I am trying to compute the covariance matrix which maximises the likelihood estimate manually without using the numpy library,but I cannot seem to get the right answer. I am trying to go by this formula:
I know i'm calculating the means correctly. So there must be an issue with the part where I actually compute the covariance but I have no idea where? This is my code:
mat = [[1,2,3],[4,6,8],[3,5,7]] #now calc covariance for each element of the matrix Cov = [] for j in range(len(means)): sum = 0 covs = [] for k in range(len(means)): for i in range(len(means)): sum += ((mat[i][j] - means[j]) * (mat[i][k] - means[k])) result = sum/ len(means) covs.append(result) Cov.append(covs) print(np.reshape(S,(3,3))) This is what I get:
[[ 1.55555556 3.66666667 6.33333333] [ 2.11111111 5. 8.66666667] [ 2.66666667 6.33333333 11. ]] This is what i'm supposed to get:
[[1.55555556 2.11111111 2.66666667] [2.11111111 2.88888889 3.66666667] [2.66666667 3.66666667 4.66666667]] 1 Answer
You should reset the sum for each entry of the covariance matrix,
covs = [] for k in range(len(means)): sum = 0 for i in range(len(means)): sum += ((mat[i][j] - means[j]) * (mat[i][k] - means[k])) covariance = sum/ len(means) covs.append(covariance) You could shorten that a bit as
covs = [] for k in range(len(means)): terms = ( (mat[i][j] - means[j]) * (mat[i][k] - means[k]) for i in range(len(means)) ) covariance = sum(terms) / len(means) covs.append(covariance) Be sure to clear the workspace so that sum is again a built-in function and not a number.
