Article Information

• Posted By : Raji Reddy A
• Posted On : Feb 05, 2021
• Views : 416
• Category : Predictive and Prescriptive Modeling » Machine Learning
• Description : Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics

Overview

•                                                                    Bayesian Analysis
  
  Probability is a numerical description of how likely an event is to occur after many repeated trials.

  If two or more events occurring simultaneously and If they are independent

  P(outcome1 AND outcome2) =  P(outcome1) * P(outcome2)

  If two or more events occur simultaneously and If they are dependent, P(outcome 2 I outcome 1) refers to the conditional probability of outcome 2 occurring given outcome 1 has already occurred.

  P(outcome 1 AND outcome 2) = P(outcome1) * P(outcome 2 | outcome 1)

  Probability of either one event or the other occurring and If they are independent P(outcome 1 or outcome 2) = P(outcome 1) + P(outcome 2)

  Probability of either one event or the other occurring (both happen simultaneously) and If they are dependent

  P(outcome 1 or outcome 2) = P(outcome 1) + P(outcome 2) - P(outcome1 AND outcome2)
  
  
                  
                 
  
  

  P(Red) = ?

  P(Red) = Total Red/Total Items = 60/180

   

  P(Necklace) = ?

  P(Necklace) = Total Necklace/Total Items = 60/180

   

  P(Red Necklace) = ?

  P(Red Necklace) = Total Red Necklace/Total Items = 30/180

   

  Calculating Conditional Probability
  
              
  

   Bayesian Analysis in Python:

  Consider Carseats data on which we apply the above classification algorithms to predict the sales of carseats

  Import the libraries and load the dataset with pandas
  
  

  import pandas as pd
  import graphviz
  from subprocess import call
  

   

  from sklearn.model_selection import train_test_split
  from sklearn.naive_bayes import GaussianNB
  
  Path = "D:\\DSA Course\\Datasets\\R Inbuilt Datasets\\Carseats.csv"
  data = pd.read_csv(Path)
  

  Replace all the values above 4  in the Sales column to ‘Yes’ and below ‘No’ as this will be our target column to predict. Then separate the features and label columns, and factorize categorical columns

  data.loc[data.Sales > 4, 'Sale'] = 'Yes'
  data.loc[data.Sales < 4, 'Sale'] = 'No'
  
  class_names = data['Sale']
  data = data.loc[:,data.columns != 'Sales']
  data['Sale'],_ = pd.factorize(data['Sale'])
  data['ShelveLoc'],_ = pd.factorize(data['ShelveLoc'])
  data['Urban'],_= pd.factorize(data['Urban'])
  data['US'],_ = pd.factorize(data['US'])
  data.info()
  
  X = data.loc[:,data.columns != 'Sale']
  Y = data.Sale
  
  feature_names = X.columns
  

  X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.3, random_state=0)
  
  nb = GaussianNB()
  # train the model
  nb.fit(X_train, y_train)
  # make class predictions for X_test
  y_pred_class = nb.predict(X_test)
  # calculate accuracy of class predictions
  NB_Accuracy = metrics.accuracy_score(y_test, y_pred_class)
  # print the confusion matrix
  metrics.confusion_matrix(y_test, y_pred_class)
  print('NB_Accuracy: {:.2f}'.format(NB_Accuracy))
  

  Output:
  
  

  NB_Accuracy: 0.93

  For code file refer here:https://www.cluzters.ai/vault/274/1029/classification-algorithms-code