most recent 30 from http://mathoverflow.net 2013-05-23T22:38:59Z http://mathoverflow.net/feeds/question/111807 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111807/define-a-posterior-probability-of-y-given-x-when-the-model-is-not-probabilistic shna 2012-11-08T12:44:44Z 2012-11-08T12:44:44Z

<p>Suppose we have a very simple online k-means where each new data-point is assigned to its nearest center (the mean is updated incrementally). Each center (cluster) is labelled with the most common label of data-points assigned to that cluster. In this special configuration: is it possible to compute a sort of "posterior probability"? I.e., can the posterior probability of a class label $y$ given a data-point $x$ ($P(y|x)$) just be $1/\text{distance}(x, m_y)$, where $m_y$ is a center labelled with $y$ which is nearest to $x$?</p>