(X_train, y_train)))
# Compute R squared     
rsquared1 =linreg.score(X_test, y_test)
print('R-squared score - Polynomial degree 1 (test): {:.3f}'.format(linreg.score(X_test, y_test)))

# Polynomial degree 2
poly = PolynomialFeatures(degree=2)
X_poly = poly.fit_transform(X)
X_train, X_test, y_train, y_test = train_test_split(X_poly, y,random_state = 0)
linreg = LinearRegression().fit(X_train, y_train)

# Compute R squared
print('R-squared score - Polynomial degree 2 (training): {:.3f}'.format(linreg.score(X_train, y_train)))
rsquared2 =linreg.score(X_test, y_test)
print('R-squared score - Polynomial degree 2 (test): {:.3f}\n'.format(linreg.score(X_test, y_test)))

#Polynomial degree 3

poly = PolynomialFeatures(degree=3)
X_poly = poly.fit_transform(X)
X_train, X_test, y_train, y_test = train_test_split(X_poly, y,random_state = 0)
linreg = LinearRegression().fit(X_train, y_train)
print('(R-squared score -Polynomial degree 3  (training): {:.3f}'
     .format(linreg.score(X_train, y_train)))
# Compute R squared     
rsquared3 =linreg.score(X_test, y_test)
print('R-squared score Polynomial degree 3 (test): {:.3f}\n'.format(linreg.score(X_test, y_test)))
degree=[1,2,3]
rsquared =[rsquared1,rsquared2,rsquared3]
fig2=plt.plot(degree,rsquared)
fig2=plt.title("Polynomial regression - R squared vs Degree of polynomial")
fig2=plt.xlabel("Degree")
fig2=plt.ylabel("R squared")
fig2.figure.savefig('foo2.png', bbox_inches='tight')
print "Finished plotting and saving"
## R-squared score - Polynomial degree 1 (training): 0.811
## R-squared score - Polynomial degree 1 (test): 0.799
## R-squared score - Polynomial degree 2 (training): 0.861
## R-squared score - Polynomial degree 2 (test): 0.847
## 
## (R-squared score -Polynomial degree 3  (training): 0.933
## R-squared score Polynomial degree 3 (test): 0.710
## 
## Finished plotting and saving

1.4 K Nearest Neighbors

The code below implements KNN Regression both for R and Python. This is done for different neighbors. The R squared is computed in each case. This is repeated after performing feature scaling. It can be seen the model fit is much better after feature scaling. Normalization refers to

X_{normalized} = \frac{X-min(X)}{max(X-min(X))}

Another technique that is used is Standardization which is

X_{standardized} = \frac{X-mean(X)}{sd(X)}

1.4a K Nearest Neighbors Regression – R( Unnormalized)

The R code below does not use feature scaling

# KNN regression requires the FNN package
df=read.csv("auto_mpg.csv",stringsAsFactors = FALSE) # Data from UCI
df1 <- as.data.frame(sapply(df,as.numeric))
df2 <- df1 %>% select(cylinder,displacement, horsepower,weight, acceleration, year,mpg)
df3 <- df2[complete.cases(df2),]

# Split train and test
train_idx <- trainTestSplit(df3,trainPercent=75,seed=5)
train <- df3[train_idx, ]
test <- df3[-train_idx, ]
#  Select the feature variables
train.X=train[,1:6]
# Set the target for training
train.Y=train[,7]
# Do the same for test set
test.X=test[,1:6]
test.Y=test[,7]

rsquared <- NULL
# Create a list of neighbors
neighbors <-c(1,2,4,8,10,14)
for(i in seq_along(neighbors)){
    # Perform a KNN regression fit
    knn=knn.reg(train.X,test.X,train.Y,k=neighbors[i])
    # Compute R sqaured
    rsquared[i]=knnRSquared(knn$pred,test.Y)
}

# Make a dataframe for plotting
df <- data.frame(neighbors,Rsquared=rsquared)
# Plot the number of neighors vs the R squared
ggplot(df,aes(x=neighbors,y=Rsquared)) + geom_point() +geom_line(color="blue") +
    xlab("Number of neighbors") + ylab("R squared") +
    ggtitle("KNN regression - R squared vs Number of Neighors (Unnormalized)")

1.4b K Nearest Neighbors Regression – Python( Unnormalized)

The Python code below does not use feature scaling

import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.neighbors import KNeighborsRegressor
autoDF =pd.read_csv("auto_mpg.csv",encoding="ISO-8859-1")
autoDF.shape
autoDF.columns
autoDF1=autoDF[['mpg','cylinder','displacement','horsepower','weight','acceleration','year']]
autoDF2 = autoDF1.apply(pd.to_numeric, errors='coerce')
autoDF3=autoDF2.dropna()
autoDF3.shape
X=autoDF3[['cylinder','displacement','horsepower','weight','acceleration','year']]
y=autoDF3['mpg']

# Perform a train/test split
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state = 0)
# Create a list of neighbors
rsquared=[]
neighbors=[1,2,4,8,10,14]
for i in neighbors:
        # Fit a KNN model
        knnreg = KNeighborsRegressor(n_neighbors = i).fit(X_train, y_train)
        # Compute R squared
        rsquared.append(knnreg.score(X_test, y_test))
        print('R-squared test score: {:.3f}'
        .format(knnreg.score(X_test, y_test)))
# Plot the number of neighors vs the R squared        
fig3=plt.plot(neighbors,rsquared)
fig3=plt.title("KNN regression - R squared vs Number of neighbors(Unnormalized)")
fig3=plt.xlabel("Neighbors")
fig3=plt.ylabel("R squared")
fig3.figure.savefig('foo3.png', bbox_inches='tight')
print "Finished plotting and saving"
## R-squared test score: 0.527
## R-squared test score: 0.678
## R-squared test score: 0.707
## R-squared test score: 0.684
## R-squared test score: 0.683
## R-squared test score: 0.670
## Finished plotting and saving

1.4c K Nearest Neighbors Regression – R( Normalized)

It can be seen that R squared improves when the features are normalized.

df=read.csv("auto_mpg.csv",stringsAsFactors = FALSE) # Data from UCI
df1 <- as.data.frame(sapply(df,as.numeric))
df2 <- df1 %>% select(cylinder,displacement, horsepower,weight, acceleration, year,mpg)
df3 <- df2[complete.cases(df2),]

# Perform MinMaxScaling of feature variables 
train.X.scaled=MinMaxScaler(train.X)
test.X.scaled=MinMaxScaler(test.X)

# Create a list of neighbors
rsquared <- NULL
neighbors <-c(1,2,4,6,8,10,12,15,20,25,30)
for(i in seq_along(neighbors)){
    # Fit a KNN model
    knn=knn.reg(train.X.scaled,test.X.scaled,train.Y,k=i)
    # Compute R ssquared
    rsquared[i]=knnRSquared(knn$pred,test.Y)
    
}

df <- data.frame(neighbors,Rsquared=rsquared)
# Plot the number of neighors vs the R squared 
ggplot(df,aes(x=neighbors,y=Rsquared)) + geom_point() +geom_line(color="blue") +
    xlab("Number of neighbors") + ylab("R squared") +
    ggtitle("KNN regression - R squared vs Number of Neighors(Normalized)")

1.4d K Nearest Neighbors Regression – Python( Normalized)

R squared improves when the features are normalized with MinMaxScaling

import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
from sklearn.neighbors import KNeighborsRegressor
from sklearn.preprocessing import MinMaxScaler
autoDF =pd.read_csv("auto_mpg.csv",encoding="ISO-8859-1")
autoDF.shape
autoDF.columns
autoDF1=autoDF[['mpg','cylinder','displacement','horsepower','weight','acceleration','year']]
autoDF2 = autoDF1.apply(pd.to_numeric, errors='coerce')
autoDF3=autoDF2.dropna()
autoDF3.shape
X=autoDF3[['cylinder','displacement','horsepower','weight','acceleration','year']]
y=autoDF3['mpg']

# Perform a train/ test  split
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state = 0)
# Use MinMaxScaling
scaler = MinMaxScaler()
X_train_scaled = scaler.fit_transform(X_train)
# Apply scaling on test set
X_test_scaled = scaler.transform(X_test)

# Create a list of neighbors
rsquared=[]
neighbors=[1,2,4,6,8,10,12,15,20,25,30]
for i in neighbors:
    # Fit a KNN model
    knnreg = KNeighborsRegressor(n_neighbors = i).fit(X_train_scaled, y_train)
    # Compute R squared
    rsquared.append(knnreg.score(X_test_scaled, y_test))
    print('R-squared test score: {:.3f}'
        .format(knnreg.score(X_test_scaled, y_test)))

# Plot the number of neighors vs the R squared 
fig4=plt.plot(neighbors,rsquared)
fig4=plt.title("KNN regression - R squared vs Number of neighbors(Normalized)")
fig4=plt.xlabel("Neighbors")
fig4=plt.ylabel("R squared")
fig4.figure.savefig('foo4.png', bbox_inches='tight')
print "Finished plotting and saving"
## R-squared test score: 0.703
## R-squared test score: 0.810
## R-squared test score: 0.830
## R-squared test score: 0.838
## R-squared test score: 0.834
## R-squared test score: 0.828
## R-squared test score: 0.827
## R-squared test score: 0.826
## R-squared test score: 0.816
## R-squared test score: 0.815
## R-squared test score: 0.809
## Finished plotting and saving

Conclusion

In this initial post I cover the regression models when the output is continous. I intend to touch upon other Machine Learning algorithms.
Comments, suggestions and corrections are welcome.

Watch this this space!

To be continued….

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24 thoughts on “Practical Machine Learning with R and Python – Part 1

  1. Pingback: Practical Machine Learning with R and Python – Part 1 – Mubashir Qasim

  2. Pingback: Practical Machine Learning with R and Python – Part 1 | A bunch of data

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  4. Pingback: Practical Machine Learning with R and Python – Part 2 | Giga thoughts …

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  6. from sklearn.model_selection import train_test_split
    I am still not able to get the above code to go through, can you help?

    should it something like
    from sklearn import model_selection, train_test_split
    ?
    above also cannot run.

  7. Pingback: Practical Machine Learning with R and Python – Part 3 | Giga thoughts …

  8. Pingback: Practical Machine Learning with R and Python – Part 3 | A bunch of data

  9. Pingback: Practical Machine Learning with R and Python – Part 3 – Mubashir Qasim

  10. Pingback: Practical Machine Learning with R and Python – Part 4 | Giga thoughts …

  11. Pingback: Practical Machine Learning with R and Python – Part 4 – Cloud Data Architect

  12. Pingback: Getting Started with R – The REPL MC

  13. Pingback: Practical Machine Learning with R and Python – Part 5 | Giga thoughts …

  14. Pingback: Practical Machine Learning with R and Python – Part 5 – Cloud Data Architect

  15. Pingback: Practical Machine Learning with R and Python – Part 6 | Giga thoughts …

  16. Pingback: Practical Machine Learning with R and Python – Part 6 – Cloud Data Architect

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