为什么我的 sigmoid 函数返回的值不在区间 ]0,1[ 中？

Question

I am implementing logistic regression in Python with numpy. I have generated the following data set:

# class 0:
# covariance matrix and mean
cov0 = np.array([[5,-4],[-4,4]])
mean0 = np.array([2.,3])
# number of data points
m0 = 1000

# class 1
# covariance matrix
cov1 = np.array([[5,-3],[-3,3]])
mean1 = np.array([1.,1])
# number of data points
m1 = 1000

# generate m gaussian distributed data points with
# mean and cov.
r0 = np.random.multivariate_normal(mean0, cov0, m0)
r1 = np.random.multivariate_normal(mean1, cov1, m1)

X = np.concatenate((r0,r1))

Now I have implemented the sigmoid function with the aid of the following methods:

def logistic_function(x):
    """ Applies the logistic function to x, element-wise. """
    return 1.0 / (1 + np.exp(-x))

def logistic_hypothesis(theta):
    return lambda x : logistic_function(np.dot(generateNewX(x), theta.T))

def generateNewX(x):
    x = np.insert(x, 0, 1, axis=1)
    return x 

After applying logistic regression, I found out that the best thetas are:

best_thetas = [-0.9673200946417307, -1.955812236119612, -5.060885703369424]

However, when I apply the logistic function with these thetas, then the output is numbers that are not inside the interval [0,1]

Example:

data = logistic_hypothesis(np.asarray(best_thetas))(X)
print(data

This gives the following result:

[2.67871968e-11 3.19858822e-09 3.77845881e-09 ... 5.61325410e-03
 2.19767618e-01 6.23288747e-01]

Can someone help me understand what has gone wrong with my implementation? I cannot understand why I am getting such big values. Isnt the sigmoid function supposed to only give results in the [0,1] interval?

Answer 1

It does, it's just in scientific notation .

'e' Exponent notation. Prints the number in scientific notation using the letter 'e' to indicate the exponent.

>>> a = [2.67871968e-11, 3.19858822e-09, 3.77845881e-09, 5.61325410e-03]
>>> [0 <= i <= 1 for i in a]
[True, True, True, True]