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I would like to extract coefficients of indexed variables from a large sum. The following is an example motivated by linear regression to illustrate the problem.

Consider the (unnormalised) log likelihood of a linear regression problem with design matrix X, observations y, and regression parameters w given by

logLikelihood = -gamma / 2 * Sum[(y[i] - Sum[X[i, j] w[j], {j, 1, p}]) ^ 2, {i, 1, n}]

I would like to use Mathematica to extract coefficients of indexed variables from the log-likelihood. For example, I would like to apply

SomeFunction[logLikelihood, w[k]^2]

and get the following result

- gamma / 2 * Sum[X[i,k] ^ 2, {i, 1, n}]

I have tried Coefficient and differentiating with respect to the variable of interest but both are not quite working as I would like.

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  • $\begingroup$ Are n and p left as a variables, or do you plug in numbers for them? $\endgroup$
    – march
    Commented Dec 10, 2015 at 22:18
  • $\begingroup$ I would like to leave n and p as variables. $\endgroup$
    – Till Hoffmann
    Commented Dec 10, 2015 at 22:19
  • $\begingroup$ You might want to look at mathematica.stackexchange.com/questions/65471/…. $\endgroup$
    – JimB
    Commented Dec 10, 2015 at 22:36

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