Markov Random Field Model Research Articles

Exploring drought-responsive crucial genes in Sorghum

Drought severely affects global food production. Sorghum is a typical drought-resistant model crop. Based on RNA-seq data for Sorghum with multiple time points and the gray correlation coefficient, this paper firstly selects candidate genes via mean variance test and constructs weighted gene differential co-expression networks (WGDCNs); then, based on guilt-by-rewiring principle, the WGDCNs and the hidden Markov random field model, drought-responsive crucial genes are identified for five developmental stages respectively. Enrichment and sequence alignment analysis reveal that the screened genes may play critical functional roles in drought responsiveness. A multilayer differential co-expression network for the screened genes reveals that Sorghum is very sensitive to pre-flowering drought. Furthermore, a crucial gene regulatory module is established, which regulates drought responsiveness via plant hormone signal transduction, MAPK cascades, and transcriptional regulations. The proposed method can well excavate crucial genes through RNA-seq data, which have implications in breeding of new varieties with improved drought tolerance.

Seasonal Habitat Selection by American White Pelicans

Resource utilization strategies of avian migrants are a major concern for conservation and management. Understanding seasonal habitat selection by migratory birds helps us explain the ongoing continental declines of migratory bird populations. Our objective was to compare the second-order and third-order habitat selection by the American White Pelican (Pelecanus erythrorhynchos; hereafter pelican) between the breeding and non-breeding grounds. We tested the Lack hypothesis that habitat selection by migratory birds is stronger on the breeding grounds than on the non-breeding grounds. We used random-effect Dirichlet-multinomial models to estimate the second-order habitat selection between the seasons with the GPS locations of 32 tracked pelicans. We used Gaussian Markov random field models to estimate the third-order habitat selection by pelicans at the breeding and non-breeding grounds, accounting for spatial autocorrelation. Pelicans strongly selected waterbodies and wetlands at both non-breeding and breeding grounds, tracking their foraging habitats between the seasons at the home range level. However, pelicans exhibited seasonal differences in the strength of the third-order selection of wetlands and waterbodies with foraging habitat selection being stronger at the breeding grounds than at the non-breeding grounds, supporting the Lack hypothesis.

HMRFS–TP: long-term daily gap-free snow cover products over the Tibetan Plateau from 2002 to 2021 based on hidden Markov random field model

Abstract. Snow cover plays an essential role in climate change and the hydrological cycle of the Tibetan Plateau. The widely used Moderate Resolution Imaging Spectroradiometer (MODIS) snow products have two major issues: massive data gaps due to frequent clouds and relatively low estimate accuracy of snow cover due to complex terrain in this region. Here we generate long-term daily gap-free snow cover products over the Tibetan Plateau at 500 m resolution by applying a hidden Markov random field (HMRF) technique to the original MODIS snow products over the past two decades. The data gaps of the original MODIS snow products were fully filled by optimally integrating spectral, spatiotemporal, and environmental information within HMRF framework. The snow cover estimate accuracy was greatly increased by incorporating the spatiotemporal variations of solar radiation due to surface topography and sun elevation angle as the environmental contextual information in HMRF-based snow cover estimation. We evaluated our snow products, and the accuracy is 98.29 % in comparison with in situ observations, and 91.36 % in comparison with high-resolution snow maps derived from Landsat images. Our evaluation also suggests that the incorporation of spatiotemporal solar radiation as the environmental contextual information in HMRF modeling, instead of the simple use of surface elevation as the environmental contextual information, results in the accuracy of the snow products increases by 2.71 % and the omission error decreases by 3.59 %. The accuracy of our snow products is especially improved during snow transitional period, and over complex terrains with high elevation and sunny slopes. The new products can provide long-term and spatiotemporally continuous information of snow cover distribution, which is critical for understanding the processes of snow accumulation and melting, analyzing its impact on climate change, and facilitating water resource management in Tibetan Plateau. This dataset can be freely accessed from the National Tibetan Plateau Data Center at https://doi.org/10.11888/Cryos.tpdc.272204 (Huang and Xu, 2022).

A Holistic Approach for Role Inference and Action Anticipation in Human Teams

The ability to anticipate human actions is critical to many cyber-physical systems, such as robots and autonomous vehicles. Computer vision and sensing algorithms to date have focused on extracting and predicting visual features that are explicit in the scene, such as color, appearance, actions, positions, and velocities, using video and physical measurements, such as object depth and motion. Human actions, however, are intrinsically influenced and motivated by many implicit factors such as context, human roles and interactions, past experience, and inner goals or intentions. For example, in a sport team, the team strategy, player role, and dynamic circumstances driven by the behavior of the opponents, all influence the actions of each player. This article proposes a holistic framework for incorporating visual features, as well as hidden information, such as social roles, and domain knowledge. The approach, relying on a novel dynamic Markov random field (DMRF) model, infers the instantaneous team strategy and, subsequently, the players’ roles that are temporally evolving throughout the game. The results from the DMRF inference stage are then integrated with instantaneous visual features, such as individual actions and position, in order to perform holistic action anticipation using a multi-layer perceptron (MLP). The approach is demonstrated on the team sport of volleyball, by first training the DMRF and MLP offline with past videos, and, then, by applying them to new volleyball videos online. These results show that the method is able to infer the players’ roles with an average accuracy of 86.99%, and anticipate future actions over a sequence of up to 46 frames with an average accuracy of 80.50%. Additionally, the method predicts the onset and duration of each action achieving a mean relative error of 14.57% and 15.67%, respectively.

A Markov random field model with cumulative logistic functions for spatially dependent ordinal data

This paper presents a class of regression models with cumulative logistic functions that are chiefly designed to analyse spatially dependent ordinal data. In contrast to previous works, the proposed model requires neither the sites to be regularly spaced nor the assumption of an underlying continuous variable. It belongs to a more general class of Markov random field models, and can be considered an extension of the ordinal regression model with the proportional odds link function. Our proposed model allows practitioners to interpret the model parameters using odds ratios. Apart from the theoretical developments, this work also highlights the practical aspects of model fitting, including parameterisation, selection of neighbourhood, and calculation of standard errors. Simulation studies with regularly and irregularly spaced sites were conducted. Modelling strategies including pseudo-likelihood methods were found to be useful in both settings. The proposed model and the non-spatial counterpart were applied to the daily air quality index measured in the United Kingdom. The results indicate the presence of spatial effects and the incorporation of spatial effects led to better model performance in terms of various goodness-of-fit measures.

Fitting double hierarchical models with the integrated nested Laplace approximation

Double hierarchical generalized linear models (DHGLM) are a family of models that are flexible enough as to model hierarchically the mean and scale parameters. In a Bayesian framework, fitting highly parameterized hierarchical models is challenging when this problem is addressed using typical Markov chain Monte Carlo (MCMC) methods due to the potential high correlation between different parameters and effects in the model. The integrated nested Laplace approximation (INLA) could be considered instead to avoid dealing with these problems. However, DHGLM do not fit within the latent Gaussian Markov random field (GMRF) models that INLA can fit. In this paper, we show how to fit DHGLM with INLA by combining INLA and importance sampling (IS) algorithms. In particular, we will illustrate how to split DHGLM into submodels that can be fitted with INLA so that the remainder of the parameters are fit using adaptive multiple IS (AMIS) with the aid of the graphical representation of the hierarchical model. This is illustrated using a simulation study on three different types of models and two real data examples.

Stochastic stratigraphic modeling using Bayesian machine learning

Stratigraphic modeling with quantified uncertainty is an open question in engineering geology. In this study, a novel stratigraphic stochastic simulation approach is developed by integrating a Markov random field (MRF) model and a discriminant adaptive nearest neighbor-based k-harmonic mean distance (DANN-KHMD) classifier into a Bayesian framework. The DANN-KHMD classifier is effective for extracting anisotropic patterns from sparse and heterogeneous spatial categorical data such as borehole logs. The MRF parameters can be initially estimated roughly or customized (if site-specific knowledge is available). Later these parameters can be updated and regularized in an unsupervised manner with constraints from site exploration results in a Bayesian manner. Throughout the learning process, both the soil profile and the MRF parameters are updated in a probabilistic manner. The advantages of the proposed approach can be summarized into four points: 1) inferring stratigraphic profile and associated uncertainty in an automatic and fully unsupervised manner; 2) reasonable initial stratigraphic configurations can be sampled and hence lower the computational cost; 3) both stratigraphic uncertainty and model uncertainty are taken into consideration throughout the inferential process; 4) relying on no training stratigraphy images. To illustrate the effectiveness of the developed approach, two synthetic cases and three real-world cases are studied and the advantages of the new approach over existing approaches are demonstrated.

Non-additive image steganographic framework based on variational inference in Markov Random Fields

The majority of image steganography methods lie within the additive scheme that assumes the pixel modifications are independent. Whereas, adapting the embedding modifications based on the mutual embedding impact of neighboring pixels reduce changes in the higher-order statistics of the cover imposed by embedding. However, non-additive schemes are more challenging due to the lack of practical embedding codes that minimize an arbitrary distortion function. In this paper, we propose a general non-additive image steganographic framework based on Markov Random Fields (MRF) which generalizes a few existing research in many aspects and offers an elegant way to model the mutual dependencies between neighborhood modifications in terms of pairwise cliques. The proposed model satisfies spatial coherence by penalizing the desynchronized embedding changes, which orients the changes towards the direction of the majority of changes in the neighbors. Mean Field (MF) inference is used to iteratively estimate the marginal probability at each pixel based on its neighbors so that the original interactions are information projected to the resulting marginals. MF replaces the values of variables with expectations so the result is compatible with practical embedding methods.The proposed framework can be applied to any additive scheme; the initial cost assignment is done by an additive method and MRF modeling defines a non-additive distortion related to statistical detectability that encourages the adjacent changes to synchronize. We study our framework in both symmetric and asymmetric schemes. In the symmetric scheme, a parallel MF is used as an adaptive filter to encourage synchronized embedding changes. The framework can upgrade to an asymmetric scheme that reduces the detectability by conditioning embedding based on the message using clamping exerted in a structural MF. Therefore, our framework is compatible with and generalizes existing non-additive methods, and as shown in experimental results, outperforms the state-of-the-art in both schemes.

ZipHiC: a novel Bayesian framework to identify enriched interactions and experimental biases in Hi-C data.

MotivationSeveral computational and statistical methods have been developed to analyze data generated through the 3C-based methods, especially the Hi-C. Most of the existing methods do not account for dependency in Hi-C data.ResultsHere, we present ZipHiC, a novel statistical method to explore Hi-C data focusing on the detection of enriched contacts. ZipHiC implements a Bayesian method based on a hidden Markov random field (HMRF) model and the Approximate Bayesian Computation (ABC) to detect interactions in two-dimensional space based on a Hi-C contact frequency matrix. ZipHiC uses data on the sources of biases related to the contact frequency matrix, allows borrowing information from neighbours using the Potts model and improves computation speed using the ABC model. In addition to outperforming existing tools on both simulated and real data, our model also provides insights into different sources of biases that affects Hi-C data. We show that some datasets display higher biases from DNA accessibility or Transposable Elements content. Furthermore, our analysis in Drosophila melanogaster showed that approximately half of the detected significant interactions connect promoters with other parts of the genome indicating a functional biological role. Finally, we found that the micro-C datasets display higher biases from DNA accessibility compared to a similar Hi-C experiment, but this can be corrected by ZipHiC.Availability and implementationThe R scripts are available at https://github.com/igosungithub/HMRFHiC.git.Supplementary information Supplementary data are available at Bioinformatics online.

Network assisted analysis of de novo variants using protein-protein interaction information identified 46 candidate genes for congenital heart disease.

De novo variants (DNVs) with deleterious effects have proved informative in identifying risk genes for early-onset diseases such as congenital heart disease (CHD). A number of statistical methods have been proposed for family-based studies or case/control studies to identify risk genes by screening genes with more DNVs than expected by chance in Whole Exome Sequencing (WES) studies. However, the statistical power is still limited for cohorts with thousands of subjects. Under the hypothesis that connected genes in protein-protein interaction (PPI) networks are more likely to share similar disease association status, we developed a Markov Random Field model that can leverage information from publicly available PPI databases to increase power in identifying risk genes. We identified 46 candidate genes with at least 1 DNV in the CHD study cohort, including 18 known human CHD genes and 35 highly expressed genes in mouse developing heart. Our results may shed new insight on the shared protein functionality among risk genes for CHD.

Patterns Simulations Using Gibbs/MRF Auto-Poisson Models

Pattern analysis is the process where characteristics of big data can be recognized using specific methods. Recognition of the data, especially images, can be achieved by applying spatial models, explaining the neighborhood structure of the patterns. These models can be introduced by Markov random field (MRF) models where conditional distribution of the pixels may be defined by a specific distribution. Various spatial models could be introduced, explaining the real patterns of the data; one class of these models is based on the Poisson distribution, called auto-Poisson models. The main advantage of these models is the consideration of the local characteristics of the image. Based on the local analysis, various patterns can be introduced and models that better explain the real data can be estimated, using advanced statistical techniques like Monte Carlo Markov Chains methods. These methods are based on simulations where the proposed distribution must converge to the original (final) one. In this work, an analysis of a MRF model under Poisson distribution would be defined and simulations would be illustrated based on Monte Carlo Markov Chains (MCMC) process like Gibbs sampler. Results would be illustrated using simulated and real patterns data.

Bayesian non‐parametric spatial prior for traffic crash risk mapping: A case study of Victoria, Australia

SummaryWe develop a Bayesian non‐parametric (BNP) model coupled with Markov random fields (MRFs) for risk mapping, to infer homogeneous spatial regions in terms of risks. In contrast to most existing methods, the proposed approach does not require an arbitrary commitment to a specified number of risk classes and determines their risk levels automatically. We consider settings in which the relevant information are counts and propose a so‐called BNP hidden MRF (BNP‐HMRF) model that is able to handle such data. The model inference is carried out using a variational Bayes expectation–maximisation algorithm and the approach is illustrated on traffic crash data in the state of Victoria, Australia. The obtained results corroborate well with the traffic safety literature. More generally, the model presented here for risk mapping offers an effective, convenient and fast way to conduct partition of spatially localised count data.

The node-wise Pseudo-marginal method: model selection with spatial dependence on latent graphs

Motivated by problems from neuroimaging in which existing approaches make use of “mass univariate” analysis which neglects spatial structure entirely, but the full joint modelling of all quantities of interest is computationally infeasible, a novel method for incorporating spatial dependence within a (potentially large) family of model-selection problems is presented. Spatial dependence is encoded via a Markov random field model for which a variant of the pseudo-marginal Markov chain Monte Carlo algorithm is developed and extended by a further augmentation of the underlying state space. This approach allows the exploitation of existing unbiased marginal likelihood estimators used in settings in which spatial independence is normally assumed thereby facilitating the incorporation of spatial dependence using non-spatial estimates with minimal additional development effort. The proposed algorithm can be realistically used for analysis of moderately sized data sets such as 2D slices of whole 3D dynamic PET brain images or other regions of interest. Principled approximations of the proposed method, together with simple extensions based on the augmented spaces, are investigated and shown to provide similar results to the full pseudo-marginal method. Such approximations and extensions allow the improved performance obtained by incorporating spatial dependence to be obtained at negligible additional cost. An application to measured PET image data shows notable improvements in revealing underlying spatial structure when compared to current methods that assume spatial independence.

Development and Application of Information Resources for Education and Teaching of Yarn History Based on 5G Network Technology

Yarn education is a crucial step in producing high-quality textile end products. By offering quick insights into yarn quality, online yarn testing can reduce latency in critical process control, resulting in the manufacture of higher-quality yarns. This paper proposes the development and application of information resources for the education and teaching of yarn history based on fifth-generation (5G) network technologies. Firstly, the yarn database is preprocessed using greyscale transformation and image filtering methods. Secondly, yarn segmentation is implemented using a Multiresolution Markov Random Field (MRMRF) model. Fourier transform and two-scale attention models are used to extract statistical and relative characteristics, respectively. For classifying the yarn photos, we propose using Improved Support Vector Machine (ISVM) classification. The 5G network has been set up, and data is transferred using the Transmission Control Protocol. To enhance the performance, we propose an Improved Particle Swarm Optimization (IPSO) algorithm. The performance of the suggested methodology is analyzed and compared with existing methodologies using the MATLAB simulation tool. The suggested algorithm's classification performance suggests that the 5G framework could provide an accurate, rapid, reliable, and cost-effective solution to industrial automation.

A Markov random field model-based approach for differentially expressed gene detection from single-cell RNA-seq data.

The development of single-cell RNA-sequencing (scRNA-seq) technologies has offered insights into complex biological systems at the single-cell resolution. In particular, these techniques facilitate the identifications of genes showing cell-type-specific differential expressions (DE). In this paper, we introduce MARBLES, a novel statistical model for cross-condition DE gene detection from scRNA-seq data. MARBLES employs a Markov Random Field model to borrow information across similar cell types and utilizes cell-type-specific pseudobulk count to account for sample-level variability. Our simulation results showed that MARBLES is more powerful than existing methods to detect DE genes with an appropriate control of false positive rate. Applications of MARBLES to real data identified novel disease-related DE genes and biological pathways from both a single-cell lipopolysaccharide mouse dataset with 24 381 cells and 11 076 genes and a Parkinson’s disease human data set with 76 212 cells and 15 891 genes. Overall, MARBLES is a powerful tool to identify cell-type-specific DE genes across conditions from scRNA-seq data.

Bayesian Analysis of Social Influence

AbstractThe network influence model is a model for binary outcome variables that accounts for dependencies between outcomes for units that are relationally tied. The basic influence model was previously extended to afford a suite of new dependence assumptions and because of its relation to traditional Markov random field models it is often referred to as the auto logistic actor-attribute model (ALAAM). We extend on current approaches for fitting ALAAMs by presenting a comprehensive Bayesian inference scheme that supports testing of dependencies across subsets of data and the presence of missing data. We illustrate different aspects of the procedures through three empirical examples: masculinity attitudes in an all-male Australian school class, educational progression in Swedish schools, and unemployment among adults in a community sample in Australia.

Analyzing Spatial Transcriptomics Data Using Giotto.

Spatial transcriptomic technologies have been developed rapidly in recent years. The addition of spatial context to expression data holds the potential to revolutionize many fields in biology. However, the lack of computational tools remains a bottleneck that is preventing the broader utilization of these technologies. Recently, we have developed Giotto as a comprehensive, generally applicable, and user-friendly toolbox for spatial transcriptomic data analysis and visualization. Giotto implements a rich set of algorithms to enable robust spatial data analysis. To help users get familiar with the Giotto environment and apply it effectively in analyzing new datasets, we will describe the detailed protocols for applying Giotto without any advanced programming skills. © 2022 Wiley Periodicals LLC. Basic Protocol 1: Getting Giotto set up for use Basic Protocol 2: Pre-processing Basic Protocol 3: Clustering and cell-type identification Basic Protocol 4: Cell-type enrichment and deconvolution analyses Basic Protocol 5: Spatial structure analysis tools Basic Protocol 6: Spatial domain detection by using a hidden Markov random field model Support Protocol 1: Spatial proximity-associated cell-cell interactions Support Protocol 2: Assembly of a registered 3D Giotto object from 2D slices.

Active Sampling for the Quickest Detection of Markov Networks

Consider <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> random variables forming a Markov random field (MRF). The true model of the MRF is unknown, and it is assumed to belong to a binary set. The objective is to sequentially sample the random variables (one-at-a-time) such that the true MRF model can be detected with the fewest number of samples, while in parallel, the decision reliability is controlled. The core element of an optimal decision process is a rule for selecting and sampling the random variables over time. Such a process, at every time instant and adaptively to the collected data, selects the random variable that is expected to be most informative about the model, rendering an overall minimized number of samples required for reaching a reliable decision. The existing studies on detecting MRF structures generally sample the entire network at the same time and focus on designing optimal detection rules without regard to the data-acquisition process. This paper characterizes the sampling process for general MRFs, which is shown to be optimal in the asymptote of large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> . The critical insight in designing the sampling process is devising an information measure that captures the decisions’ inherent statistical dependence over time. Furthermore, when the MRFs can be modeled by acyclic probabilistic graphical models, the sampling rule is shown to take a computationally simple form. Performance analysis for the general case is provided, and the results are interpreted in several special cases: Gaussian MRFs, non-asymptotic regimes, Chernoff’s rule for controlled (active) sensing, and the problem of cluster detection.

Joint dimension reduction and clustering analysis of single-cell RNA-seq and spatial transcriptomics data.

Dimension reduction and (spatial) clustering is usually performed sequentially; however, the low-dimensional embeddings estimated in the dimension-reduction step may not be relevant to the class labels inferred in the clustering step. We therefore developed a computation method, Dimension-Reduction Spatial-Clustering (DR-SC), that can simultaneously perform dimension reduction and (spatial) clustering within a unified framework. Joint analysis by DR-SC produces accurate (spatial) clustering results and ensures the effective extraction of biologically informative low-dimensional features. DR-SC is applicable to spatial clustering in spatial transcriptomics that characterizes the spatial organization of the tissue by segregating it into multiple tissue structures. Here, DR-SC relies on a latent hidden Markov random field model to encourage the spatial smoothness of the detected spatial cluster boundaries. Underlying DR-SC is an efficient expectation-maximization algorithm based on an iterative conditional mode. As such, DR-SC is scalable to large sample sizes and can optimize the spatial smoothness parameter in a data-driven manner. With comprehensive simulations and real data applications, we show that DR-SC outperforms existing clustering and spatial clustering methods: it extracts more biologically relevant features than conventional dimension reduction methods, improves clustering performance, and offers improved trajectory inference and visualization for downstream trajectory inference analyses.

Multi-Agent Reinforcement Learning with Optimal Equivalent Action of Neighborhood

In a multi-agent system, the complex interaction among agents is one of the difficulties in making the optimal decision. This paper proposes a new action value function and a learning mechanism based on the optimal equivalent action of the neighborhood (OEAN) of a multi-agent system, in order to obtain the optimal decision from the agents. In the new Q-value function, the OEAN is used to depict the equivalent interaction between the current agent and the others. To deal with the non-stationary environment when agents act, the OEAN of the current agent is inferred simultaneously by the maximum a posteriori based on the hidden Markov random field model. The convergence property of the proposed methodology proved that the Q-value function can approach the global Nash equilibrium value using the iteration mechanism. The effectiveness of the method is verified by the case study of the top-coal caving. The experiment results show that the OEAN can reduce the complexity of the agents’ interaction description, meanwhile, the top-coal caving performance can be improved significantly.