Generative Flow Networks (GFlowNets), a class of generative models over discrete and structured sample spaces, have been previously applied to the problem of inferring the marginal posterior distribution over the directed acyclic graph (DAG) of a Bayesian Network, given a dataset of observations. Based on recent advances extending this framework to non-discrete sample spaces, we propose in this paper to approximate the joint posterior over not only the structure of a Bayesian Network, but also the parameters of its conditional probability distributions. We use a single GFlowNet whose sampling policy follows a two-phase process: the DAG is first generated sequentially one edge at a time, and then the corresponding parameters are picked once the full structure is known. Since the parameters are included in the posterior distribution, this leaves more flexibility for the local probability models of the Bayesian Network, making our approach applicable even to non-linear models parametrized by neural networks. We show that our method, called JSP-GFN, offers an accurate approximation of the joint posterior, while comparing favorably against existing methods on both simulated and real data.
Yale School of Public Health（耶鲁大学公共卫生学院）；University of Washington（华盛顿大学）；Ohio State University（俄亥俄州立大学）
In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shrinkage and model selection simultaneously. We develop an EM algorithm that performs fast and dynamic explorations of posterior modes. Our approach selects sparse models efficiently with substantially smaller bias than would be induced by alternative regularization procedures. The…
University of Edinburgh（爱丁堡大学）；Pharmatics Ltd（Pharmatics有限公司）
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bayesian inference of sparse structures of Gaussian graphical models (GGMs). One is based on a simple modification of the cutting-edge block Gibbs sampler for sparse GGMs, which results in significant computational gains in high dimensions. The other method is based on a specific co…
In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain insights in the nature of the unidentifiability inherent in such models, the way posterior densities will be sensitive to prior densities and the typical geometrical form these posterior densities might take. Many of these insights carry over into more complicated Bayesian networks with systematic missing data.
Tsinghua University（清华大学）；University of Amsterdam（阿姆斯特丹大学）；Canadian Institute for Advanced Research（加拿大高等研究院）
We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of generative adversarial networks on learning expressive dependency functions. We introduce a structured recognition model to infer the posterior distribution of latent variables given observations. We generalize the Expectation Propagation (EP) algorithm to learn the generative model and recognition model jointly. Finally, we present two important instances of Gr…
A new Bayesian modeling method is proposed by combining the maximization of the marginal likelihood with a momentum-space renormalization group transformation for Gaussian graphical models. Moreover, we present a scheme for computint the statistical averages of hyperparameters and mean square errors in our proposed method based on a momentumspace renormalization transformation.
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov Chain Monte Carlo) schemes giving the correct equilibrium distribution over parameters. While this intractability, due to the partition function, is familiar to those performing parameter optimisation, Bayesian learning of posterior distributions over undirected model parameters has been unexplored and poses novel challenges. we propose several approximate MC…
In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emphasis is then placed on the Bayesian model averaging which takes full account of the class-specific model uncertainty by averaging over the posterior graph model probabilities. An explicit evaluation of the model probabilities is well known to be infeasible. To address this issue…
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks with several families of local distributions, are curved exponential families (CEFs) and graphical models with hidden variables are stratified exponential families (SEFs). An SEF is a finite union of CEFs satisfying a frontier condition. In addition, we illustrate how one can aut…
University of Alberta（阿尔伯塔大学）；University of Waterloo（滑铁卢大学）
We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum margin Markov networks. The main difficulty is that the parameters in a Bayesian network must satisfy additional normalization constraints that an undirected graphical model need not respect. These additional constraints complicate the optimization task. Nevertheless, we derive an effective training algorithm that solves the maximum margin training problem for …
In Bayesian learning of Gaussian graphical model structure, it is common to restrict attention to certain classes of graphs and approximate the posterior distribution by repeatedly moving from one graph to another, using MCMC or methods such as stochastic shotgun search (SSS). I give two corrected versions of an algorithm for non-decomposable graphs and discuss random graph distributions, in particular as prior distributions. The main topic of the thesis is Bayesian structure-learning with forests or trees. Restricting attention to these graphs can be justified using theorems on random graphs.…
It is common practice in using regression type models for inferring causal effects, that inferring the correct causal relationship requires extra covariates are included or ``adjusted for''. Without performing this adjustment erroneous causal effects can be inferred. Given this phenomenon it is common practice to include as many covariates as possible, however such advice comes unstuck in the presence of M-bias. M-Bias is a problem in causal inference where the correct estimation of treatment effects requires that certain variables are not adjusted for i.e. are simply neglected from inclusion …
Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes enormous, rendering even state-of-the-art Bayesian stochastic search computationally infeasible. We propose a deterministic alternative to estimate Gaussian and Gaussian copula graphical models using an Expectation Conditional Maximization (ECM) algorithm, extending the EM approach from Bayesian variable selection to graphical model estimation. We show that the …
We propose a new probabilistic graphical model that jointly models the difficulties of questions, the abilities of participants and the correct answers to questions in aptitude testing and crowdsourcing settings. We devise an active learning/adaptive testing scheme based on a greedy minimization of expected model entropy, which allows a more efficient resource allocation by dynamically choosing the next question to be asked based on the previous responses. We present experimental results that confirm the ability of our model to infer the required parameters and demonstrate that the adaptive te…
Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible functions from scalars to vectors. In this work, we revisit these transformations as probabilistic graphical models, showing they reduce to Bayesian networks with a pre-defined topology and a learnable density at each node. From this new perspective, we propose the graphical normalizing flow, a new invertible transformation with either a prescribed or a lear…
We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic process and represents an important tool in many fields. We propose an empirical Bayes estimator of sparse autoregressive graphical models and latent-variable autoregressive graphical models. Numerical experiments show the benefit to take this Bayesian perspective for learning these types of graphical models.
We consider the problem of change-point detection in multivariate time-series. The multivariate distribution of the observations is supposed to follow a graphical model, whose graph and parameters are affected by abrupt changes throughout time. We demonstrate that it is possible to perform exact Bayesian inference whenever one considers a simple class of undirected graphs called spanning trees as possible structures. We are then able to integrate on the graph and segmentation spaces at the same time by combining classical dynamic programming with algebraic results pertaining to spanning trees.…
Graphical models, used to express conditional dependence between random variables observed at various nodes, are used extensively in many fields such as genetics, neuroscience, and social network analysis. While most current statistical methods for estimating graphical models focus on scalar data, there is interest in estimating analogous dependence structures when the data observed at each node are functional, such as signals or images. In this paper, we propose a fully Bayesian regularization scheme for estimating functional graphical models. We first consider a direct Bayesian analog of the…
We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be intractable without any restriction on the considered graphs, so we limit our exploration to mixtures of spanning trees. We consider the inference of the structure of an undirected graphical model in a Bayesian framework. To avoid convergence issues and highly demanding Monte Carlo sampling, we focus on exact inference. More specifically we aim at achieving the i…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors of exact and approximate message-passing algorithms that arise in a sequential change point detection problem formulated via a latent variable directed graphical model. The sequential inference algorithm and its supporting theory are illustrated by simulated examples.
Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the $\ell_2$ penalty enjoys a smaller computational footprint in GGM estimation, whilst the $\ell_1$ penalty encourages sparsity in the estimand. The Bayesian adaptive graphical lasso prior is used as a departure point in the formulation of a computationally efficient graphical ridge-type prior for events where accurate associations are prioritised over sparse representations. A novel block Gibbs sample…
We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs to vary over the functional domain. The model involves estimation of graphical models that evolve functionally in a nonparametric fashion while accounting for within-functional correlations and borrowing strength across functional positions so contiguous locations are encouraged but not forced to have similar graph structure and edge strength. We utilize a st…
This paper deals with the Bayesian estimation of high dimensional Gaussian graphical models. We develop a quasi-Bayesian implementation of the neighborhood selection method of Meinshausen and Buhlmann (2006) for the estimation of Gaussian graphical models. The method produces a product-form quasi-posterior distribution that can be efficiently explored by parallel computing. We derive a non-asymptotic bound on the contraction rate of the quasi-posterior distribution. The result shows that the proposed quasi-posterior distribution contracts towards the true precision matrix at a rate given by th…
This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on the interaction parameters calculated within marginal distributions. We undertake a comprehensive Bayesian analysis of these models, involving suitable choices of prior distributions, estimation, model determination, as well as the allied computational issues. The methodology is illustrated with reference to two real data sets.
A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations. We consider a Bayesian approach to inference in a nonparanormal graphical model in which we put priors on the unknown transformations through a random series based on B-splines. We use a regression formulation to construct the likelihood through the Cholesky decomposition on the underlying precision matrix of the transformed variables and put …
This work introduces a Bayesian methodology for fitting large discrete graphical models with spike-and-slab priors to encode sparsity. We consider a quasi-likelihood approach that enables node-wise parallel computation resulting in reduced computational complexity. We introduce a scalable Langevin MCMC algorithm for sampling from the quasi-posterior distribution which enables variable selection and estimation simultaneously. We present extensive simulation results to demonstrate scalability and accuracy of the method. We also analyze the 16 Personality Factors (PF) dataset to illustrate perfor…
We consider the problem of learning the structure of a high dimensional precision matrix under sparsity assumptions. We propose to use a shrinkage prior, called the DL-graphical prior based on the Dirichlet-Laplace prior used for the Gaussian mean problem. A posterior sampling scheme based on Gibbs sampling is also provided along with theoretical guarantees of the method by obtaining the posterior convergence rate of the precision matrix.
Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the…
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Two, a Bayesian network can be used to learn causal relationships, and hence can be used to gain understanding about a problem domain and to predict the consequences of intervention. Three, because the model has both a causal and probabilisti…
This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class covariance, which is proportional to the between-class covariance in the conjugate prior. The scalar proportionality constant is the only plugin parameter. All other model parameters are intergated out in closed form. An expression is given for the model evidence, which can be used to make plugin estimates for the proportionality constant. Pattern recognition is done …
The structure of a Bayesian network includes a great deal of information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study its variability, which can be used to compare the performance of different learning algorithms and to measure the strength of any arbitrary subset of arcs. In this paper we will introduce some descriptive statistics and the corresponding parametric and Monte Carlo tests on the undirected graph underlying the structure of a Bayesian network, modeled as a multivariate …
Variable clustering is important for explanatory analysis. However, only few dedicated methods for variable clustering with the Gaussian graphical model have been proposed. Even more severe, small insignificant partial correlations due to noise can dramatically change the clustering result when evaluating for example with the Bayesian Information Criteria (BIC). In this work, we try to address this issue by proposing a Bayesian model that accounts for negligible small, but not necessarily zero, partial correlations. Based on our model, we propose to evaluate a variable clustering result using …
Carbon capture and storage (CCS) can aid decarbonization of the atmosphere to limit further global temperature increases. A framework utilizing unsupervised learning is used to generate a range of subsurface geologic volumes to investigate potential sites for long-term storage of carbon dioxide. Generative adversarial networks are used to create geologic volumes, with a further neural network used to sample the posterior distribution of a trained Generator conditional to sparsely sampled physical measurements. These generative models are further conditioned to historic dynamic fluid flow data …
Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for continuous variables where it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations on each of them. We consider a Bayesian approach in the nonparanormal graphical model by putting priors on the unknown transformations through a random series based on B-splines where the coefficients are ordere…
Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality assumption may be restrictive in many settings. A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables where it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformation. We consider a Bayesian approach for the nonparanormal graphic…
Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices and they are generated under a multivariate normal joint distribution. However, they suffer from several shortcomings since they are based on Gaussian distribution assumptions. In this article, we propose a Bayesian quantile based approach for sparse estimation of graphs. We demonstrate that th…
Department of Statistics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校统计学系）
We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian standpoint, we investigate the MAP (maximum a posteriori) estimator from a penalized likelihood perspective that gives rise to a new non-convex penalty approximating the $\ell_0$ penalty. Optimal error rates for estimation consistency in terms of various matrix norms along with selection consistency for sparse structure recovery are shown for the unique MAP estimator …
A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs. For this prior the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional independence between random functions, and construct a framework for Bayesian inference of undirected, decomposable graphs in the multivariate functional data context. This framework is based on extending Markov distributions and hyper Markov laws from random variables to random processes, providing a principled alternative to naive application of multivariate m…
Vector autoregression model is ubiquitous in classical time series data analysis. With the rapid advance of social network sites, time series data over latent graph is becoming increasingly popular. In this paper, we develop a novel Bayesian grouped network autoregression model to simultaneously estimate group information (number of groups and group configurations) and group-wise parameters. Specifically, a graphically assisted Chinese restaurant process is incorporated under framework of the network autoregression model to improve the statistical inference performance. An efficient Markov cha…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience and the social sciences. This work develops a Bayesian approach that decomposes the model parameters across the multiple graphical models into shared components across subsets of models and edges, and idiosyncratic ones. Further, it leverages a novel multivariate prior distribution, coupled with a pseudo-likelihood that enables fast computations through a robu…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either no sparsity, sparsity, group sparsity or even sparse-group sparsity for a bi-level selection through partial correlations (direct links) between predictors and responses, thanks to spike-and-slab priors corresponding to each setting. Adaptative and global shrinkages are also incorporated in the Bayesian modeling of the direct links. An existing result for mo…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and conditional independence structures between variables by multiple testing of hypotheses. Specifically, we introduce closed-form Bayes factors under the Gaussian conjugate model to evaluate the null hypotheses of marginal and conditional independence between variables. Their computation for all pairs of variables is shown to be extremely efficient, thereby allowing…
Distributed estimation methods have recently been used to compute the maximum likelihood estimate of the precision matrix for large graphical Gaussian models. Our aim, in this paper, is to give a Bayesian estimate of the precision matrix for large graphical Gaussian models with, additionally, symmetry constraints imposed by an underlying graph which is coloured. We take the sample posterior mean of the precision matrix as our estimate. We study its asymptotic behaviour under the regular asymptotic regime when the number of variables p is fixed and under the double asymptotic regime when both p…
Although the block Gibbs sampler for the Bayesian graphical LASSO proposed by Wang (2012) has been widely applied and extended to various shrinkage priors in recent years, it has a less noticeable but possibly severe disadvantage that the positive definiteness of a precision matrix in the Gaussian graphical model is not guaranteed in each cycle of the Gibbs sampler. Specifically, if the dimension of the precision matrix exceeds the sample size, the positive definiteness of the precision matrix will be barely satisfied and the Gibbs sampler will almost surely fail. In this paper, we propose mod…
Probabilistic Graphical Model using Graph Neural Networks for Bayesian Inversion of Discrete Structural Component States
Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology（工信部智能防灾减灾重点实验室）；Harbin Institute of Technology（哈尔滨工业大学）；Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, School of Civil Engineering, Harbin, Institute of Technology（教育部结构动力行为与控制重点实验室，土木工程学院）；The Institute of Statistical Mathematics, Research Organization of Information and Systems（统计数学研究所，信息与系统研究机构）；The Graduate University for Advanced Studies, SOKENDAI（高等研究大学，SOKENDAI）；Division of Engineering and Applied Science, California Institute of Technology（工程与应用科学系，加州理工学院）
We consider a class of colored graphical Gaussian models obtained by placing symmetry constraints on the precision matrix in a Bayesian framework. The prior distribution on the precision matrix is the colored $G$-Wishart prior which is the Diaconis-Ylvisaker conjugate prior. In this paper, we develop a computationally efficient model search algorithm which combines linear regression with a double reversible jump Markov chain Monte Carlo (MCMC) method. The latter is to estimate the Bayes factors expressed as the ratio of posterior probabilities of two competing models. We also establish the asy…
Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wishart. With this prior, the transition probabilities in the search algorithms necessitate evaluating the ratios of the prior normalizing constants of G-Wishart. In moderate to high-dimensions, this ratio is often approximated using sampling-based methods as computationally expensiv…
Managing a large-scale portfolio with many assets is one of the most challenging tasks in the field of finance. It is partly because estimation of either covariance or precision matrix of asset returns tends to be unstable or even infeasible when the number of assets $p$ exceeds the number of observations $n$. For this reason, most of the previous studies on portfolio management have focused on the case of$ p < n$. To deal with the case of $p > n$, we propose to use a new Bayesian framework based on adaptive graphical LASSO for estimating the precision matrix of asset returns in a large-scale …
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and computer security, etc. Despite of their generic applicability and wide adoptance, the constraints imposed by undirected graphical models and Bayesian networks have also been recognized to be unnecessarily stringent under certain circumstances. This observation has led to the proposal of several generalizations that aim at more relaxed constraints by which …
Dupuytren disease is a fibroproliferative disorder with unknown etiology that often progresses and eventually can cause permanent contractures of the affected fingers. In this paper, we provide a computationally efficient Bayesian framework to discover potential risk factors and investigate which fingers are jointly affected. Our Bayesian approach is based on Gaussian copula graphical models, which are one potential way to discover the underlying conditional independence structure of variables in multivariate mixed data. In particular, we combine the semiparametric Gaussian copula with extende…
We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious parameterization of the precision matrix, which is essential in several applications involving learning relationships among the variables. In this context, we introduce a novel type of selection prior that develops a sparse structure on the precision matrix by making most of the elements exactly zero, in addition to ensuring positive definiteness -- thus cond…
Northeastern University（东北大学）；Mitsubishi Electric Research Laboratories (MERL)（三菱电机研究实验室（MERL））
Learning data representations that capture task-related features, but are invariant to nuisance variations remains a key challenge in machine learning. We introduce an automated Bayesian inference framework, called AutoBayes, that explores different graphical models linking classifier, encoder, decoder, estimator and adversarial network blocks to optimize nuisance-invariant machine learning pipelines. AutoBayes also enables learning disentangled representations, where the latent variable is split into multiple pieces to impose various relationships with the nuisance variation and task labels. …
Probabilistic graphical models are powerful tools which allow us to formalise our knowledge about the world and reason about its inherent uncertainty. There exist a considerable number of methods for performing inference in probabilistic graphical models; however, they can be computationally costly due to significant time burden and/or storage requirements; or they lack theoretical guarantees of convergence and accuracy when applied to large scale graphical models. To this end, we propose the Universal Marginaliser Importance Sampler (UM-IS) -- a hybrid inference scheme that combines the flexi…
A goal of systems biology is to understand the dynamics of intracellular systems. Stochastic chemical kinetic models are often utilized to accurately capture the stochastic nature of these systems due to low numbers of molecules. Collecting system data allows for estimation of stochastic chemical kinetic rate parameters. We describe a well-known, but typically impractical data augmentation Markov chain Monte Carlo algorithm for estimating these parameters. The impracticality is due to the use of rejection sampling for latent trajectories with fixed initial and final endpoints which can have di…
Differential networks (DN) are important tools for modeling the changes in conditional dependencies between multiple samples. A Bayesian approach for estimating DNs, from the classical viewpoint, is introduced with a computationally efficient threshold selection for graphical model determination. The algorithm separately estimates the precision matrices of the DN using the Bayesian adaptive graphical lasso procedure. Synthetic experiments illustrate that the Bayesian DN performs exceptionally well in numerical accuracy and graphical structure determination in comparison to state-of-the-art met…
