Bdtjtk

I am calculating the theta for my AI like so:

theta = opt.fmin_cg(cost, initial_theta, gradient, (newX, y))

Which works great and gives me this output:

Optimization terminated successfully.

         Current function value: 0.684355

         Iterations: 6

         Function evaluations: 15

         Gradient evaluations: 15

When I print theta, I get this:

[ 0.         -0.28132729  0.158859  ]

I now want to plot this on my scatter graph as a line, my expected output looks like this:

But when I try to perform this on my graph with the algorithm:

weights * features = weight0 + weight1 * feature1 + weight2 * feature2

Like so:

x_axis = np.array([min(newX[:, 1]), max(newX[:, 1])])

y_axis = x_axis * theta[1:]

ax.plot(x_axis, y_axis, linewidth=2)

plt.show()

The output looks like this:

What should y_axis = x_axis * theta[1:] be to match the algorithm?

Update:

newX derives from my training data frame and is created like this:

newX = np.zeros(shape=(x.shape[0], x.shape[1] + 1))

newX[:, 1:] = x.values

It now looks like this, the concept is 0 is the free weight:

[[0. 8. 2.]

 [0. 0. 0.]

 [0. 0. 0.]

 ...

 [0. 0. 0.]

 [0. 0. 0.]

 [0. 1. 1.]]

IIUC, you are trying to plot your decision boundary for the logistic regression. This is not simply a y = mx + b problem, well it is but you first need to determine where your decision boundary is, typically it's at probability of 0.5. I assume the model you are going with something looks like h(x) = g(theta_0*x_0 + theta_1*x_1 + theta_2*x_2), where g(x) = 1 / (1 + e^-x) and x_1 and x_2 are your features that you are plotting, ie your y and x axis (I don't know which is y and which is x since I don't know your data). So for probability 0.5, you want to solve for h(x) = 0.5, ie theta_0*x_0 + theta_1*x_1 + theta_2*x_2 = 0

So what you want to plot is the line 0 = theta_0*x_0 + theta_1*x_1 + theta_2*x_2. Let's just say you have x_1 on your x axis and x_2 on your y axis. (x_0 is just 1, corresponding to theta_0, your intercept.)

So you'll need to pick (somewhat arbitrarily) x_1 values that will give you a good illustration of the boundary line. Min/max of your dataset works, which you've done. Then solve for x_2 given the formula above. You can define a function here: lambda x_1: (theta[0] + theta[1] * x_1) / theta[2]. I'm assuming your theta variable corresponds to [intercept, coeff for x_1, coeff for x_2]. So you'll end up with something like:

theta = [0., -0.28132729, 0.158859]

x = np.array([0, 10])

f = lambda x_1: (theta[0] + theta[1] * x_1) / theta[2]

y = f(x)

plt.plot(x, y)