We want to fit a logistic regression model to some data. The model is of the form $y = h_\theta(x) = \sigma(\theta_0 + \theta_1 x_1 + \theta_2 x_2)$, and the error function for $m$ datapoints is given by $E(\theta) = -log[\prod_{i=1}^{m} (h_\theta(x^i))^{y^i} (1 - h_\theta(x^i))^{1 - y^i}]$.
Consider the first training datapoint: $(x_1, x_2) = (2, 3)$ from class $y = 0$. Perform one iteration of gradient descent with this data point. The initial parameters are $(\theta_0, \theta_1, \theta_2) = (-1, -1, 0.5)$ and $\alpha = 0.1$.
Which answer most closely resembles the updated values of the parameters?
Select one:
a. $(\theta_0, \theta_1, \theta_2) = (-1.28, -1.36, 0.41)$
b. $(\theta_0, \theta_1, \theta_2) = (-1.88, -2.06, 0.76)$
c. $(\theta_0, \theta_1, \theta_2) = (-1.05, -1.09, 0.41)$
d. $(\theta_0, \theta_1, \theta_2) = (-0.37, -0.55, 0.67)$
e. $(\theta_0, \theta_1, \theta_2) = (-0.83, -0.79, 0.44)$
f. $(\theta_0, \theta_1, \theta_2) = (-0.95, -0.91, 0.57)$
g. $(\theta_0, \theta_1, \theta_2) = (-0.98, -0.95, 0.53)$
h. $(\theta_0, \theta_1, \theta_2) = (-1.02, -1.04, 0.45)$
