Estimation of gene expression by a bank of particle filters

Abstract

This paper addresses the problem of joint estimation of time series of gene expressions and identification of the coefficients of gene interactions defining the network. The proposed method exploits a state-space structure describing the system so that a bank of particle filters can be used to efficiently track each of the time series separately. Since each gene interacts with some of the other genes, the individual filters need to exchange information about the states (genes) that they track. The analytical derivation of the posterior distribution of the states given the observed data allows for marginalization of the matrix describing the interactions in the network and for efficient implementation of the method. Computer simulations reveal a promising performance of the proposed approach when compared to the conventional particle filter that attempts to track the time series of all the genes and which, as a result, suffers from the curse-of-dimensionality.

A comparative study of nonlinear Bayesian filtering algorithms for estimation of gene expression time series data

“…We estimated the gene expression problem using various nonlinear Bayesian filtering algorithms, including the EKF, UKF, PF, EKF-PF, UKF-PF, and PF-MCMC. We computed the coefficients of regulatory relationship matrix A in the same method presented in [2,3], where the priors of these coefficients were calculated using a normal distribution.…”

“…However, the estimation of gene expression is formulated as a nonlinear problem, and the unknown state has a high dimensional state space model. Various techniques have been introduced to estimate the gene expression time series including extended Kalman filter (EKF) [1] and multiparticle filtering [2].…”

“…A gene regulatory network is a group of genes that interact with each other and with other substances to control the functions of the cell. Inference of gene regulatory relationships is a very important problem in biology [2,3]. The unknown state is estimated based on time series data that represent the evolution of the genomic expressions [1,4].…”

Bayesian learning of nonlinear gene regulatory networks with switching architectures

“…To this extent, state-space models provide a mathematical framework that captures the dynamical behavior of GRNs, including their subcircuits, over time. GRN estimation using a state space approach has been extensively studied (Noor et al, 2012;Bugallo et al, 2015;Ancherbak et al, 2016;Pirgazi and Khanteymoori, 2018;Amor et al, 2019). However, these approaches assume that the network structure is static across all time.…”

“…Specifically, the authors in (Xiong and Zhou, 2013;Pirgazi and Khanteymoori, 2018) use Kalman filtering for inference by assuming a linear state-space model. In (Noor et al, 2012;Bugallo et al, 2015;Ancherbak et al, 2016), particle filtering is used to infer the dynamic network and the process and measurement noise are assumed to be known and constant. This may not capture changes in the noise statistics that can arise when a change in the regulatory network structure occurs.…”