arXiv subjects

Adrien Corenflos

Publications and source records attributed to Adrien Corenflos.

22 records · Page 2Linked to original sources

arXiv2022

De-Sequentialized Monte Carlo: a parallel-in-time particle smoother

Particle smoothers are SMC (Sequential Monte Carlo) algorithms designed to approximate the joint distribution of the states given observations from a state-space model. We propose dSMC (de-Sequentialized Monte Carlo), a new particle smoother that is able to process $T$ observations in $\mathcal{O}(\log T)$ time on parallel architecture. This compares favourably with standard particle smoothers, the complexity of which is linear in $T$. We derive $\mathcal{L}_p$ convergence results for dSMC, with an explicit upper bound, polynomial in $T$. We then discuss how to reduce the variance of the smoothing estimates computed by dSMC by (i) designing good proposal distributions for sampling the particles at the initialization of the algorithm, as well as by (ii) using lazy resampling to increase the number of particles used in dSMC. Finally, we design a particle Gibbs sampler based on dSMC, which is able to perform parameter inference in a state-space model at a $\mathcal{O}(\log(T))$ cost on parallel hardware.

stat.CO↗

arXiv2021

Differentiable Particle Filtering via Entropy-Regularized Optimal Transport

Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.

stat.ML↗

arXiv2021

Temporal Gaussian Process Regression in Logarithmic Time

The aim of this article is to present a novel parallelization method for temporal Gaussian process (GP) regression problems. The method allows for solving GP regression problems in logarithmic O(log N) time, where N is the number of time steps. Our approach uses the state-space representation of GPs which in its original form allows for linear O(N) time GP regression by leveraging the Kalman filtering and smoothing methods. By using a recently proposed parallelization method for Bayesian filters and smoothers, we are able to reduce the linear computational complexity of the temporal GP regression problems into logarithmic span complexity. This ensures logarithmic time complexity when run on parallel hardware such as a graphics processing unit (GPU). We experimentally demonstrate the computational benefits on simulated and real datasets via our open-source implementation leveraging the GPflow framework.

cs.LG↗

arXiv2021

Parallel Iterated Extended and Sigma-point Kalman Smoothers

The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these problems. However, these methods are inherently sequential and do not in their standard formulation allow for parallelization in the time domain. In this paper, we present a set of parallel formulas that replace the existing sequential ones in order to achieve lower time (span) complexity. Our experimental results done with a graphics processing unit (GPU) illustrate the efficiency of the proposed methods over their sequential counterparts.

cs.DC↗