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Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

SMOTE and Best Subset Selection for Linear Regression in R

M
Muhammad Last Updated : 23 Apr, 2021
5 min read
This article was published as a part of the Data Science Blogathon.

Introduction

subset selection smote
Victoriano Izquierdo on Unsplash

Best subset selection is one of the methods in linear model selection. The aim of the method is to improve the simple linear regression. This method worked by identifying the subset of predictors that related to the response so that the variables will be reduced. We will also cover SMOTE in this article.

The code in R

Let’s import the necessary libraries. The tidyverse is the main library, it includes common package like dplyr, gglplot2, and many more. Smotefamily will be used to overcome the imbalanced dataset. Caret and Leaps are for the regression.

library(tidyverse)
library(smotefamily)
library(caret)
library(leaps)

The dataset

The dataset is heart disease data from kaggle. The goal of this dataset is to classify whether or not the patient will have coronary heart disease in 10-years.

Let’s load the dataset, and just remove the missing value using na.omit(). Actually, there are some ways to resolve the missing values. It can be replaced by the average value, or simply omit the row containing the missing value.

k <- read.csv("../input/heart-disease-prediction-using-logistic-regression/framingham.csv")
k <- na.omit(k)

If we print all the predictors, we can see the first predictor named “male”. This is not representative, it should be named “sex”.

smote data

We can change the name of the predictors like this

k <- k %>% rename(sex = male)

Imbalanced dataset

It’s a good practice to always review the class distribution of our dataset first. One way to look at the class distribution is by using a histogram.

hist(k$TenYearCHD, col="maroon")

The histogram shows that the dataset is imbalanced. The ratio of the positive class to the negative class is too low. This situation is very common, especially in medical datasets. Because in reality, the data from positive illness is low, unless in the pandemic case like Covid-19.

This imbalanced dataset will lead to imbalanced accuracy or imbalanced prediction. This means that the prediction will always inclined towards the majority class, in this case, the negative class. You might see a high accuracy number, but don’t be fooled by that number. Because the sensitivity is low. Therefore, we have to combat this imbalanced dataset before going further.

smote imbalanced data

SMOTE

SMOTE stands for Synthetic Minority Oversampling Technique. This technique will help us resolves the imbalanced dataset problem. As the name implies, this technique will be oversampling the minority class in a synthetic way.

smote <- SMOTE(k[,-16], k$TenYearCHD)
new <- smote$data

Now our dataset is contained on the new variable, and the label is now on a column named class. We can see in the histogram that our class is now balanced. The number of the data doesn’t have to be exactly the same, but the difference has to be minimum.

hist(new$class, col=”coral”)

smote histogram

We can also print the number of the data from each class

new$class <- as.numeric(new$class)
table(new$class)
new$class

and we can print the percentage like this

prop.table(table(new$class))
new$class prop table

Best model selection

The function for model selection in R is regsubsets(), where the Nvmax is the number of predictors. After applying the regsubsets function to the dataset, then we save the summary.

model <- regsubsets(as.factor(class)~.,data=new,nvmax=15)
model.sum <- summary(model)

To select the best model, the cross-validated prediction error is used. They are Adjusted R2, Cp , and BIC.

Adj.R2 <- which.max(model.sum$adjr2)
CP <- which.min(model.sum$cp)
BIC <- which.min(model.sum$bic)
data.frame(Adj.R2, CP, BIC)

Here we get the results from the three metrics. Adjusted R2and Cp shows the same result, whereas the BIC show different. The best model from Adjusted R2is the model with a higher number. While Cp and BIC show the best model where the result is minimum.

dataframe

We also can plot the number of predictors to better see the result from regsubsets().

par(mfrow=c(2,2))
plot(model.sum$adjr2,xlab="Number of Variables",ylab="Adjusted RSq",type="l")
points(Adj.R2,model.sum$adjr2[Adj.R2], col="red",cex=2,pch=20)
plot(model.sum$cp,xlab="Number of Variables",ylab="Cp",type="l")
points(CP,model.sum$cp[CP],col="red",cex=2,pch=20)
plot(model.sum$bic,xlab="Number of Variables",ylab="BIC",type="l")
points(BIC,model.sum$bic[BIC],col="red",cex=2,pch=20)

The red dots show the number of predictors which produce the best model from each metric.

SMOTE red dot

These are the best twelve predictors. We can show them via the coefision function.

The best linear regression model can be achieved using these twelve predictors. It means that we can get better or the same regression result using just these twelve predictors instead of fifteen.

as.data.frame(coef(model, 12))
dataframe

Compare the linear regression model

Now let’s compare the linear regression model using all the predictors and using best subset selection. First, we do a linear regression using all the predictors.

lm.fit.before <- lm(class~., data=new)

lm.probs.before <- predict(lm.fit.before, type="response")

lm.pred.before <- rep(0, length(lm.probs.before))

lm.pred.before[lm.probs.before > 0.5] <- 1

table(lm.pred.before, new$class)
predict

Further, we can print the confusion matrix to get a better insight. Here we get 68% accuracy before the implementation of the best subset selection.

Other than accuracy, we can also look at the sensitivity and specificity measurement. We get the number that isn’t too far apart between the two. This happens because we have implemented SMOTE before.

lm.before <- confusionMatrix(data =  as.factor(lm.pred.before), reference = as.factor(new$class), positive="1")
lm.before
confusion Matrix

Then, we do a linear regression using twelve predictors from the best subset selection.

lm.fit.after <- lm(class~sex+age+education+currentSmoker+cigsPerDay+BPMeds+prevalentStroke+prevalentHyp+totChol+sysBP+heartRate+glucose, data=new)
lm.probs.after <- predict(lm.fit.after, type="response")
lm.pred.after <- rep(0, length(lm.probs.after))
lm.pred.after[lm.probs.after > 0.5] <- 1
table(lm.pred.after, new$class)
smote predict

The result is the accuracy also 68%, the same with all fifteen predictors. The same accuracy acquired using fewer predictors.

lm.after <- confusionMatrix(data =  as.factor(lm.pred.after), reference = as.factor(new$class), positive="1")
lm.after
confusion matrix

Short Author Bio

My name is Muhammad Arnaldo, a machine learning and data science enthusiast. Currently a master’s student of computer science in Indonesia.

The media shown in this article are not owned by Analytics Vidhya and is used at the Author’s discretion. 

M
Muhammad

My name is Muhammad Arnaldo, a machine learning and data science enthusiast. Currently a master’s student of computer science in Indonesia.

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