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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
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

Data Scientist’s Guide to Logistic regression

Shipra Saxena
Shipra Saxena Last Updated : 05 Mar, 2021
6 min read

Objective

  • Why the Linear regression model will not work for classification problems.
  • How Logistic regression model is derived from a simple linear model.

 

Introduction

While working with the machine learning models,  one question that generally comes into our mind for a given problem whether I should use the regression model or the classification model.

Regression and Classification both are supervised learning algorithms. In regression, the predicted values are of continuous nature and in classification predicted values are of a categorical type.

Note: If you are more interested in learning concepts in an Audio-Visual format, We have this entire article explained in the video below. If not, you may continue reading.

In simple terms, If you have a dataset with marks of a student in five subjects and you have to predict the marks in another subject it will be a regression problem. On the other hand, if I ask you to predict whether a student is pass or fail based on the marks it will be a classification problem.

Now let’s talk about Logistic regression. What do you think of what kind of algorithm is Logistic regression? A classification or a regression one.

logo

To our surprise, Logistic regression is actually a classification algorithm. Now you must be wondering if it is a classification algorithm why it is called regression.

Let’s consider a small example, here is a plot on the x-axis Age of the persons, and the y-axis shows they have a smartphone. It is a classification problem where given the age of a person and we have to predict if he posses a smartphone or not.

binary regression

In such a classification problem,  can we use linear regression?

 

Issues with Linear regression

To solve the above prediction problem, let’s first use a Linear model. On the plot, we can draw a line that separates the data points into two groups. with a threshold Age value. All the data points below that threshold will be classified as 0 i.e those who do not have smartphones. Similarly, all the observations above the threshold will be classified as 1 which means these people have smartphones as shown in the image below.

Issues with Linear regression

Don’t you think it is successfully working? let me discuss some scenarios.

Case 1

Suppose we got a new data point on the extreme right in the plot, suddenly you see the slope of the line changes. Now we have to inadvertently change the threshold of our model. Hence, this is the first issue we have with linear regression, our threshold of Age can not be changed in a predicting algorithm.

Logistic Regression Case 1

Case 2

The other issue with Linear regression is when you extend this line it will give you values above 1 and below 0. In our classification problem, we do not know what the values greater than one and below 0 represents. so it is not the natural extension of the linear model. Further, it makes the model interpretation at extremes a challenge.

 

logistic regression Case 2

 

From Linear to logistic regression

Here the Logistic regression comes in. let’s try and build a new model known as Logistic regression. Suppose the equation of this linear line is From Linear to logistic regression formula

Now we want a function Q( Z) that transforms the values between 0 and 1 as shown in the following image. This is the time when a sigmoid function or logit function comes in handy.

From Linear to logistic regression graph

This sigmoid function transforms the linear line into a curve. This will constraint the values between 0 and 1. Now it doesn’t matter how many new points I add to each extreme it will not affect my model.

The other important aspect is, for each observation model will give a continuous value between 0 and 1. This continuous value is the prediction probability of that data point. If the prediction probability is near 1 then the data point will be classified as 1 else 0.

 

The cost function for Logistic regression

For linear regression, the cost function is mostly we use Mean squared error represented as the difference y_predicted and y_actual iterated overall data points, and then you do a square and take the average. It is a convex function as shown below. This cost function can be optimized easily using gradient descent.

The cost function for Logistic regression

Whereas, If we use the same cost function for the Logistic regression is a non-linear function, it will have a non-convex plot. It will create unnecessary complications if use gradient descent for model optimization.

non-convex

Hence, we need a different cost function for our new model. Here comes the log loss in the picture.  As you can see, we have replaced the probability in the log loss equation with y_hat

log loss

In the first case when the class is 1 and the probability is close to 1, the left side of the equation becomes active and the right part vanishes. You will notice in the plot below as the predicted probability moves towards 0 the cost increases sharply.

Logistic regression cost function

Similarly, when the actual class is 0 and the predicted probability is 0, the right side becomes active and the left side vanishes. Increasing the cost of the wrong predictions. Later, these two parts will be added.

actual class is 0

To understand log loss in detail, I will suggest you go through this article Binary Cross Entropy/Log Loss for Binary Classification

 

Optimize the model

Once we have our model and the appropriate cost function handy, we can use “The Gradient Descent Algorithm” to optimize our model parameters. As we do in the case of linear regression.

Although gradient descent is a separate topic still I will quickly explain it as shown in the following image. We have the cost function J and the parameters B and b. Now we can differentiate the cost function J with parameters B and b. Once we have our values of GB and Gb, we can update our parameters.

Optimize the model

The whole process will go iteratively until we get our best parameters.

To understand how gradient descent algorithms work please go through the following article-

Understanding the Gradient Descent Algorithm

 

Endnote

To summarise, in this article we learn why linear regression doesn’t work in the case of classification problems and the issues. Also, how the logistic regression is different from linear regression and it resolves the challenges of the linear models.

If you are looking to kick start your Data Science Journey and want every topic under one roof, your search stops here. Check out Analytics Vidhya’s Certified AI & ML BlackBelt Plus Program

Let us know if you have any queries in the comments below.

 

Shipra Saxena
Shipra Saxena

Shipra is a Data Science enthusiast, Exploring Machine learning and Deep learning algorithms. She is also interested in Big data technologies. She believes learning is a continuous process so keep moving.

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