Python Machine Learning

Gaussian Naive Bayes

sepal length sepal width petal length petal width species
5.1 3.5 1.4 0.2 setosa
4.9 3.0 1.4 0.2 setosa
4.7 3.2 1.3 0.2 setosa
4.6 3.1 1.5 0.2 setosa
5.0 3.6 1.4 0.2 setosa
5.4 3.9 1.7 0.4 setosa
4.6 3.4 1.4 0.3 setosa
5.0 3.4 1.5 0.2 setosa
4.4 2.9 1.4 0.2 setosa
4.9 3.1 1.5 0.1 setosa
5.4 3.7 1.5 0.2 setosa
4.8 3.4 1.6 0.2 setosa
4.8 3.0 1.4 0.1 setosa
4.3 3.0 1.1 0.1 setosa
5.8 4.0 1.2 0.2 setosa
5.7 4.4 1.5 0.4 setosa
5.4 3.9 1.3 0.4 setosa
5.1 3.5 1.4 0.3 setosa
5.7 3.8 1.7 0.3 setosa
5.1 3.8 1.5 0.3 setosa
5.4 3.4 1.7 0.2 setosa
5.1 3.7 1.5 0.4 setosa
4.6 3.6 1.0 0.2 setosa
5.1 3.3 1.7 0.5 setosa
4.8 3.4 1.9 0.2 setosa
5.0 3.0 1.6 0.2 setosa
5.0 3.4 1.6 0.4 setosa
5.2 3.5 1.5 0.2 setosa
5.2 3.4 1.4 0.2 setosa
4.7 3.2 1.6 0.2 setosa
4.8 3.1 1.6 0.2 setosa
5.4 3.4 1.5 0.4 setosa
5.2 4.1 1.5 0.1 setosa
5.5 4.2 1.4 0.2 setosa
4.9 3.1 1.5 0.1 setosa
5.0 3.2 1.2 0.2 setosa
5.5 3.5 1.3 0.2 setosa
4.9 3.1 1.5 0.1 setosa
4.4 3.0 1.3 0.2 setosa
5.1 3.4 1.5 0.2 setosa
5.0 3.5 1.3 0.3 setosa
4.5 2.3 1.3 0.3 setosa
4.4 3.2 1.3 0.2 setosa
5.0 3.5 1.6 0.6 setosa
5.1 3.8 1.9 0.4 setosa
4.8 3.0 1.4 0.3 setosa
5.1 3.8 1.6 0.2 setosa
4.6 3.2 1.4 0.2 setosa
5.3 3.7 1.5 0.2 setosa
5.0 3.3 1.4 0.2 setosa
7.0 3.2 4.7 1.4 versicolor
6.4 3.2 4.5 1.5 versicolor
6.9 3.1 4.9 1.5 versicolor
5.5 2.3 4.0 1.3 versicolor
6.5 2.8 4.6 1.5 versicolor
5.7 2.8 4.5 1.3 versicolor
6.3 3.3 4.7 1.6 versicolor
4.9 2.4 3.3 1.0 versicolor
6.6 2.9 4.6 1.3 versicolor
5.2 2.7 3.9 1.4 versicolor
5.0 2.0 3.5 1.0 versicolor
5.9 3.0 4.2 1.5 versicolor
6.0 2.2 4.0 1.0 versicolor
6.1 2.9 4.7 1.4 versicolor
5.6 2.9 3.6 1.3 versicolor
6.7 3.1 4.4 1.4 versicolor
5.6 3.0 4.5 1.5 versicolor
5.8 2.7 4.1 1.0 versicolor
6.2 2.2 4.5 1.5 versicolor
5.6 2.5 3.9 1.1 versicolor
5.9 3.2 4.8 1.8 versicolor
6.1 2.8 4.0 1.3 versicolor
6.3 2.5 4.9 1.5 versicolor
6.1 2.8 4.7 1.2 versicolor
6.4 2.9 4.3 1.3 versicolor
6.6 3.0 4.4 1.4 versicolor
6.8 2.8 4.8 1.4 versicolor
6.7 3.0 5.0 1.7 versicolor
6.0 2.9 4.5 1.5 versicolor
5.7 2.6 3.5 1.0 versicolor
5.5 2.4 3.8 1.1 versicolor
5.5 2.4 3.7 1.0 versicolor
5.8 2.7 3.9 1.2 versicolor
6.0 2.7 5.1 1.6 versicolor
5.4 3.0 4.5 1.5 versicolor
6.0 3.4 4.5 1.6 versicolor
6.7 3.1 4.7 1.5 versicolor
6.3 2.3 4.4 1.3 versicolor
5.6 3.0 4.1 1.3 versicolor
5.5 2.5 4.0 1.3 versicolor
5.5 2.6 4.4 1.2 versicolor
6.1 3.0 4.6 1.4 versicolor
5.8 2.6 4.0 1.2 versicolor
5.0 2.3 3.3 1.0 versicolor
5.6 2.7 4.2 1.3 versicolor
5.7 3.0 4.2 1.2 versicolor
5.7 2.9 4.2 1.3 versicolor
6.2 2.9 4.3 1.3 versicolor
5.1 2.5 3.0 1.1 versicolor
5.7 2.8 4.1 1.3 versicolor
6.3 3.3 6.0 2.5 virginica
5.8 2.7 5.1 1.9 virginica
7.1 3.0 5.9 2.1 virginica
6.3 2.9 5.6 1.8 virginica
6.5 3.0 5.8 2.2 virginica
7.6 3.0 6.6 2.1 virginica
4.9 2.5 4.5 1.7 virginica
7.3 2.9 6.3 1.8 virginica
6.7 2.5 5.8 1.8 virginica
7.2 3.6 6.1 2.5 virginica
6.5 3.2 5.1 2.0 virginica
6.4 2.7 5.3 1.9 virginica
6.8 3.0 5.5 2.1 virginica
5.7 2.5 5.0 2.0 virginica
5.8 2.8 5.1 2.4 virginica
6.4 3.2 5.3 2.3 virginica
6.5 3.0 5.5 1.8 virginica
7.7 3.8 6.7 2.2 virginica
7.7 2.6 6.9 2.3 virginica
6.0 2.2 5.0 1.5 virginica
6.9 3.2 5.7 2.3 virginica
5.6 2.8 4.9 2.0 virginica
7.7 2.8 6.7 2.0 virginica
6.3 2.7 4.9 1.8 virginica
6.7 3.3 5.7 2.1 virginica
7.2 3.2 6.0 1.8 virginica
6.2 2.8 4.8 1.8 virginica
6.1 3.0 4.9 1.8 virginica
6.4 2.8 5.6 2.1 virginica
7.2 3.0 5.8 1.6 virginica
7.4 2.8 6.1 1.9 virginica
7.9 3.8 6.4 2.0 virginica
6.4 2.8 5.6 2.2 virginica
6.3 2.8 5.1 1.5 virginica
6.1 2.6 5.6 1.4 virginica
7.7 3.0 6.1 2.3 virginica
6.3 3.4 5.6 2.4 virginica
6.4 3.1 5.5 1.8 virginica
6.0 3.0 4.8 1.8 virginica
6.9 3.1 5.4 2.1 virginica
6.7 3.1 5.6 2.4 virginica
6.9 3.1 5.1 2.3 virginica
5.8 2.7 5.1 1.9 virginica
6.8 3.2 5.9 2.3 virginica
6.7 3.3 5.7 2.5 virginica
6.7 3.0 5.2 2.3 virginica
6.3 2.5 5.0 1.9 virginica
6.5 3.0 5.2 2.0 virginica
6.2 3.4 5.4 2.3 virginica
5.9 3.0 5.1 1.8 virginica
5.1, 3.5, 1.4, 0.2, setosa
4.9, 3.0, 1.4, 0.2, setosa
4.7, 3.2, 1.3, 0.2, setosa
4.6, 3.1, 1.5, 0.2, setosa
5.0, 3.6, 1.4, 0.2, setosa
5.4, 3.9, 1.7, 0.4, setosa
4.6, 3.4, 1.4, 0.3, setosa
5.0, 3.4, 1.5, 0.2, setosa
4.4, 2.9, 1.4, 0.2, setosa
4.9, 3.1, 1.5, 0.1, setosa
5.4, 3.7, 1.5, 0.2, setosa
4.8, 3.4, 1.6, 0.2, setosa
4.8, 3.0, 1.4, 0.1, setosa
4.3, 3.0, 1.1, 0.1, setosa
5.8, 4.0, 1.2, 0.2, setosa
5.7, 4.4, 1.5, 0.4, setosa
5.4, 3.9, 1.3, 0.4, setosa
5.1, 3.5, 1.4, 0.3, setosa
5.7, 3.8, 1.7, 0.3, setosa
5.1, 3.8, 1.5, 0.3, setosa
5.4, 3.4, 1.7, 0.2, setosa
5.1, 3.7, 1.5, 0.4, setosa
4.6, 3.6, 1.0, 0.2, setosa
5.1, 3.3, 1.7, 0.5, setosa
4.8, 3.4, 1.9, 0.2, setosa
5.0, 3.0, 1.6, 0.2, setosa
5.0, 3.4, 1.6, 0.4, setosa
5.2, 3.5, 1.5, 0.2, setosa
5.2, 3.4, 1.4, 0.2, setosa
4.7, 3.2, 1.6, 0.2, setosa
4.8, 3.1, 1.6, 0.2, setosa
5.4, 3.4, 1.5, 0.4, setosa
5.2, 4.1, 1.5, 0.1, setosa
5.5, 4.2, 1.4, 0.2, setosa
4.9, 3.1, 1.5, 0.1, setosa
5.0, 3.2, 1.2, 0.2, setosa
5.5, 3.5, 1.3, 0.2, setosa
4.9, 3.1, 1.5, 0.1, setosa
4.4, 3.0, 1.3, 0.2, setosa
5.1, 3.4, 1.5, 0.2, setosa
5.0, 3.5, 1.3, 0.3, setosa
4.5, 2.3, 1.3, 0.3, setosa
4.4, 3.2, 1.3, 0.2, setosa
5.0, 3.5, 1.6, 0.6, setosa
5.1, 3.8, 1.9, 0.4, setosa
4.8, 3.0, 1.4, 0.3, setosa
5.1, 3.8, 1.6, 0.2, setosa
4.6, 3.2, 1.4, 0.2, setosa
5.3, 3.7, 1.5, 0.2, setosa
5.0, 3.3, 1.4, 0.2, setosa
7.0, 3.2, 4.7, 1.4, versicolor
6.4, 3.2, 4.5, 1.5, versicolor
6.9, 3.1, 4.9, 1.5, versicolor
5.5, 2.3, 4.0, 1.3, versicolor
6.5, 2.8, 4.6, 1.5, versicolor
5.7, 2.8, 4.5, 1.3, versicolor
6.3, 3.3, 4.7, 1.6, versicolor
4.9, 2.4, 3.3, 1.0, versicolor
6.6, 2.9, 4.6, 1.3, versicolor
5.2, 2.7, 3.9, 1.4, versicolor
5.0, 2.0, 3.5, 1.0, versicolor
5.9, 3.0, 4.2, 1.5, versicolor
6.0, 2.2, 4.0, 1.0, versicolor
6.1, 2.9, 4.7, 1.4, versicolor
5.6, 2.9, 3.6, 1.3, versicolor
6.7, 3.1, 4.4, 1.4, versicolor
5.6, 3.0, 4.5, 1.5, versicolor
5.8, 2.7, 4.1, 1.0, versicolor
6.2, 2.2, 4.5, 1.5, versicolor
5.6, 2.5, 3.9, 1.1, versicolor
5.9, 3.2, 4.8, 1.8, versicolor
6.1, 2.8, 4.0, 1.3, versicolor
6.3, 2.5, 4.9, 1.5, versicolor
6.1, 2.8, 4.7, 1.2, versicolor
6.4, 2.9, 4.3, 1.3, versicolor
6.6, 3.0, 4.4, 1.4, versicolor
6.8, 2.8, 4.8, 1.4, versicolor
6.7, 3.0, 5.0, 1.7, versicolor
6.0, 2.9, 4.5, 1.5, versicolor
5.7, 2.6, 3.5, 1.0, versicolor
5.5, 2.4, 3.8, 1.1, versicolor
5.5, 2.4, 3.7, 1.0, versicolor
5.8, 2.7, 3.9, 1.2, versicolor
6.0, 2.7, 5.1, 1.6, versicolor
5.4, 3.0, 4.5, 1.5, versicolor
6.0, 3.4, 4.5, 1.6, versicolor
6.7, 3.1, 4.7, 1.5, versicolor
6.3, 2.3, 4.4, 1.3, versicolor
5.6, 3.0, 4.1, 1.3, versicolor
5.5, 2.5, 4.0, 1.3, versicolor
5.5, 2.6, 4.4, 1.2, versicolor
6.1, 3.0, 4.6, 1.4, versicolor
5.8, 2.6, 4.0, 1.2, versicolor
5.0, 2.3, 3.3, 1.0, versicolor
5.6, 2.7, 4.2, 1.3, versicolor
5.7, 3.0, 4.2, 1.2, versicolor
5.7, 2.9, 4.2, 1.3, versicolor
6.2, 2.9, 4.3, 1.3, versicolor
5.1, 2.5, 3.0, 1.1, versicolor
5.7, 2.8, 4.1, 1.3, versicolor
6.3, 3.3, 6.0, 2.5, virginica
5.8, 2.7, 5.1, 1.9, virginica
7.1, 3.0, 5.9, 2.1, virginica
6.3, 2.9, 5.6, 1.8, virginica
6.5, 3.0, 5.8, 2.2, virginica
7.6, 3.0, 6.6, 2.1, virginica
4.9, 2.5, 4.5, 1.7, virginica
7.3, 2.9, 6.3, 1.8, virginica
6.7, 2.5, 5.8, 1.8, virginica
7.2, 3.6, 6.1, 2.5, virginica
6.5, 3.2, 5.1, 2.0, virginica
6.4, 2.7, 5.3, 1.9, virginica
6.8, 3.0, 5.5, 2.1, virginica
5.7, 2.5, 5.0, 2.0, virginica
5.8, 2.8, 5.1, 2.4, virginica
6.4, 3.2, 5.3, 2.3, virginica
6.5, 3.0, 5.5, 1.8, virginica
7.7, 3.8, 6.7, 2.2, virginica
7.7, 2.6, 6.9, 2.3, virginica
6.0, 2.2, 5.0, 1.5, virginica
6.9, 3.2, 5.7, 2.3, virginica
5.6, 2.8, 4.9, 2.0, virginica
7.7, 2.8, 6.7, 2.0, virginica
6.3, 2.7, 4.9, 1.8, virginica
6.7, 3.3, 5.7, 2.1, virginica
7.2, 3.2, 6.0, 1.8, virginica
6.2, 2.8, 4.8, 1.8, virginica
6.1, 3.0, 4.9, 1.8, virginica
6.4, 2.8, 5.6, 2.1, virginica
7.2, 3.0, 5.8, 1.6, virginica
7.4, 2.8, 6.1, 1.9, virginica
7.9, 3.8, 6.4, 2.0, virginica
6.4, 2.8, 5.6, 2.2, virginica
6.3, 2.8, 5.1, 1.5, virginica
6.1, 2.6, 5.6, 1.4, virginica
7.7, 3.0, 6.1, 2.3, virginica
6.3, 3.4, 5.6, 2.4, virginica
6.4, 3.1, 5.5, 1.8, virginica
6.0, 3.0, 4.8, 1.8, virginica
6.9, 3.1, 5.4, 2.1, virginica
6.7, 3.1, 5.6, 2.4, virginica
6.9, 3.1, 5.1, 2.3, virginica
5.8, 2.7, 5.1, 1.9, virginica
6.8, 3.2, 5.9, 2.3, virginica
6.7, 3.3, 5.7, 2.5, virginica
6.7, 3.0, 5.2, 2.3, virginica
6.3, 2.5, 5.0, 1.9, virginica
6.5, 3.0, 5.2, 2.0, virginica
6.2, 3.4, 5.4, 2.3, virginica
5.9, 3.0, 5.1, 1.8, virginica

$$P(x_i|y)=\frac{1}{\sqrt{2\pi \sigma_y^2}}exp(-\frac{(x_i-\mu_y)^2}{2\sigma^2_y})$$

Iris-setosa
sepal length sepal width petal length petal width
Count 50
Mean 5.006 3.418 1.464 0.244
Variance 0.12424898 0.145179592 0.030106122 0.011493878
P(xi|Iris-setosa) 1.092247767 1.023057621 2.148024964 3.420590178
Iris-versicolor
sepal length sepal width petal length petal width
Count 50
Mean 5.936 2.77 4.26 1.326
Variance 0.266432653 0.098469388 0.220816327 0.039106122
P(xi|Iris-versicolor) 0.208211139 0.084936543 7.67727E-09 1.83893E-07
Iris-virginica
sepal length sepal width petal length petal width
Count 50
Mean 6.588 2.974 5.552 2.026
Variance 0.404342857 0.104004082 0.304587755 0.075432653
P(xi|Iris-virginica) 0.040593549 0.327130259 3.70614E-13 3.66254E-10

P(Iris-setosa|xi)=2.736783069

P(Iris-versicolor|xi)=8.32243E-18

P(Iris-virginica|xi)=6.00842E-25