The "right" way to calculate the overall covariance for GMM?

[sergeant-wizard]

Hi, thanks for publishing this code. It is helping us a lot.

I want to ask about the part where you calculate the overall covariance for GMM. If my understanding is correct, the overall covariance for GMM with weight w_i is:

So I think the corresponding change to your current implementation is:

--- a/python/gps/utility/gmm.py
+++ b/python/gps/utility/gmm.py
@@ -89,7 +89,7 @@ class GMM(object):
         # For some reason this version works way better than the "right"
         # one... could we be computing xxt wrong?
         diff = self.mu - np.expand_dims(mu, axis=0)
-        diff_expand = np.expand_dims(diff, axis=1) * \
+        diff_expand = np.expand_dims(self.mu, axis=1) * \
                 np.expand_dims(diff, axis=2)
         wts_expand = np.expand_dims(wts, axis=2)
         sigma = np.sum((self.sigma + diff_expand) * wts_expand, axis=0)

The comment in your code suggests that you're aware that the current code is not theoretically derived, so I'd like to know if my modified version is what you tried as the "right" version, and if so, how it performed "worse" compared to the current version.

I did try the above modification with mcj_badmm_example, and I couldn't find any significant difference between the original version.

Thanks!

[justinjfu]

Hi,

We're aware that the code is mathematically incorrect. If you would like, you can make a PR and we can run the benchmark tasks to make sure there is no performance degradation.

We've been planning on replacing this GMM with a version based on the scikit-learn implementation, so this code will likely be removed in the future.

[sergeant-wizard]

Thanks for the response. I submitted a PR as #73 if only for the reason that I get to see the benchmark results. Look forward to hearing from you.