CODEWITHSUNDEEP
pythonnumpymachine-learningmathprobability
user346880
user346880

Reputation: 1

Multiplying subarrays of tensor

I am trying to implement a multivariate Gaussian Mixture Model and am trying to calculate the probability distribution function using tensors. There are n data points, k clusters, and d dimensions. So far, I have two tensors. One is a (n,k,d) tensor of centered data points and the other is a kxdxd tensor of covariance matricies. I can compute an nxk matrix of probabilities by doing

centered = np.repeat(points[:,np.newaxis,:],K,axis=1) - mu[np.newaxis,:] # KxNxD
prob = np.zeros(n,k)
constant = 1/2/np.pow(np.pi, d/2)
for n in range(centered.shape[1]):
    for k in range(centered.shape[0]):
        p = centered[n,k,:][np.newaxis] # 1xN
        power = -1/2*(p @ np.linalg.inv(sigma[k,:,:]) @ p.T)
        prob[n,k] = constant * np.linalg.det(sigma[k,:,:]) * np.exp(power)

where sigma is the triangularized kxdxd matrix of covariances and centered are mypoints. What is a more pythonic way of doing this using numpy's tensor capabilites?

Upvotes: 0

Views: 52

Answers (1)

hpaulj
hpaulj

Reputation: 231615

Just a couple of quick observations:

  • I don't see you using p in the loop; is this a mistake? Using n instead?

  • The T in centered[n,k,:].T does nothing; with that index the array is 1d

  • I'm not sure if np.linal.inv can handle batches of arrays, allowing np.linalg.inv(sigma).

  • @ allows batches, just so long as the last 2 dim are the ones entering into the dot (with the usual last of A, 2nd to the last of B rule; einsum can also be used.

  • again does np.linalg.det handle batches?

Upvotes: 0

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