A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure

Gait Recognition in the Presence of Occlusion: A New Dataset and Baseline Algorithms

Human gait is an important biometric feature for identification of people. In this paper we present a new dataset for gait recognition. The presented database overcomes a crucial limitation of other state-of-the-art gait recognition databases. More specifically this database addresses the problem of dynamic and static inter object occlusion. Furthermore this dataset offers three new kinds of gait variations, which allow for challenging evaluation of recognition algorithms. In addition to presenting the database we present two baseline algorithms (Color histograms, Gait Energy Image) to perform person identification using gait. These algorithms already show promising results on the presented database