A Biologically Plausible Transform for Visual Recognition that is Invariant to Translation, Scale, and Rotation

Visual object recognition occurs easily despite differences in position, size, and rotation of the object, but the neural mechanisms responsible for this invariance are not known. We have found a set of transforms that achieve invariance in a neurally plausible way. We find that a transform based on local spatial frequency analysis of oriented segments and on logarithmic mapping, when applied twice in an iterative fashion, produces an output image that is unique to the object and that remains constant as the input image is shifted, scaled, or rotated

Nested R^\widehat R: Assessing the convergence of Markov chain Monte Carlo when running many short chains

The growing availability of hardware accelerators such as GPUs has generated interest in Markov chains Monte Carlo (MCMC) workflows which run a large number of chains in parallel. Each chain still needs to forget its initial state but the subsequent sampling phase can be almost arbitrarily short. To determine if the resulting short chains are reliable, we need to assess how close the Markov chains are to convergence to their stationary distribution. The $\widehat R$ statistic is a battle-tested convergence diagnostic but unfortunately can require long chains to work well. We present a nested design to overcome this challenge, and introduce tuning parameters to control the reliability, bias, and variance of convergence diagnostics