Bayesian probabilistic network modeling from multiple independent replicates

Often protein (or gene) time-course data are collected for multiple replicates. Each replicate generally has sparse data with the number of time points being less than the number of proteins. Usually each replicate is modeled separately. However, here all the information in each of the replicates is used to make a composite inference about signal networks. The composite inference comes from combining well structured Bayesian probabilistic modeling with a multi-faceted Markov Chain Monte Carlo algorithm. Based on simulations which investigate many different types of network interactions and experimental variabilities, the composite examination uncovers many important relationships within the networks. In particular, when the edge's partial correlation between two proteins is at least moderate, then the composite's posterior probability is large

Nonparametric Bayes Modeling of Populations of Networks

Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly characterize the probabilistic generative mechanism underlying these network-valued data. Available models for a single network are not designed specifically for inference on the entire probability mass function of a network-valued random variable and therefore lack flexibility in characterizing the distribution of relevant topological structures. We propose a flexible Bayesian nonparametric approach for modeling the population distribution of network-valued data. The joint distribution of the edges is defined via a mixture model which reduces dimensionality and efficiently incorporates network information within each mixture component by leveraging latent space representations. The formulation leads to an efficient Gibbs sampler and provides simple and coherent strategies for inference and goodness-of-fit assessments. We provide theoretical results on the flexibility of our model and illustrate improved performance --- compared to state-of-the-art models --- in simulations and application to human brain networks

Towards a Multi-Subject Analysis of Neural Connectivity

Directed acyclic graphs (DAGs) and associated probability models are widely used to model neural connectivity and communication channels. In many experiments, data are collected from multiple subjects whose connectivities may differ but are likely to share many features. In such circumstances it is natural to leverage similarity between subjects to improve statistical efficiency. The first exact algorithm for estimation of multiple related DAGs was recently proposed by Oates et al. 2014; in this letter we present examples and discuss implications of the methodology as applied to the analysis of fMRI data from a multi-subject experiment. Elicitation of tuning parameters requires care and we illustrate how this may proceed retrospectively based on technical replicate data. In addition to joint learning of subject-specific connectivity, we allow for heterogeneous collections of subjects and simultaneously estimate relationships between the subjects themselves. This letter aims to highlight the potential for exact estimation in the multi-subject setting.Comment: to appear in Neural Computation 27:1-2

Scalable Population Synthesis with Deep Generative Modeling

Population synthesis is concerned with the generation of synthetic yet realistic representations of populations. It is a fundamental problem in the modeling of transport where the synthetic populations of micro-agents represent a key input to most agent-based models. In this paper, a new methodological framework for how to 'grow' pools of micro-agents is presented. The model framework adopts a deep generative modeling approach from machine learning based on a Variational Autoencoder (VAE). Compared to the previous population synthesis approaches, including Iterative Proportional Fitting (IPF), Gibbs sampling and traditional generative models such as Bayesian Networks or Hidden Markov Models, the proposed method allows fitting the full joint distribution for high dimensions. The proposed methodology is compared with a conventional Gibbs sampler and a Bayesian Network by using a large-scale Danish trip diary. It is shown that, while these two methods outperform the VAE in the low-dimensional case, they both suffer from scalability issues when the number of modeled attributes increases. It is also shown that the Gibbs sampler essentially replicates the agents from the original sample when the required conditional distributions are estimated as frequency tables. In contrast, the VAE allows addressing the problem of sampling zeros by generating agents that are virtually different from those in the original data but have similar statistical properties. The presented approach can support agent-based modeling at all levels by enabling richer synthetic populations with smaller zones and more detailed individual characteristics.Comment: 27 pages, 15 figures, 4 table