# How to calculate true positive, true negative, false positive, negative and postive with Bayes Classifer from scratch

I am working on implementing a Naive Bayes Classification algorithm. I have a method def prob_continous_value which is supposed to return the probability density function for an attribute given a class attribute. The problem requires classifying the following datasets:

Venue,color,Model,Category,Location,weight,Veriety,Material,Volume
1,6,4,4,4,1,1,1,6
2,5,4,4,4,2,6,1,1
1,6,2,1,4,1,4,2,4
1,6,2,1,4,1,2,1,2
2,6,5,5,5,2,2,1,2
1,5,4,4,4,1,6,2,2
1,3,3,3,3,1,6,2,2
1,5,2,1,1,1,2,1,2
1,4,4,4,1,1,5,3,6
1,4,4,4,4,1,6,4,6
2,5,4,4,4,2,4,4,1
2,4,3,3,3,2,1,1,1
Venue,color,Model,Category,Location,weight,Veriety,Material,Volume
2,6,4,4,4,2,2,1,1
1,2,4,4,4,1,6,2,6
1,5,4,4,4,1,2,1,6
2,4,4,4,4,2,6,1,4
1,4,4,4,4,1,2,2,2
2,4,3,3,3,2,1,1,1
1,5,2,1,4,1,6,2,6
1,2,3,3,3,1,2,1,6
2,6,4,4,4,2,3,1,1
1,4,4,4,4,1,2,1,6
1,5,4,4,4,1,2,1,4
1,4,5,5,5,1,6,2,4
2,5,4,4,4,2,3,1,1

The code for this is written like so:

from numpy.core.defchararray import count, index
import pandas as pd
import numpy as np
import math
from sklearn.decomposition import PCA
from numpy import linalg as LA
from sklearn.tree import DecisionTreeClassifier
from sklearn.naive_bayes import GaussianNB

test_set_Bayes = pd.read_csv("Assignment 2--Training set for Bayes.csv")
training_set_Bayes = pd.read_csv("Assignment 2--Test set for Bayes.csv")

def calculate_metrics(tp, tn, fn, fp, p, n):
# calculate the accuracy, error rate, sensitivity, specificity, and precision for the selected classifier in reference to the corresponding test set.
accuracy = tp + tn /(p+n)
error_rate = fp + fn /(p + n)
sensitivity = tp/ p
precision = tp/ (tp+fp)
specificity = tn/n

display_metrics(accuracy, error_rate, sensitivity, precision, specificity)

def display_metrics(accuracy, error_rate, sensitivity, precision, specificity):
print(f'Accuracy: {accuracy}, Error_rate:{error_rate}, Sensitivity:{sensitivity}, Precision:{precision}, specificity:{specificity}')

def prob_continous_value(A, v, classAttribute, dataset, x):
# calcuate the average for all values of A in dataset with class = x
a = dataset[dataset[classAttribute] == x][A].mean()
# calculate the standard deviation for all values A in dataset with class = x
stdev = 1
stdev = dataset[dataset[classAttribute] == x][A].std()
v = dataset[A].iloc[0]
if stdev == 0.0:
stdev = 0.00000000000001
return (1/(math.sqrt(2*math.pi)*stdev))*math.exp(-((v-a)*(v-a))/(2*stdev*stdev))

def BayesClassifier(training_set,test_set):
classAttribute = 'Volume'
products = []
max = -math.inf
classWithMaxValue = ""
for x in training_set[classAttribute].unique():
D = len(training_set[classAttribute].index)
d = len(training_set[training_set[classAttribute] == x].index)
pClassAttribute = d/D
print("********")
print(f'Step 1 calculate p({classAttribute}={x})={pClassAttribute}')
p = 0
probabilitiesProduct = 1
print("********")
print("Step 2 calculate product of probabilities")
for A, values in training_set.iteritems():
if not A == classAttribute:
v = training_set[A].iloc[0]
p = prob_continous_value(A, v, classAttribute, training_set, x)
print(f'p({A}={v}|{classAttribute}={x})={p}')
probabilitiesProduct *= p
print(f"probabilitiesProduct={probabilitiesProduct}")
print("********")
# products.append(probabilitiesProduct)
ptotal = pClassAttribute*probabilitiesProduct
print(f'p({classAttribute}={x}|x)={ptotal}')
if ptotal > max:
max = ptotal
classWithMaxValue = x
print(f"winner is {classAttribute}={classWithMaxValue}")

tp = len(test_set[test_set[classAttribute] == classWithMaxValue].index)
tn = len(test_set[test_set[classAttribute] != classWithMaxValue].index)
p  = len(test_set[classAttribute].index)
n  = len(test_set[classAttribute].index)
fp = len(test_set[classAttribute].index)
fn = len(test_set[classAttribute].index)

calculate_metrics(tp, tn, fn, fp, p, n)

# prompt user to select either ID3 or Bayes classifier.
selection = "Bayes" #= input("Please enter your selection for either ID3 or Bayes classification: ")

if(selection == "Bayes"):
BayesClassifier(training_set_Bayes,test_set_Bayes)

Expected:

A total displaying the following metrics accuracy, error rate, sensitivity, specificity, and precision for the selected classifier in reference to the corresponding test set.

Actual:

Accuracy: 56.42328767123288, Error_rate:365.5, Sensitivity:0.15342465753424658, Precision:0.1330166270783848, specificity:0.8465753424657534

The last iteration prints out:

Step 1 calculate p(Volume=5)=0.06818181818181818
********
Step 2 calculate product of probabilities
p(Venue=1|Volume=5)=0.5849089671682236
p(color=6|Volume=5)=0.00019621509920999636
p(Model=4|Volume=5)=0.04484934763369217
p(Category=4|Volume=5)=0.0
p(Location=4|Volume=5)=0.0
p(Weight=1.5|Volume=5)=0.46792717373457876
p(Variety=1|Volume=5)=0.0003021925272993778
p(Material=1.1|Volume=5)=0.31395152365343143
probabilitiesProduct=0.0
********
p(Volume=5|x)=0.0
winner is Volume=2

This block of code is where I need help

tp = len(test_set[test_set[classAttribute] == classWithMaxValue].index)
tn = len(test_set[test_set[classAttribute] != classWithMaxValue].index)
p  = len(test_set[classAttribute].index)
n  = len(test_set[classAttribute].index)
fp = len(test_set[classAttribute].index)
fn = len(test_set[classAttribute].index)

calculate_metrics(tp, tn, fn, fp, p, n)

If someone could explain how to determine these parameters

p  = len(test_set[classAttribute].index)
n  = len(test_set[classAttribute].index)
fp = len(test_set[classAttribute].index)
fn = len(test_set[classAttribute].index)

I would be greatly appreciated. Thank you.

There are some serious errors in your solution:

• Currently part of your evaluation (tp and tn) use the training set. It's crucial for the evaluation to use only the test set.
• The classification status doesn't work like this at all, see below.

I think that the main confusion is that you don't know/define which one is the positive class. I don't know your data and you don't show the class, but let's assume that the labels are 0 and 1 and that 0 is negative while 1 is positive:

• A True Positive (TP) is an instance for which the true label is 1 and the predicted label is 1.
• A False Positive (FP) is an instance for which the true label is 0 but the predicted label is 1.
• A False Negative (FN) is an instance for which the true label is 1 but the predicted label is 0.
• A True Negative (TN) is an instance for which the true label is 0 and the predicted label is 0.

So for instance the line for TP should be:

tp = len(test_set[test_set[classAttribute] == 1 and classWithMaxValue == 1].index)

Same thing for the other cases.

There might also be some other problems but I don't understand everything in the code (and don't have that much time to spend in it). In particular I have strong doubts about classWithMaxValue, is this a vector with a value for every instance? If not you have another serious problem there.

• Are you suggesting that I hard code a value in the metrics calculation? Nov 28, 2021 at 19:09
• @EvanGertis you can receive it as parameter if you want, but you must know which class is the positive and which class is the negative. Otherwise you can only use accuracy and error rate, they are the only two where the pos/neg distinction doesn't matter. Nov 28, 2021 at 19:17
• What do you mean by which class is the positive and which class is the negative? Nov 28, 2021 at 19:18
• @EvanGertis most classification evaluation measures are strictly for binary classification (i.e. 2 classes) and rely on the fact that one of the two is the positive class while the other is the negative class. The difference is important because the focus is the positive class. For example if one wants to predict a disease in the population, the positive class would be people who have the disease and the negative class those who don't. Precision, sensitivity and specificity (in your case) require defining the positive/negative class, they don't make any sense otherwise. Nov 28, 2021 at 23:44
• Another way to deal with this is to calculate the evaluation score considering both cases, where the first class is positive and when the other class is positive. Nov 28, 2021 at 23:49

I believe this will do it.

from numpy.core.defchararray import count, index
import pandas as pd
import numpy as np
import math
from sklearn.decomposition import PCA
from numpy import linalg as LA
from sklearn.tree import DecisionTreeClassifier
from sklearn.naive_bayes import GaussianNB

test_set_Bayes = pd.read_csv("Assignment 2--Training set for Bayes.csv")
training_set_Bayes = pd.read_csv("Assignment 2--Test set for Bayes.csv")

def calculate_metrics(training_set,test_set,classAttribute,classValue):
# calculate the accuracy, error rate, sensitivity, specificity, and precision for the selected classifier in reference to the corresponding test set.
tp = len(training_set[training_set[classAttribute] == classValue].index)
fp = len(test_set[test_set[classAttribute] == classValue].index)
tn = len(training_set[training_set[classAttribute] == classValue].index)
fn = len(test_set[test_set[classAttribute] != classValue].index)
p  = tp + fp
n  = tn + fn
print(f" \t      \t\t {classValue} \t not {classValue} \t \t TOTAL")
print(f" \t      \t\t  \t  \t \t ")
print(f" \t      \t {classValue} \t {tp}  \t {fp} \t {p}")
print(f" \t not  \t {classValue} \t {fn}  \t {tn} \t {n}")
print(f" \t total\t\t {tp+fn} \t {fn+tn}  \t {p+n} \t")

accuracy = tp + tn /(p+n)
error_rate = fp + fn /(p + n)
sensitivity = tp/ p
precision = tp/ (tp+fp)
specificity = tn/n

display_metrics(accuracy, error_rate, sensitivity, precision, specificity)

def display_metrics(accuracy, error_rate, sensitivity, precision, specificity):
print(f'Accuracy: {accuracy}, Error_rate:{error_rate}, Sensitivity:{sensitivity}, Precision:{precision}, specificity:{specificity}')

def prob_continous_value(A, v, classAttribute, dataset, x):
# calcuate the average for all values of A in dataset with class = x
a = dataset[dataset[classAttribute] == x][A].mean()
# calculate the standard deviation for all values A in dataset with class = x
stdev = 1
stdev = dataset[dataset[classAttribute] == x][A].std()
v = dataset[A].iloc[0]
if stdev == 0.0:
stdev = 0.00000000000001
return (1/(math.sqrt(2*math.pi)*stdev))*math.exp(-((v-a)*(v-a))/(2*stdev*stdev))

def BayesClassifier(training_set,test_set):
classAttribute = 'Volume'
products = []
max = -math.inf
classWithMaxValue = ""
for x in training_set[classAttribute].unique():
D = len(training_set[classAttribute].index)
d = len(training_set[training_set[classAttribute] == x].index)
pClassAttribute = d/D
print("********")
print(f'Step 1 calculate p({classAttribute}={x})={pClassAttribute}')
p = 0
probabilitiesProduct = 1
print("********")
print("Step 2 calculate product of probabilities")
for A, values in training_set.iteritems():
if not A == classAttribute:
v = training_set[A].iloc[0]
p = prob_continous_value(A, v, classAttribute, training_set, x)
print(f'p({A}={v}|{classAttribute}={x})={p}')
probabilitiesProduct *= p
print(f"probabilitiesProduct={probabilitiesProduct}")
print("********")
# products.append(probabilitiesProduct)
ptotal = pClassAttribute*probabilitiesProduct
print(f'p({classAttribute}={x}|x)={ptotal}')
if ptotal > max:
max = ptotal
classWithMaxValue = x
print(f"winner is {classAttribute}={classWithMaxValue}")

calculate_metrics(tp, tn, fn, fp, p, n)

# prompt user to select either ID3 or Bayes classifier.
selection = "Bayes" #= input("Please enter your selection for either ID3 or Bayes classification: ")

if(selection == "Bayes"):
BayesClassifier(training_set_Bayes,test_set_Bayes)
$$`$$