variational particle approximations
In the plane to Montréal, today, I read this paper by Kulkarni, Saeedi and Gershman, which will be presented at AISTATS. The main idea is to create a mix between particle Monte Carlo and a kind of quasi-Monte Carlo technique (qNC is not mentionned in the paper), using variational inference (and coordinate ascent) to optimise the location and weight of the particles. It is however restricted to cases with finite support (as a product of N latent variables) as in an HMM with a finite state space. There is also something I do not get in the HMM case, which is that the variational approximation to the filtering is contracted sequentially. This means that at time the K highest weight current particles are selected while the past remains unchanged. Is this due to the Markovian nature of the hidden model? (Blame oxygen deprivation, altitude dizziness or travelling stress, then!) I also fail to understand how for filtering, “at each time step, the algorithm selects the K continuations (new variable assignments of the current particle set) that maximize the variational free energy.” Because the weight function to be optimised (eqn (11)) seems to freeze the whole past path of particles… I presume I will find an opportunity while in Reykjavik to discuss those issues with the authors.