tag:blogger.com,1999:blog-6555947.post6193313973434558737..comments2024-08-05T05:53:31.445-06:00Comments on The Geomblog: Metrics on distributions defined over metric spacesSuresh Venkatasubramanianhttp://www.blogger.com/profile/15898357513326041822noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6555947.post-45764608371105773852010-05-04T19:55:21.520-06:002010-05-04T19:55:21.520-06:00ah cool. it looks like it's exactly what I was...ah cool. it looks like it's exactly what I was talking about. excellent. and I note that they have metrizing results as well.Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-11058650104172493182010-05-04T18:41:01.430-06:002010-05-04T18:41:01.430-06:00Hey, look what just popped up (literally) in my RS...Hey, look what just popped up (literally) in my RSS feeds:<br /><a href="http://jmlr.csail.mit.edu/papers/v11/sriperumbudur10a.html" rel="nofollow">Hilbert Space Embeddings and Metrics on Probability Measures</a>. I guess this fills my monthly allowance of one-in-a-million coincidences.Cosma Shalizihttp://bactra.org/weblog/noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-31196688549813253582010-05-04T14:23:52.968-06:002010-05-04T14:23:52.968-06:00Cosma, that's an excellent question. I don'...Cosma, that's an excellent question. I don't have an answer for you off the top of my head. One good thing about the current distance is that it embeds in an RKHS which is "nice" in many ways, so there's some hope that a metrizing result exists. I'll have to think more about it.Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-3572788995017677902010-05-04T10:51:53.599-06:002010-05-04T10:51:53.599-06:00Ooh, Cosma nailed what I was thinking about.Ooh, Cosma nailed what I was thinking about.Davidnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-77915760598133698092010-05-04T07:44:42.662-06:002010-05-04T07:44:42.662-06:00For the earth mover distance, say I have u,v, and ...For the earth mover distance, say I have u,v, and EMD(u,v) = e.<br /><br />Can I say given v, e, that the inverse of EMD=e given v is exactly u? If so, do I get the same guarantee from Levy-Prokhorov?Davidnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-26988819913933312962010-05-04T07:43:31.545-06:002010-05-04T07:43:31.545-06:00One reason for interest in the Mallows and Prohoro...One reason for interest in the Mallows and Prohorov metrics on the part of probabilists and statisticians is that they metrize convergence in distribution, i.e., for a sequence of probability measures <i>P_n</i> and a limit measure <i>P</i>, <i>d</i>(<i>P_n</i>,<i>P</i>) -> 0 in these metrics iff <i>P_n</i> converges to <i>P</i> in distribution. A bunch of other metrics or divergences on probability distributions which are more intuitive (like Kullback-Leibler divergence) actually induce finer topologies than that of convergence in distribution. Do you happen to know if the current distance also metrizes convergence in distribution?Cosma Shalizihttp://bactra.org/weblog/noreply@blogger.com