Paul Viola, Nicol Schraudolph, Terrence J. Sejnowski
No finite sample is sufficient to determine the density, and therefore the entropy, of a signal directly. Some assumption about either the functional form of the density or about its smoothness is necessary. Both amount to a prior over the space of possible density functions. By far the most common approach is to assume that the density has a parametric form.
By contrast we derive a differential learning rule called EMMA that optimizes entropy by way of kernel density estimation. En(cid:173) tropy and its derivative can then be calculated by sampling from this density estimate. The resulting parameter update rule is sur(cid:173) prisingly simple and efficient.
We will show how EMMA can be used to detect and correct cor(cid:173) ruption in magnetic resonance images (MRI). This application is beyond the scope of existing parametric entropy models.