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Python Program to Implement the Naïve Bayesian Classifier for Pima Indians Diabetes problem
Exp. No. 5. Write a program to implement the Naïve Bayesian classifier for a sample training data set stored as a .CSV file. Compute the accuracy of the classifier, considering few test data sets.
Bayes’ Theorem is stated as:
Where,
P(h|D) is the probability of hypothesis h given the data D. This is called the posterior probability.
P(D|h) is the probability of data d given that the hypothesis h was true.
P(h) is the probability of hypothesis h being true. This is called the prior probability of h. P(D) is the probability of the data. This is called the prior probability of D
After calculating the posterior probability for a number of different hypotheses h, and is interested in finding the most probable hypothesis h ∈ H given the observed data D. Any such maximally probable hypothesis is called a maximum a posteriori (MAP) hypothesis.
Bayes theorem to calculate the posterior probability of each candidate hypothesis is hMAP is a MAP hypothesis provided.
(Ignoring P(D) since it is a constant)
Gaussian Naive Bayes
A Gaussian Naive Bayes algorithm is a special type of Naïve Bayes algorithm. It’s specifically used when the features have continuous values. It’s also assumed that all the features are following a Gaussian distribution i.e., normal distribution
Representation for Gaussian Naive Bayes
We calculate the probabilities for input values for each class using a frequency. With real- valued inputs, we can calculate the mean and standard deviation of input values (x) for each class to summarize the distribution.
This means that in addition to the probabilities for each class, we must also store the mean and standard deviations for each input variable for each class.
Gaussian Naive Bayes Model from Data
The probability density function for the normal distribution is defined by two parameters (mean and standard deviation) and calculating the mean and standard deviation values of each input variable (x) for each class value.
Examples:
The data set used in this program is the Pima Indians Diabetes problem.
This data set is comprised of 768 observations of medical details for Pima Indians patents. The records describe instantaneous measurements taken from the patient such as their age, the number of times pregnant and blood workup. All patients are women aged 21 or older. All attributes are numeric, and their units vary from attribute to attribute.
The attributes are Pregnancies, Glucose, BloodPressure, SkinThickness, Insulin, BMI, DiabeticPedigreeFunction, Age, Outcome
Each record has a class value that indicates whether the patient suffered an onset of diabetes within 5 years of when the measurements were taken (1) or not (0)
Sample Examples:
Examples | Pregnancies | Glucose | BloodPressure | SkinThickness | Insulin | BMI | Diabetic Pedigree Function | Age | Outcome |
1 | 6 | 148 | 72 | 35 | 33.6 | 0.627 | 50 | 1 | |
2 | 1 | 85 | 66 | 29 | 26.6 | 0.351 | 31 | ||
3 | 8 | 183 | 64 | 23.3 | 0.672 | 32 | 1 | ||
4 | 1 | 89 | 66 | 23 | 94 | 28.1 | 0.167 | 21 | |
5 | 137 | 40 | 35 | 168 | 43.1 | 2.288 | 33 | 1 | |
6 | 5 | 116 | 74 | 25.6 | 0.201 | 30 | |||
7 | 3 | 78 | 50 | 32 | 88 | 31 | 0.248 | 26 | 1 |
8 | 10 | 115 | 35.3 | 0.134 | 29 | ||||
9 | 2 | 197 | 70 | 45 | 543 | 30.5 | 0.158 | 53 | 1 |
10 | 8 | 125 | 96 | 0.232 | 54 | 1 |
Click here to download dataset
Python Program to Implement and Demonstrate Naïve Bayesian Classifier Machine Learning
import csv import random import math def loadcsv(filename): lines = csv.reader(open(filename, "r")); dataset = list(lines) for i in range(len(dataset)): #converting strings into numbers for processing dataset[i] = [float(x) for x in dataset[i]] return dataset def splitdataset(dataset, splitratio): #67% training size trainsize = int(len(dataset) * splitratio); trainset = [] copy = list(dataset); while len(trainset) < trainsize: #generate indices for the dataset list randomly to pick ele for training data index = random.randrange(len(copy)); trainset.append(copy.pop(index)) return [trainset, copy] def separatebyclass(dataset): separated = {} #dictionary of classes 1 and 0 #creates a dictionary of classes 1 and 0 where the values are #the instances belonging to each class for i in range(len(dataset)): vector = dataset[i] if (vector[-1] not in separated): separated[vector[-1]] = [] separated[vector[-1]].append(vector) return separated def mean(numbers): return sum(numbers)/float(len(numbers)) def stdev(numbers): avg = mean(numbers) variance = sum([pow(x-avg,2) for x in numbers])/float(len(numbers)-1) return math.sqrt(variance) def summarize(dataset): #creates a dictionary of classes summaries = [(mean(attribute), stdev(attribute)) for attribute in zip(*dataset)]; del summaries[-1] #excluding labels +ve or -ve return summaries def summarizebyclass(dataset): separated = separatebyclass(dataset); #print(separated) summaries = {} for classvalue, instances in separated.items(): #for key,value in dic.items() #summaries is a dic of tuples(mean,std) for each class value summaries[classvalue] = summarize(instances) #summarize is used to cal to mean and std return summaries def calculateprobability(x, mean, stdev): exponent = math.exp(-(math.pow(x-mean,2)/(2*math.pow(stdev,2)))) return (1 / (math.sqrt(2*math.pi) * stdev)) * exponent def calculateclassprobabilities(summaries, inputvector): probabilities = {} # probabilities contains the all prob of all class of test data for classvalue, classsummaries in summaries.items():#class and attribute information as mean and sd probabilities[classvalue] = 1 for i in range(len(classsummaries)): mean, stdev = classsummaries[i] #take mean and sd of every attribute for class 0 and 1 seperaely x = inputvector[i] #testvector's first attribute probabilities[classvalue] *= calculateprobability(x, mean, stdev);#use normal dist return probabilities def predict(summaries, inputvector): #training and test data is passed probabilities = calculateclassprobabilities(summaries, inputvector) bestLabel, bestProb = None, -1 for classvalue, probability in probabilities.items():#assigns that class which has he highest prob if bestLabel is None or probability > bestProb: bestProb = probability bestLabel = classvalue return bestLabel def getpredictions(summaries, testset): predictions = [] for i in range(len(testset)): result = predict(summaries, testset[i]) predictions.append(result) return predictions def getaccuracy(testset, predictions): correct = 0 for i in range(len(testset)): if testset[i][-1] == predictions[i]: correct += 1 return (correct/float(len(testset))) * 100.0 def main(): filename = 'naivedata.csv' splitratio = 0.67 dataset = loadcsv(filename); trainingset, testset = splitdataset(dataset, splitratio) print('Split {0} rows into train={1} and test={2} rows'.format(len(dataset), len(trainingset), len(testset))) # prepare model summaries = summarizebyclass(trainingset); #print(summaries) # test model predictions = getpredictions(summaries, testset) #find the predictions of test data with the training data accuracy = getaccuracy(testset, predictions) print('Accuracy of the classifier is : {0}%'.format(accuracy)) main()
Output
Split 768 rows into train=514 and test=254
Rows Accuracy of the classifier is : 71.65354330708661%
Summary
This tutorial discusses how to Implement and demonstrate the Naïve Bayesian Classifier in Python. If you like the tutorial share it with your friends. Like the Facebook page for regular updates and YouTube channel for video tutorials.
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