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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
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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
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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
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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
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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
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Logistic Regression- Supervised Learning Algorithm for Classification

Sarvagya
Sarvagya Last Updated : 23 May, 2021
5 min read

This article was published as a part of the Data Science Blogathon

Introduction

This article will talk about Logistic Regression, a method for classifying the data in Machine Learning. Logistic regression is generally used where we have to classify the data into two or more classes. One is binary and the other is multi-class logistic regression. As the name suggests, the binary class has 2 classes that are Yes/No, True/False, 0/1, etc. In multi-class classification, there are more than 2 classes for classifying data. But, before we go let us first define the logistic regression:

” Logistic Regression is a classification algorithm for categorical variables like Yes/No, True/False, 0/1, etc.” 

How is it different from linear regression?

You may have also heard about linear regression. Let me tell you that there is a big difference between both linear regression and logistic regression. Linear regression is used for generating continuous values like the price of the house, income, population, etc. In logistic regression, we generally compute the probability which lies between the interval 0 and 1 (inclusive of both). Then probability can be used to classify the data. For example, if the computed probability comes out to be greater than 0.5, then the data belonged to class A and otherwise, for less than 0.5, the data belonged to class B.

But my question to you is that can we still use linear regression for classification? My answer will be “Yes! why not? But sure it is an absurd idea.” My reason will be that you can assign a threshold value for linear regression, that is if the predicted value is greater than the threshold value, it belonged to class A otherwise class B. But it will give out a large error and a poor model with low accuracy, which we really don’t want. Right? I would suggest you use classification algorithms only.

Now let’s look at the graph of linear regression shown below

Logistic regression algorithm difference

(Courtesy: https://www.ablebits.com/)

The graph is a straight line passing through some points since we always avoid underfitting and overfitting curves.

Now let’s have a look at the logistic regression graph:

test passed

The graph is a curved line instead of the straight line, unlike linear regression.

This is a major difference between the two types of regression that we just talked about. So my next question is.

Why do we have a curved line for logistic regression instead of a straight line?

To answer this question, we will walk through linear regression a bit and from there we will arrive at the logistic regression curve. Is that okay? Let’s begin.

Equation for a linear classifier in logistic regression

For now, the equation for the linear classifier is:

hx

We will now define the values of the variable weights :

theta_0=-1 and theta=0.1

So our equation looks like this and the following is the graph representing the equation in the 2-D plane:

h2

Above is an equation of a line for the given equation:

h(x)=-1 + 0.1x

The value of function h(x) when x=13 is:

h(13)=-1+ (0.1)*(13)= 0.3

As described earlier in this article, I am defining the threshold to be 0.5 which is any value of h greater than (equal to) 0.5 will be labeled as 1 and otherwise 0.  We can define it as follows in the form of step function:

ycap

Now according to this h has a value of 0.3, hence the value of y_hat= 0 as per the function defined above.

Now one thing you must note here that every value greater than 0.5, suppose I say the value of ‘h’ is 1000 for some value of x, then it will be labeled as 1 only, there is no difference between the value 1 and 1000 as both are classified as 1 only. Is it right? Can we accept this solution? Well, No! I would not accept it!!!

One more thing, what is the probability that the h has a value of 0.3? All these questions are left unanswered. For these reasons, data scientists do not prefer to use linear regression for classification purposes.

Before we move on I want to show you how the y_hat function behaves graphically:

cappning value Logistic Regression Algorithm

It will be better if we have a smoother curve instead of on given above. Let’s see:

smooth curve

The above curve is known as the Sigmoid function which we will be using throughout this article. Here I will introduce the Sigmoid function.

What is Sigmoid Function?

The sigmoid function is represented by the symbol sigma. Its graphical behavior has been described in the above figure. The mathematical equation for the sigmoid function is described as follows:

 

Logistic Regression Algorithm ycap

The sigmoid function gives out the probability of data belonging to a particular class which lies in the interval [0,1]. It accepts the dot product of transpose of theta and feature vector X as the parameter. The resulting value is the probability.

Hence when P(Y=1 | X)= sigmoid(theta*X)

P(Y=0 | X) =1- sigmoid(theta*X)

Also, I want you to note the behavior of the sigmoid function:

  • When theta(transpose)*X becomes very bigger the value of the sigmoid becomes equal to 1
  • When theta(transpose)*X becomes very small  the value of the sigmoid becomes equal to 0

Applications of Logistic Regression

In this section, I would like to discuss some of the applications of logistic regression.

1. Predicting a probability of a person having a heart attack

2. Predicting a customer’s propensity to purchase a product or halt a subscription.

3. Predicting the probability of failure of a given process or product.

Before I end this article, I just want to recap when you should use logistic regression:

  • When your data is binary: 0/1, True/False, Yes/No
  • When you need probabilistic results
  • When your data is linearly separable
  • When you need to understand the impact of the feature.

Many other classification algorithms are widely used other than logistic regression like kNN, decision trees, random forest, and clustering algorithms like k-means clustering. But logistic regression is a widely used algorithm and also easy to implement.

So this was all about the logistic regression algorithm for a beginner. We have discussed everything you should know about the theory of Logistic Regression. Hope you enjoyed my article!

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

Sarvagya
Sarvagya

Hi, I'm Sarvagya Agrawal, Software Engineer, with a strong passion for utilizing technology to drive positive change in society. I believe that technology is not just a skill, but an art form that can be leveraged to transform the world.
My primary focus lies in machine learning and web development, with strong programming skills in Python. I have worked on innovative projects, including developing an AI model to calculate cardiovascular risk factors from OCTA scans using computer vision algorithms and creating an AI-based web application for calculating financial risk based on an individual's spending trends.

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Responses From Readers

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Anshul Saini
Anshul Saini

Hello Sarvagya, Hope you are doing well. I was having some trouble with logistic regression and luckily I found your article. It is very well explained and really liked it. All the information was collectively present on one page. I still have some doubts and I was wondering if you could help me out. 1) Is there any derivation for the log loss function (from where did this function came)? 2) How does gradient descent work in logistic regression? Like in linear regression our y was (y = b0 + b1x) and what we did there was randomly select a value for b1 and then kept updating it until we get a minimum MSE or the global minima. Here, in Logistic regression, our (y = sigmoid function), just wanted to know how gradient descent will work here? In linear regression we used a random value for b1, what will be that random value in logistic regression? 3) After reading tons of articles I also got to know that logistic regression uses MLE(Maximum likelihood estimation). I couldn't figure out where exactly we use MLE in this algorithm I have read almost each and every article on google regarding these 3 topics but I couldn't get the perfect solution for this. It would be really helpful If you take out some time to help me out. Thanks Anshul Saini

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