12 research outputs found
Joint Structure Learning of Multiple Non-Exchangeable Networks
Several methods have recently been developed for joint structure learning of
multiple (related) graphical models or networks. These methods treat individual
networks as exchangeable, such that each pair of networks are equally
encouraged to have similar structures. However, in many practical applications,
exchangeability in this sense may not hold, as some pairs of networks may be
more closely related than others, for example due to group and sub-group
structure in the data. Here we present a novel Bayesian formulation that
generalises joint structure learning beyond the exchangeable case. In addition
to a general framework for joint learning, we (i) provide a novel default prior
over the joint structure space that requires no user input; (ii) allow for
latent networks; (iii) give an efficient, exact algorithm for the case of time
series data and dynamic Bayesian networks. We present empirical results on
non-exchangeable populations, including a real data example from biology, where
cell-line-specific networks are related according to genomic features.Comment: To appear in Proceedings of the Seventeenth International Conference
on Artificial Intelligence and Statistics (AISTATS
Joint estimation of multiple related biological networks
Graphical models are widely used to make inferences concerning interplay in
multivariate systems. In many applications, data are collected from multiple
related but nonidentical units whose underlying networks may differ but are
likely to share features. Here we present a hierarchical Bayesian formulation
for joint estimation of multiple networks in this nonidentically distributed
setting. The approach is general: given a suitable class of graphical models,
it uses an exchangeability assumption on networks to provide a corresponding
joint formulation. Motivated by emerging experimental designs in molecular
biology, we focus on time-course data with interventions, using dynamic
Bayesian networks as the graphical models. We introduce a computationally
efficient, deterministic algorithm for exact joint inference in this setting.
We provide an upper bound on the gains that joint estimation offers relative to
separate estimation for each network and empirical results that support and
extend the theory, including an extensive simulation study and an application
to proteomic data from human cancer cell lines. Finally, we describe
approximations that are still more computationally efficient than the exact
algorithm and that also demonstrate good empirical performance.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A new Bayesian piecewise linear regression model for dynamic network reconstruction
Background: Linear regression models are important tools for learning regulatory networks from gene expression time series. A conventional assumption for non-homogeneous regulatory processes on a short time scale is that the network structure stays constant across time, while the network parameters are time-dependent. The objective is then to learn the network structure along with changepoints that divide the time series into time segments. An uncoupled model learns the parameters separately for each segment, while a coupled model enforces the parameters of any segment to stay similar to those of the previous segment. In this paper, we propose a new consensus model that infers for each individual time segment whether it is coupled to (or uncoupled from) the previous segment. Results: The results show that the new consensus model is superior to the uncoupled and the coupled model, as well as superior to a recently proposed generalized coupled model. Conclusions: The newly proposed model has the uncoupled and the coupled model as limiting cases, and it is able to infer the best trade-off between them from the data
Towards a dynamic view of genetic networks: A Kalman filtering framework for recovering temporally-rewiring stable networks from undersampled data
It is widely accepted that cellular requirements and environmental conditions dictate the architecture of genetic regulatory networks. Nonetheless, the status quo in regulatory network modeling and analysis assumes an invariant network topology over time. We refocus on a dynamic perspective of genetic networks, one that can uncover substantial topological changes in network structure during biological processes such as developmental growth and cancer progression. We propose a novel outlook on the inference of time-varying genetic networks, from a limited number of noisy observations, by formulating the networks estimation as a target tracking problem. Assuming linear dynamics, we formulate a constrained Kalman ltering framework, which recursively computes the minimum mean-square, sparse and stable estimate of the network connectivity at each time point. The sparsity constraint is enforced using the weighted l1-norm; and the stability constraint is incorporated using the Lyapounov stability condition. The proposed constrained Kalman lter is formulated to preserve the convex nature of the problem. The algorithm is applied to estimate the time-varying networks during the life cycle of the Drosophila Melanogaster (fruit fly)
The Local Edge Machine: inference of dynamic models of gene regulation
We present a novel approach, the Local Edge Machine, for the inference of regulatory interactions directly from time-series gene expression data. We demonstrate its performance, robustness, and scalability on in silico datasets with varying behaviors, sizes, and degrees of complexity. Moreover, we demonstrate its ability to incorporate biological prior information and make informative predictions on a well-characterized in vivo system using data from budding yeast that have been synchronized in the cell cycle. Finally, we use an atlas of transcription data in a mammalian circadian system to illustrate how the method can be used for discovery in the context of large complex networks.Department of Applied Mathematic
Non-homogeneous dynamic Bayesian networks with Bayesian regularization for inferring gene regulatory networks with gradually time-varying structure
The proper functioning of any living cell relies on complex networks of gene regulation. These regulatory interactions are not static but respond to changes in the environment and evolve during the life cycle of an organism. A challenging objective in computational systems biology is to infer these time-varying gene regulatory networks from typically short time series of transcriptional profiles. While homogeneous models, like conventional dynamic Bayesian networks, lack the flexibility to succeed in this task, fully flexible models suffer from inflated inference uncertainty due to the limited amount of available data. In the present paper we explore a semi-flexible model based on a piecewise homogeneous dynamic Bayesian network regularized by gene-specific inter-segment information sharing. We explore different choices of prior distribution and information coupling and evaluate their performance on synthetic data. We apply our method to gene expression time series obtained during the life cycle of Drosophila melanogaster, and compare the predicted segmentation with other state-of-the-art techniques. We conclude our evaluation with an application to synthetic biology, where the objective is to predict an in vivo regulatory network of five genes in Saccharomyces cerevisiae subjected to a changing environment
Estimation of dynamic networks for high-dimensional nonstationary time series
This paper is concerned with the estimation of time-varying networks for
high-dimensional nonstationary time series. Two types of dynamic behaviors are
considered: structural breaks (i.e., abrupt change points) and smooth changes.
To simultaneously handle these two types of time-varying features, a two-step
approach is proposed: multiple change point locations are first identified
based on comparing the difference between the localized averages on sample
covariance matrices, and then graph supports are recovered based on a
kernelized time-varying constrained -minimization for inverse matrix
estimation (CLIME) estimator on each segment. We derive the rates of
convergence for estimating the change points and precision matrices under mild
moment and dependence conditions. In particular, we show that this two-step
approach is consistent in estimating the change points and the piecewise smooth
precision matrix function, under certain high-dimensional scaling limit. The
method is applied to the analysis of network structure of the S\&P 500 index
between 2003 and 2008
Post-Regularization Inference for Time-Varying Nonparanormal Graphical Models
We propose a novel class of time-varying nonparanormal graphical models,
which allows us to model high dimensional heavy-tailed systems and the
evolution of their latent network structures. Under this model, we develop
statistical tests for presence of edges both locally at a fixed index value and
globally over a range of values. The tests are developed for a high-dimensional
regime, are robust to model selection mistakes and do not require commonly
assumed minimum signal strength. The testing procedures are based on a high
dimensional, debiasing-free moment estimator, which uses a novel kernel
smoothed Kendall's tau correlation matrix as an input statistic. The estimator
consistently estimates the latent inverse Pearson correlation matrix uniformly
in both the index variable and kernel bandwidth. Its rate of convergence is
shown to be minimax optimal. Our method is supported by thorough numerical
simulations and an application to a neural imaging data set