The problem of unsupervised dimensionality reduction of stochastic variables while pre­ serving their most relevant characteristics is fundamental for the analysis of complex data. Unfortunately, this problem is ill defined since natural datasets inherently contain al­ ternative underlying structures. In this paper we address this problem by extending the re­ cently introduced "Sufficient Dimen...

We express some criticism about the definition of an algorithmic sufficient statistic and, in particular, of an algorithmic minimal sufficient statistic. We propose another definition, which has better properties.

Inverse problems in image and audio, and super-resolution in particular, can be seen as high-dimensional structured prediction problems, where the goal is to characterize the conditional distribution of a high-resolution output given its lowresolution corrupted observation. When the scaling ratio is small, point estimates achieve impressive performance, but soon they suffer from the regression-...