# Practical Machine Learning with R and Python – Part 1

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# 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

- Statistical Learning, Prof Trevor Hastie & Prof Robert Tibesherani, Online Stanford
- 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

**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

Another technique that is used is Standardization which is

## 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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