Modeling Gene Regulatory Networks from Time Series Data using Particle Filtering

This thesis considers the problem of learning the structure of gene regulatory networks using gene expression time series data. A more realistic scenario where the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter based state estimation algorithm is studied instead of the contemporary linear approximation based approaches. The parameters signifying the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then fed to a LASSO based least squares regression operation, which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with Extended Kalman filtering (EKF), employing Mean Square Error as fidelity criterion using synthetic data and real biological data. Extensive computer simulations illustrate that the particle filter based gene network inference algorithm outperforms EKF and therefore, it can serve as a natural framework for modeling gene regulatory networks

Gene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information

Examinar a ampliação do uso de TICs por organizações sociais e governamentais na gestão da cidade é o objetivo do presente estudo. Nossa intenção é entender de que forma as tecnologias da informação e comunicação podem ser uma via alternativa que redefine as relações entre Estado e sociedade, substituindo políticas urbanas tradicionais por formas colaborativas de interação dos atores sociais. Entre os resultados alcançados pela pesquisa, é possível destacar a elaboração de uma metodologia capaz de mapear os princípios de organização, articulação, conexão e interação que constituem a existência de redes tecnossociais. A aplicação da metodologia nas cidades do Rio de Janeiro e de São Paulo demonstrou indicadores, gráficos e práticas políticas. A análise desses dados revela como as redes se constituem por uma arquitetura móvel, fluída, flexível, organizadas em torno de políticas comuns de ação e formadas por uma identidade coletiva que aproxima os atores das redes tecnossociais. Os princípios que mediam esta coesão são de compartilhamento, confiança e solidariedade, que redefinem as formas da organização do poder em direção a alternativas de organização política e desenvolvimento social

Bayesian Inference for Genomic Data Analysis

High-throughput genomic data contain gazillion of information that are influenced by the complex biological processes in the cell. As such, appropriate mathematical modeling frameworks are required to understand the data and the data generating processes. This dissertation focuses on the formulation of mathematical models and the description of appropriate computational algorithms to obtain insights from genomic data. Specifically, characterization of intra-tumor heterogeneity is studied. Based on the total number of allele copies at the genomic locations in the tumor subclones, the problem is viewed from two perspectives: the presence or absence of copy-neutrality assumption. With the presence of copy-neutrality, it is assumed that the genome contains mutational variability and the three possible genotypes may be present at each genomic location. As such, the genotypes of all the genomic locations in the tumor subclones are modeled by a ternary matrix. In the second case, in addition to mutational variability, it is assumed that the genomic locations may be affected by structural variabilities such as copy number variation (CNV). Thus, the genotypes are modeled with a pair of (Q + 1)-ary matrices. Using the categorical Indian buffet process (cIBP), state-space modeling framework is employed in describing the two processes and the sequential Monte Carlo (SMC) methods for dynamic models are applied to perform inference on important model parameters. Moreover, the problem of estimating gene regulatory network (GRN) from measurement with missing values is presented. Specifically, gene expression time series data may contain missing values for entire expression values of a single point or some set of consecutive time points. However, complete data is often needed to make inference on the underlying GRN. Using the missing measurement, a dynamic stochastic model is used to describe the evolution of gene expression and point-based Gaussian approximation (PBGA) filters with one-step or two-step missing measurements are applied for the inference. Finally, the problem of deconvolving gene expression data from complex heterogeneous biological samples is examined, where the observed data are a mixture of different cell types. A statistical description of the problem is used and the SMC method for static models is applied to estimate the cell-type specific expressions and the cell type proportions in the heterogeneous samples

Bayesian Inference for Duplication-Mutation with Complementarity Network Models

We observe an undirected graph $G$ without multiple edges and self-loops, which is to represent a protein-protein interaction (PPI) network. We assume that $G$ evolved under the duplication-mutation with complementarity (DMC) model from a seed graph, $G_0$, and we also observe the binary forest $\Gamma$ that represents the duplication history of $G$. A posterior density for the DMC model parameters is established, and we outline a sampling strategy by which one can perform Bayesian inference; that sampling strategy employs a particle marginal Metropolis-Hastings (PMMH) algorithm. We test our methodology on numerical examples to demonstrate a high accuracy and precision in the inference of the DMC model's mutation and homodimerization parameters

Modeling Gene Regulatory Networks from Time Series Data using Particle Filtering

This thesis considers the problem of learning the structure of gene regulatory networks using gene expression time series data. A more realistic scenario where the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter based state estimation algorithm is studied instead of the contemporary linear approximation based approaches. The parameters signifying the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then fed to a LASSO based least squares regression operation, which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with Extended Kalman filtering (EKF), employing Mean Square Error as fidelity criterion using synthetic data and real biological data. Extensive computer simulations illustrate that the particle filter based gene network inference algorithm outperforms EKF and therefore, it can serve as a natural framework for modeling gene regulatory networks