Semi-Bayesian Inference of Time Series Chain Graphical Models in Biological Networks

Farnoudkia, Hajar
Purutçuoğlu Gazi, Vilda
The construction of biological networks via time-course datasets can be performed both deterministic models such as ordinary differential equations and stochastic models such as diffusion approximation. Between these two branches, the former has wider application since more data can be available. In this study, we particularly deal with the probabilistic approaches for the steady-state or deterministic description of the biological systems when the systems are observed though time. Hence, we consider time series chain graphical model which enables to bind the activation of a system under different time points via two covariance matrices under multivariate normal distributions of states. In inference of this complex model, we propose two scenarios based on two stages. In the first plan, the time courses are supposed as sample. The covariance matrix Γ which connects the system in distinct time points via the vector of autoregressive models with different lags is estimated by the correlation of nodes in consecutive times. Then, the covariance matrix Σ which presents the activation in a single time point is inferred via Bayesian algorithms. In the second plan, Γ is estimated similar to the first plan. But, at the second stage, for each time point, Σ is estimated separately via Bayesian methods, and their union is the final estimation of the system. We perform these strategies under different dimensional and different number of observed time points’ data. The results indicate that while the dimensions of systems increase, the accuracies of estimated systems improve too irrelevant from the number of points and observations.
International Conference on Innovative Engineering Applications (CIEA’2018) (20 - 22 Eylül 2018)


Loop-based conic multivariate adaptive regression splines is a novel method for advanced construction of complex biological networks
Ayyıldız Demirci, Ezgi; Purutçuoğlu Gazi, Vilda; Weber, Gerhard Wilhelm (2018-11-01)
The Gaussian Graphical Model (GGM) and its Bayesian alternative, called, the Gaussian copula graphical model (GCGM) are two widely used approaches to construct the undirected networks of biological systems. They define the interactions between species by using the conditional dependencies of the multivariate normality assumption. However, when the system's dimension is high, the performance of the model becomes computationally demanding, and, particularly, the accuracy of GGM decreases when the observations...
Hybrid wavelet-neural network models for time series data
Kılıç, Deniz Kenan; Uğur, Ömür; Department of Financial Mathematics (2021-3-3)
The thesis aims to combine wavelet theory with nonlinear models, particularly neural networks, to find an appropriate time series model structure. Data like financial time series are nonstationary, noisy, and chaotic. Therefore using wavelet analysis helps better modeling in the sense of both frequency and time. S&P500 (∧GSPC) and NASDAQ (∧ IXIC) data are divided into several components by using multiresolution analysis (MRA). Subsequently, each part is modeled by using a suitable neural network structure. ...
Stochastic modelling of biochemical networks and inference of modelparameters
Purutçuoğlu Gazi, Vilda (null, Springer, 2018-01-01)
There are many approaches to model the biochemical systems deterministically or stochastically. In deterministic approaches, we aim to describe the steady-state behaviours of the system, whereas, under stochastic models, we present the random nature of the system, for instance, during transcription or translation processes. Here, we represent the stochastic modelling approaches of biological networks and explain in details the inference of the model parameters within the Bayesian framework.
Nonlinear optical properties of semiconductor heterostructures
Yıldırım, Hasan; Tomak, Mehmet; Department of Physics (2006)
The nonlinear optical properties of semiconductor heterostructures, such as GaAsAl/GaAs alloys, are studied with analytic and numerical methods on the basis of quantum mechanics. Particularly, second and third-order nonlinear optical properties of quantum wells described by the various types of confining potentials are considered within the density matrix formalism. We consider a Pöschl-Teller type potential which has been rarely considered in this area. It has a tunable asymmetry parameter, making it a goo...
Energy preserving integration of bi-Hamiltonian partial differential equations
Karasözen, Bülent (2013-12-01)
The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating waves and solitons. Dispersive properties of the AVF integrator are investigated for the linearized equations to ex...
Citation Formats
H. Farnoudkia and V. Purutçuoğlu Gazi, “Semi-Bayesian Inference of Time Series Chain Graphical Models in Biological Networks,” presented at the International Conference on Innovative Engineering Applications (CIEA’2018) (20 - 22 Eylül 2018), Sivas, Türkiye, 2018, Accessed: 00, 2021. [Online]. Available: