Question

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. $(\theta_0, \theta_1, \theta_2) = (-1.02, -1.04, 0.45)$

          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. $(\theta_0, \theta_1, \theta_2) = (-1.02, -1.04, 0.45)$

We want to fit a logistic regression model to some data. The model is of the form y = hθ(x) = σ(θ0 + θ1 x1 + θ2 x2), and the error function for m datapoints is given by E(θ) = -log[∏i=1^m (hθ(x^i))^y^i (1 - hθ(x^i))^1 - y^i].
Consider the first training datapoint: (x1, x2) = (2, 3) from class y = 0. Perform one iteration of gradient descent with this data point. The initial parameters are (θ0, θ1, θ2) = (-1, -1, 0.5) and α = 0.1.
Which answer most closely resembles the updated values of the parameters?
Select one:
a. (θ0, θ1, θ2) = (-1.28, -1.36, 0.41)
b. (θ0, θ1, θ2) = (-1.88, -2.06, 0.76)
c. (θ0, θ1, θ2) = (-1.05, -1.09, 0.41)
d. (θ0, θ1, θ2) = (-0.37, -0.55, 0.67)
e. (θ0, θ1, θ2) = (-0.83, -0.79, 0.44)
f. (θ0, θ1, θ2) = (-0.95, -0.91, 0.57)
g. (θ0, θ1, θ2) = (-0.98, -0.95, 0.53)
h. (θ0, θ1, θ2) = (-1.02, -1.04, 0.45)

Added by Renee T.

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