Cruising The Simplex: Hamiltonian Monte Carlo and the Dirichlet Distribution

Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo. I demonstrate a series of transformations that reshape the canonical Dirichlet distribution into a form much more amenable to MCMC algorithms.Comment: 5 pages, 0 figure

Nested Sampling with Constrained Hamiltonian Monte Carlo

Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.Comment: 15 pages, 4 figure

Detecting Hands in Egocentric Videos: Towards Action Recognition

Recently, there has been a growing interest in analyzing human daily activities from data collected by wearable cameras. Since the hands are involved in a vast set of daily tasks, detecting hands in egocentric images is an important step towards the recognition of a variety of egocentric actions. However, besides extreme illumination changes in egocentric images, hand detection is not a trivial task because of the intrinsic large variability of hand appearance. We propose a hand detector that exploits skin modeling for fast hand proposal generation and Convolutional Neural Networks for hand recognition. We tested our method on UNIGE-HANDS dataset and we showed that the proposed approach achieves competitive hand detection results