Calculate probability density mean python

Question

Let's say I have a heatmap of probability density function as a numpy ndarray(m,n). Is there a function that automatically computes mean treating this matrix as probability density? I can't seem to find a function that would automatically do that.

Of course an easy solution would be to create a weighted average with weights equal to indices of the array, but seems like there should be a built-in function that would just do that.

Clasification: Say my array is heatmap = [[0,0,0,1],[0,0,1,0],[0,0,1.5,0],[0,0,0,0]]. No if we assume that this is not normalized probability you can calculate mean and other properties of the probability density.

For example mean in x direction would be

    xx = np.arange(0,heatmap.shape[1],1)
    weights = np.tile(xx,(heatmap.shape[0],1))

    mean_x = np.average(weights, weights = heatmap_avg_left)

I'm just looking for a function in numpy or scipy that would do this and other probability properties automatically

Could you clarify your question to show a minimal example of your array and what mean you would expect? — user2653663, Jan 03 '20 at 21:30
are you looking for something like the 50th percentile of the data in each direction, or the center of mass? — Mad Physicist, Jan 03 '20 at 21:36
Just added a clarification. Yeah sort of like center of mass treating the array as probability density. — Mike Azatov, Jan 03 '20 at 21:38
Your code doesn't make much sense to someone not living in your head. Please post a complete example. — Mad Physicist, Jan 03 '20 at 21:45

Mad Physicist · Accepted Answer · 2020-01-04T01:56:50.553

3

You can find the center-of-mass of an array using scipy.ndimage.center_of_mass. If your array is indexed into a map containing the individual masses, you can transform directly:

from scipy.ndimage import center_of_mass

indices = ... # shape (m, n), values in [0, k)
mass_lookup = ... # shape (k)

result = center_of_mass(mass_lookup[indices])

In this case, mass_lookup is like a heat map. If the array contains weights instead, use it directly.

edited Jan 04 '20 at 01:56

answered Jan 03 '20 at 21:53

Mad Physicist

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Could you please explain the difference between a heat map and an array of weights? – Stef Sep 20 '21 at 15:33
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@Stef. I'm describing a situation where the integer label in the array corresponds to an index into `mass_lookup`, which is a simple lookup table. – Mad Physicist Sep 20 '21 at 17:33

Marat · Answer 2 · 2020-01-03T21:49:28.343

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# assuming the array is called pdf_arr
axis = 0  # 0 for x axis (columns), 1 for y axis (rows)
marginal_pdf = pdf_arr.sum(axis=axis)
# since it's just a sample, normalize pdf
marginal_pdf /= marginal_pdf.sum()
axis_mean = (marginal_pdf * np.arange(pdf_arr.shape[1-axis])).sum()
# repeat the same for axis = 1

edited Jan 03 '20 at 21:49

answered Jan 03 '20 at 21:43

Marat

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Thanks, this would work. I was just hoping there would be a built-in function for working with probability densities. – Mike Azatov Jan 04 '20 at 01:46

Calculate probability density mean python

2 Answers2