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I am currently reading a white paper relating to Expectation-Maximisation (EM) and would like to encode a formula so I can play with it in order to help my understanding. The formula in question is a sum over values and shown below;

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I am wondering what the advice on the best way to acheive this would be. I am currently thinking about using a for loop to create some kind of cumulative value as I iterate from t = 1 to m.

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    $\begingroup$ Have you checked out numpy? docs.scipy.org/doc/numpy/reference/generated/numpy.sum.html $\endgroup$ – StatsSorceress Jan 31 '18 at 16:34
  • $\begingroup$ I have not done it, but I would create a python list expression looping through variables (instead of for loops), which is shown to be much faster than traditional for loops. Then use np.cumsum to get cumulative sum. It would be np.cumsum(python_list_expression). Just try on a simple sum! $\endgroup$ – TwinPenguins Jan 31 '18 at 16:41
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In most cases, I would go for NumPy. Implement a Python function f(t) that calculates the $t$-th summand. Then run

import numpy as np
result = np.array([f(t) for t in range(1,m+1)]).sum()

This will be very fast, unless $m$ is so large that [f(t) for t in range(1,m+1)] does not fit into memory. In this case, I would follow your approach and use a for-loop:

result = 0
for t in range(1, m+1):
    result += f(t)
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