Python Joint Distribution of N Variables

Question

So I need to calculate the joint probability distribution for N variables. I have code for two variables, but I am having trouble generalizing it to higher dimensions. I imagine there is some sort of pythonic vectorization that could be helpful, but, right now my code is very C like (and yes I know that is not the right way to write Python). My 2D code is below: ``` import numpy import math feature1 = numpy.array([1.1,2.2,3.0,1.2,5.4,3.4,2.2,6.8,4.5,5.6,1.9,2.8,3.7,4.4,7.3,8.3,8.1,7.0,8.0,6.8,6.2,4.9,5.7,6.3,3.7,2.4,4.5,8.5,9.5,9.9]); feature2 = numpy.array([11.1,12.8,13.0,11.6,15.2,13.8,11.1,17.8,12.5,15.2,11.6,20.8,14.7,14.4,15.3,18.3,11.4,17.0,16.0,16.8,12.2,14.9,15.7,16.3,13.7,12.4,14.2,18.5,19.8,19.0]); #===Concatenate All Features===# numFrames = len(feature1); allFeatures = numpy.zeros((2,numFrames)); allFeatures[0,:] = feature1; allFeatures[1,:] = feature2; #===Create the Array to hold all the Bins===# numBins = int(0.25*numFrames); allBins = numpy.zeros((allFeatures.shape[0],…

Accepted Answer

Check out the function `numpy.histogramdd`. This function can compute histograms in arbitrary numbers of dimensions. If you set the parameter `normed=True`, it returns the bin count divided by the bin hypervolume. If you'd prefer something more like a probability mass function (where everything sums to 1), just normalize it yourself. All together, you'll have something like:

```
import numpy as np
numBins = 10  # number of bins in each dimension
data = np.random.randn(100000, 3)  # generate 100000 3-d random data points
jointProbs, edges = np.histogramdd(data, bins=numBins)
jointProbs /= jointProbs.sum()
```

Python Joint Distribution of N Variables

Solution

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