Hi all,
I see that gmm.score(x) returns the log probability of x for that
point. I'm interested in integrating this probability over a region.
For example, finding the probability of a ball being in the space
(x,y,z) +/- (delta_x, delta_y, delta_z). In this example, I'd be
using past ball locations as training data.
So the solution seems to be to integrate the probability density
function (returned by gmm.score()) over the region of interest. Right
now I'm using Scipy's integrate.nquad method. But, coupling that with
gmm.score is SLOW. I've attached an example that takes > 10 minutes
to compute on my i7. The example is in 7D because my actual use case
is in 7D. The region is pretty small -- though the actual region I'll
be using is bigger. Think delta = 0.1.
I'm wondering: Is there a way to speed this up? An analytical method
to do this? A built in method?
P.S. I accidentally sent the last email as HTML and I think that
messed up the list formatting. This one should be better.
import numpy as np
from sklearn import mixture
from scipy import integrate
data1 = 1.0
outcome_1_data = np.array([data1, data1, data1, data1, data1, data1, data1])
data2 = 2.0
outcome_2_data = np.array([data2, data2, data2, data2, data2, data2, data2])
data3 = 3.0
outcome_3_data = np.array([data3, data3, data3, data3, data3, data3, data3])
data4 = 4.0
outcome_4_data = np.array([data4, data4, data4, data4, data4, data4, data4])
data5 = 5.0
outcome_5_data = np.array([data5, data5, data5, data5, data5, data5, data5])
all_outcomes_together = np.array([outcome_1_data, outcome_2_data, outcome_3_data, outcome_4_data, outcome_5_data, ])
prob_model = mixture.GMM(n_components = 5)
prob_model.fit(all_outcomes_together)
center_point = np.array([3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0])
delta = np.array([0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001])
lower_bounds = center_point - delta
upper_bounds = center_point + delta
both_bounds = [list(a) for a in zip(lower_bounds, upper_bounds)]
print both_bounds
prob_within_delta = integrate.nquad(lambda *state: np.exp(prob_model.score([list(state)])), both_bounds)
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