机器学习——朴素贝叶斯方程
2022-05-16 本文已影响0人
sarashang
What is Naive Bayes model？
Protocol
Practical operation
What is Naive Bayes model？
给定历史训练数据集，由经验计算得到某类别的先验概率P（类别），又可以计算在某特征下属于该类别的后验概率P（类别|特征）。
优点：1. 算法逻辑简单，易于实现；2. 分类过程时空开销小
缺点：1. 由于假设模型属性之间相互独立，但在实际生活中并不成立，特别是属性/特征之间相关性较大时，分类效果不好。
原理 Principle
朴素贝叶斯算法的前提条件是假设各个特征之间相互独立。
训练数据集
先验概率分布
条件概率分布
联合概率分布
公式 Formula
Protocol
Naive Bayes Model-Protocol.png [1]
Practical operation [4]
# Example of Naive Bayes implemented from Scratch in Python
import csv
import random
import math
def loadCsv(filename):
lines = csv.reader(open(filename, "rb"))
dataset = list(lines)
for i in range(len(dataset)):
dataset[i] = [float(x) for x in dataset[i]]
return dataset
def splitDataset(dataset, splitRatio):
trainSize = int(len(dataset) * splitRatio)
trainSet = []
copy = list(dataset)
while len(trainSet) < trainSize:
index = random.randrange(len(copy))
trainSet.append(copy.pop(index))
return [trainSet, copy]
def separateByClass(dataset):
separated = {}
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):
summaries = [(mean(attribute), stdev(attribute)) for attribute in zip(*dataset)]
del summaries[-1]
return summaries
def summarizeByClass(dataset):
separated = separateByClass(dataset)
summaries = {}
for classValue, instances in separated.iteritems():
summaries[classValue] = summarize(instances)
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 = {}
for classValue, classSummaries in summaries.iteritems():
probabilities[classValue] = 1
for i in range(len(classSummaries)):
mean, stdev = classSummaries[i]
x = inputVector[i]
probabilities[classValue] *= calculateProbability(x, mean, stdev)
return probabilities
def predict(summaries, inputVector):
probabilities = calculateClassProbabilities(summaries, inputVector)
bestLabel, bestProb = None, -1
for classValue, probability in probabilities.iteritems():
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 = 'pima-indians-diabetes.data.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)
# test model
predictions = getPredictions(summaries, testSet)
accuracy = getAccuracy(testSet, predictions)
print('Accuracy: {0}%').format(accuracy)
main()
参考资料：
