The Naive Bayes Approach

The Bayesian Approach and Gaussian Processes

\(P(queen/diamond) = \dfrac{P(diamond/queen) * P(queen)}{P(diamond)}\)

$P(queen/diamond) = $

\(P(diamond/queen) = 1/4\)
\(P(queen) = 1/13\)
\(P(diamond) = 1/4\)

\(P(queen/diamond) = \dfrac{1/4 * 1/13}{1/4} = 1/13\)

import pandas as pd
df = pd.read_csv("Data/titanic.csv")
df.head()
PassengerId Name Pclass Sex Age SibSp Parch Ticket Fare Cabin Embarked Survived
0 1 Braund, Mr. Owen Harris 3 male 22.0 1 0 A/5 21171 7.2500 NaN S 0
1 2 Cumings, Mrs. John Bradley (Florence Briggs Th... 1 female 38.0 1 0 PC 17599 71.2833 C85 C 1
2 3 Heikkinen, Miss. Laina 3 female 26.0 0 0 STON/O2. 3101282 7.9250 NaN S 1
3 4 Futrelle, Mrs. Jacques Heath (Lily May Peel) 1 female 35.0 1 0 113803 53.1000 C123 S 1
4 5 Allen, Mr. William Henry 3 male 35.0 0 0 373450 8.0500 NaN S 0 
df.drop(['PassengerId','Name','SibSp','Parch','Ticket','Cabin','Embarked'],axis='columns',inplace=True)
df.head()
Pclass Sex Age Fare Survived
0 3 male 22.0 7.2500 0
1 1 female 38.0 71.2833 1
2 3 female 26.0 7.9250 1
3 1 female 35.0 53.1000 1
4 3 male 35.0 8.0500 0 
inputs = df.drop('Survived',axis='columns')
target = df.Survived
#inputs.Sex = inputs.Sex.map({'male': 1, 'female': 2})
dummies = pd.get_dummies(inputs.Sex)
dummies.head(3)
female male
0 0 1
1 1 0
2 1 0 
inputs = pd.concat([inputs,dummies],axis='columns')
inputs.head(3)
Pclass Sex Age Fare female male
0 3 male 22.0 7.2500 0 1
1 1 female 38.0 71.2833 1 0
2 3 female 26.0 7.9250 1 0

I am dropping male column as well because of dummy variable trap theory. One column is enough to repressent male vs female

inputs.drop(['Sex','male'],axis='columns',inplace=True)
inputs.head(3)
Pclass Age Fare female
0 3 22.0 7.2500 0
1 1 38.0 71.2833 1
2 3 26.0 7.9250 1 
inputs.columns[inputs.isna().any()]
Index(['Age'], dtype='object')
inputs.Age[:10]
0    22.0
1    38.0
2    26.0
3    35.0
4    35.0
5     NaN
6    54.0
7     2.0
8    27.0
9    14.0
Name: Age, dtype: float64
inputs.Age = inputs.Age.fillna(inputs.Age.mean())
inputs.head()
Pclass Age Fare female
0 3 22.0 7.2500 0
1 1 38.0 71.2833 1
2 3 26.0 7.9250 1
3 1 35.0 53.1000 1
4 3 35.0 8.0500 0 
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(inputs,target,test_size=0.3)
from sklearn.naive_bayes import GaussianNB
model = GaussianNB()
model.fit(X_train,y_train)
GaussianNB()
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model.score(X_test,y_test)
0.7910447761194029
X_test[0:10]
Pclass Age Fare female
509 3 26.000000 56.4958 0
325 1 36.000000 135.6333 1
248 1 37.000000 52.5542 0
391 3 21.000000 7.7958 0
411 3 29.699118 6.8583 0
688 3 18.000000 7.7958 0
183 2 1.000000 39.0000 0
14 3 14.000000 7.8542 1
763 1 36.000000 120.0000 1
383 1 35.000000 52.0000 1 
y_test[0:10]
509    1
325    1
248    1
391    1
411    0
688    0
183    1
14     0
763    1
383    1
Name: Survived, dtype: int64
model.predict(X_test[0:10])
array([0, 1, 0, 0, 0, 0, 0, 1, 1, 1])
model.predict_proba(X_test[:10])
array([[9.22826078e-01, 7.71739224e-02],
       [1.90547332e-04, 9.99809453e-01],
       [6.93224146e-01, 3.06775854e-01],
       [9.59335969e-01, 4.06640310e-02],
       [9.65380973e-01, 3.46190265e-02],
       [9.56271850e-01, 4.37281504e-02],
       [8.17245910e-01, 1.82754090e-01],
       [3.83233278e-01, 6.16766722e-01],
       [9.28107033e-04, 9.99071893e-01],
       [6.70466692e-02, 9.32953331e-01]])

Calculate the score using cross validation

from sklearn.model_selection import cross_val_score
cross_val_score(GaussianNB(),X_train, y_train, cv=5)
array([0.784     , 0.728     , 0.744     , 0.75806452, 0.80645161])
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