arXiv subjects

Sakira Hassan

Publications and source records attributed to Sakira Hassan.

4 recordsLinked to original sources

arXiv2023

Parallel square-root statistical linear regression for inference in nonlinear state space models

In this article, we introduce parallel-in-time methods for state and parameter estimation in general nonlinear non-Gaussian state-space models using the statistical linear regression and the iterated statistical posterior linearization paradigms. We also reformulate the proposed methods in a square-root form, resulting in improved numerical stability while preserving the parallelization capabilities. We then leverage the fixed-point structure of our methods to perform likelihood-based parameter estimation in logarithmic time with respect to the number of observations. Finally, we demonstrate the practical performance of the methodology with numerical experiments run on a graphics processing unit (GPU).

stat.CO↗

arXiv2022

Fourier--Hermite Dynamic Programming for Optimal Control

In this paper, we propose a novel computational method for solving non-linear optimal control problems. The method is based on the use of Fourier--Hermite series for approximating the action-value function arising in dynamic programming instead of the conventional Taylor series expansion used in differential dynamic programming (DDP). The coefficients of the Fourier--Hermite series can be numerically computed by using sigma-point methods, which leads to a novel class of sigma-point based dynamic programming methods. We also prove the quadratic convergence of the method and experimentally test its performance against other methods.

math.OC↗

arXiv2021

Temporal Parallelization of Inference in Hidden Markov Models

This paper presents algorithms for parallelization of inference in hidden Markov models (HMMs). In particular, we propose parallel backward-forward type of filtering and smoothing algorithm as well as parallel Viterbi-type maximum-a-posteriori (MAP) algorithm. We define associative elements and operators to pose these inference problems as parallel-prefix-sum computations in sum-product and max-product algorithms and parallelize them using parallel-scan algorithms. The advantage of the proposed algorithms is that they are computationally efficient in HMM inference problems with long time horizons. We empirically compare the performance of the proposed methods to classical methods on a highly parallel graphical processing unit (GPU).

cs.DC↗

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↗