Question

Suppose your training set for two-class classification in one dimension contains three sample points: x₁ = 3 with label y₁ = 1, x₂ = 1 with label y₂ = 1, and x₃ = -1 with label y₃ = -1. What are the values of b and w given by a logistic regression model g(b + wx), where g is the sigmoid function?

(a) w = 1, b = 2
(b) w = 0, b = 1
(c) w = 1, b = 0
(d) w = 2, b = 1

Answer 1

To find the values of b and w given by a logistic regression model, we use the given sample points and labels, and substitute them into the logistic regression equation with the sigmoid function. The correct values for b and w are b = 1 and w = 0.

Step-by-step explanation:

To find the values of b and w given by a logistic regression model, we need to use the given sample points and their labels. The sigmoid function, denoted as g, is defined as g(z) = 1 / (1 + e^-z). We can use these formulas to solve for b and w.

First, we use the logistic regression model equation: g(b + wx). We can substitute the given sample points and their labels into this equation and solve for b and w using the sigmoid function. By solving the equations, we can determine the values of b and w.

Given the sample points: x₁ = 3, y₁ = 1, x₂ = 1, y₂ = 1, x₃ = -1, y₃ = -1, we can substitute these values into the logistic regression model g(b + wx) and solve for b and w.

Using the given values and the sigmoid function, we will find that b = 1 and w = 0. Therefore, the correct option is (b) w = 0, b = 1.