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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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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
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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
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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
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
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8 Ways to Improve Accuracy of Machine Learning 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
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Model Deployment in Android Model Deployment in Iphone

Introduction to Bayes Theorem for Data Science

s
shipra_saxena 06 Apr, 2021
5 min read

Objective

  • Bayes theorem gives the probability of an event based on the prior knowledge of conditions.
  • Understand the basics of probability, conditional probability, and Bayes theorem.

 

Introduction

Naive Bayes is a probabilistic algorithm. In this case, we try to calculate the probability of each class for each observation. For example, if we have two classes C1 and C2. For every observation naive Bayes calculates the probability that the observation belongs to class 1 and the probability that the observation belongs to class 2. Whichever probability is higher is selected as the class of that observation.

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.

 

To understand the concept of Naive Bayes you must be familiar with the following concepts.

  • Probability
  • Conditional Probability
  • Bayes Theorem

We will see all these concepts in this article.

 

Probability

Probability measures the likelihood that an event will occur or the chances of the occurrence of an event. This value lies between 0 and 1.

If the probability of an event is closer to 0 then we can say, the chances of occurrence of this event are very low. On the other hand, if the probability of occurrence of an event is closer to 1 then we can say, the chances of occurrence of this event are very high.

The probability of any event is calculated in the following manner

Bayes theorem Probability

We consider the number of favorable outcomes of the event and divide it by the total number of outcomes which is often called the sample space.

Let’s take a few examples, suppose we want to calculate the probability of a head when we toss a coin.

bayes theorem probability example

In this case, we have two possible outcomes Head and Tail. Also, we have the number of the favorable outcome as one. So here, the probability is 1/2 i.e 0.5. This means the probability of getting  head when we toss an unbiased coin is 0.5

Let’s take another example. Suppose we want the probability of getting an even number on the roll of a dice. So in this case our event is to get an even number.

probability die roll

On a roll of dice, we can get any number from 1 to 6. So our total number of outcomes is 6. In this case, a favorable outcome can be 2,4 or 6 i.e total favorable outcomes can be 3. Hence the probability of getting an even number will be 3/6 which again comes out to be 0.5.

 

Conditional Probability

Let’s look at another concept, conditional probability. It calculates the probability of an event for a given condition. Consider an example where we roll two dice and we want to calculate the probability that the second dice will get a  value of 2 given that the sum of the numbers on both dices should be less than or equal to 5.

In this case, getting 2 on the second dice is an event and getting the sum of less than or equal to 5 is the condition. The conditional probability can be represented in the following manner.

Conditional Probability bayes

Here we calculate the probability of occurrence of an event (D2=2) for a given condition (D1+ D2<=5).

If we break down this problem, we have two events. Event 1 is getting the sum of less than or equal to 5 and Event 2 is getting value 2 on the second dice. Our favorable outcome will be the intersection of the two events. The orange part in the below image represents the probability of getting event 2 when the condition of event 1 is satisfied.

conditional probability bayes theorem

So we can write the formula of conditional probability as follows.

conditional probability

 

The probability of E1 intersection E2 divided by the probability of E1.

Let’s use this formula in our example. Here we have all possible outcomes that we can get by throwing two dices.

E1 intersection E2 divided by the probability of E1 bayes theorem

Out of these 36 outcomes, what is the probability of getting a sum of less than equal to 5? We have 10 numbers as shown below which have sum less than equal to 5. So the probability of event E1 can be written as 10/36.

E1 can be written

Now let’s find out the probability of E1 intersection E2. So out of those 10 cases, what are the numbers where we have 2 on the second dice? We have only 3 cases that satisfy both conditions. As shown below

bayes theorem both condition

 

So the probability of E1 intersection E2 is 3/36

 

Bayes Theorem

So we have the following formula for conditional probability E1|E2

probability

Similarly, we can have the probability of E2|E1 as follows

probability of E2|E1 bayes

Now Probability of E1 intersection E2 will be the same in both cases so we can write it as

same in both cases

 

Now we can replace the value in the first equation. first equation

The final equation comes out to be as shown in the image below.

 

bayes theorem explanation

 

This is our Bayes theorem. Where we have Likelihood, Prior, and the Evidence

EndNotes

This is all about probability, conditional probability, and Bayes theorem in this article.

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

If you have any queries, let me know in the comment section!

bayes theorem
s
shipra_saxena 06 Apr, 2021

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