Find weights and bias in neural nets in python.

fig1: Weights and Bias

Given the combination of two new perceptrons as 

w1*0.4 + w2*0.6 + b. 



Which of the following values for the weights and the bias 

would result in the final probability of the point to be 

0.88 of being blue(positive region, above the line)?

 
A.       w1=2, w2=6, bias=2
B.       w1=3, w2=5, bias=-2.2
C.       w1=5, w2=4, bias=-3
 
weights=[(2,6),(3,5),(5,4)]
bias=[2,-2.2,-3]
score1 = weights[0][0] * 0.4 + weights[0][1] * 0.6 + bias[0]
score2 = weights[1][0] * 0.4 + weights[1][1] * 0.6 + bias[1]
score3 = weights[2][0] * 0.4 + weights[2][1] * 0.6 + bias[2]


def find_weights_bias():

#result of the probability function given, 0.88 with sigmoid activation 1/(1+e-score)score is 2

#Find w1, w2 and b, for score=w1*0.4+w2*0.6+b



    weights=[(2,6),(3,5),(5,4)]

    bias=[2,-2.2,-3]

    score1 = weights[0][0] * 0.4 + weights[0][1] * 0.6 + bias[0]

    score2 = weights[1][0] * 0.4 + weights[1][1] * 0.6 + bias[1]

    score3 = weights[2][0] * 0.4 + weights[2][1] * 0.6 + bias[2]

    print(score1,score2,score3)

    #condensed form

    score1, score2, score3 = (w1 * 0.4 + w2 * 0.6 + b for (w1, w2), b in zip(weights, bias))

    print(score1,score2,score3)


    if score1 == 2.0:

        print ("First choice is correct!")

    if score2 == 2.0:

        print ("Second choice is correct!")

    elif score3 == 2.0:

        print ("Third choice is correct!")

    return score1,score2,score3

find_weights_bias()

How to use sigmoid activation function in python in basic neural nets.

The sigmoid function is defined as sigmoid(x) = 1/(1+e-x). If the score is defined by 4x1 + 5x2 - 9 = score, then which of the following points has exactly a 50% probability of being blue or red? (Choose all that are correct.)

1.  (1,1)
2. (2,4)
3.  (5,-5)
4.  (-4,5)

First, we construct a linear function to add the weights and bias term. Then, we use activation function to return the scores to probabilities. Sigmoid function returns values between 0 and 1.

fig1: sigmoid function

from math import e
#Equation: 4x1+5x2-9=score
#weights are 4,5 and bias is -9, find the sigmoid(x) = 1/(1+e-x).

features=[(1,1),(2,4),(5,-5),(-4,5)]
def linear_func(features):
    for x in features:
        score= 4*x[0]+ 5*x[1]-9
        y = 1 / (1 + e - score)
        print("X",x,score,y)
 #call the function
linear_func(features)