Markov Random Field Research Articles

Lung Cancer Prevalence in Virginia: A Spatial Zipcode-Level Analysis via INLA.

Examining lung cancer (LC) cases in Virginia (VA) is essential due to its significant public health implications. By studying demographic, environmental, and socioeconomic variables, this paper aims to provide insights into the underlying drivers of LC prevalence in the state adjusted for spatial associations at the zipcode level. We model the available VA zipcode-level LC counts via (spatial) Poisson and negative binomial regression models, taking into account missing covariate data, zipcode-level spatial association and allow for overdispersion. Under latent Gaussian Markov Random Field (GMRF) assumptions, our Bayesian hierarchical model powered by Integrated Nested Laplace Approximation (INLA) considers simultaneous (spatial) imputation of all missing covariates through elegant prediction. The spatial random effect across zip codes follows a Conditional Autoregressive (CAR) prior. Zip codes with elevated smoking indices demonstrated a corresponding increase in LC counts, underscoring the well-established connection between smoking and LC. Additionally, we observed a notable correlation between higher Social Deprivation Index (SDI) scores and increased LC counts, aligning with the prevalent pattern of heightened LC prevalence in regions characterized by lower income and education levels. On the demographic level, our findings indicated higher LC counts in zip codes with larger White and Black populations (with Whites having higher prevalence than Blacks), lower counts in zip codes with higher Hispanic populations (compared to non-Hispanics), and higher prevalence among women compared to men. Furthermore, zip codes with a larger population of elderly people (age ≥ 65 years) exhibited higher LC prevalence, consistent with established national patterns. This comprehensive analysis contributes to our understanding of the complex interplay of demographic and socioeconomic factors influencing LC disparities in VA at the zip code level, providing valuable information for targeted public health interventions and resource allocation. Implementation code is available at GitHub.

SAR image classification using deep features and neighborhood heterogeneity confidence refined spatial constraints

ABSTRACT Recently, frameworks fusing the convolutional neural network (CNN) and Markov random field (MRF) models have been successfully used in synthetic aperture radar (SAR) image classification. Over-smoothing of the details and the incapability to eliminate regional-level misclassification are two common drawbacks of these frameworks, which are caused by the use of conventional neighbourhood consistency based spatial constraints. To address these problems, a neighbourhood heterogeneity confidence – Markov random field (NHC-MRF) and CNN-based framework is proposed for SAR image classification. In this framework, an NHC index is constructed in the binary energy function of the NHC-MRF to refine the conventional spatial constraints by adaptively allowing the existence of heterogeneity in the neighbourhood. The NHC index consists of a label coexisting probability term and a top-2 label term, which are constructed based on the outputs of the CNN. By using the label coexisting probability term, the details can be protected by allowing heterogeneity, and the regional-level misclassification can be eliminated by adjusting the impact of the neighbourhoods by using label coexisting probability based weighting. The top-2 label term is used as a correction of the coexisting probability term considering the disturbance of speckle noise. The NHC-MRF is further fused with a CNN by constructing the unary energy term and initial labels based on the outputs of the CNN. The effectiveness and superiority of the proposed framework are experimentally demonstrated using three SAR datasets. The experimental results demonstrate that the superiority of the NHC-MRF is derived from the simultaneous realization of retaining details and eliminating regional-level misclassification.

Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms

Abstract Ecological analyses typically involve many interacting variables. Ecologists often specify lagged interactions in community dynamics (i.e. vector‐autoregressive models) or simultaneous interactions (e.g. structural equation models), but there is less familiarity with dynamic structural equation models (DSEM) that can include any simultaneous or lagged effect in multivariate time‐series analysis. We propose a novel approach to parameter estimation for DSEM, which involves constructing a Gaussian Markov random field (GMRF) representing simultaneous and lagged path coefficients, and then fitting this as a generalized linear mixed model to missing and/or non‐normal data. We provide a new R‐package dsem, which extends the ‘arrow interface’ from path analysis to represent user‐specified lags when constructing the GMRF. We also outline how the resulting nonseparable precision matrix can generalize existing separable models, for example, for time‐series and species interactions in a vector‐autoregressive model. We first demonstrate dsem by simulating a two‐species vector‐autoregressive model based on wolf–moose interactions on Isle Royale. We show that DSEM has improved precision when data are missing relative to a conventional dynamic linear model. We then demonstrate DSEM via two contrasting case studies. The first identifies a trophic cascade where decreased sunflower starfish has increased urchin and decreased kelp densities, while sea otters have a simultaneous positive effect on kelp in the California Current from 1999 to 2018. The second estimates how declining sea ice has decreased cold‐water habitats, driving a decreased density for fall copepod predation and inhibiting early‐life survival for Alaska pollock from 1963 to 2023. We conclude that DSEM can be fitted efficiently as a GLMM involving missing data, while allowing users to specify both simultaneous and lagged effects in a time‐series structural model. DSEM then allows conceptual models (developed with stakeholder input or from ecological expertise) to be fitted to incomplete time series and provides a simple interface for granular control over the number of estimated time‐series parameters. Finally, computational methods are sufficiently simple that DSEM can be embedded as component within larger (e.g. integrated population) models. We therefore recommend greater exploration and performance testing for DSEM relative to familiar time‐series forecasting methods.

Research on image style transfer based on deep learning

In many fields, image style transfer has been a popular topic. It also has a long history; the earliest examples date back to the previous century. A number of style transfer techniques are currently flourishing, from manual modeling to the use of neural networks. Image style transfer methods is improving and taking less time. This paper is separated into two main categories to analyze based on picture iteration and model iteration - and summarizes the various techniques of image style transfer based on deep learning in accordance with the timeline. This paper introduces maximum mean difference, Markov random field, and deep image analogy in picture iteration-based image style transfer. In terms of model iteration-based image style migration, this paper introduces generative models and image reconstruction decoders. Finally, the paper presents some recommendations and outlook on the future.

Partial Sequence Labeling With Structured Gaussian Processes.

Existing partial sequence labeling models mainly focus on a max-margin framework that fails to provide an uncertainty estimation of the prediction. Furthermore, the unique ground-truth disambiguation strategy employed by these models may include wrong label information for parameter learning. In this article, we propose structured Gaussian processes for partial sequence labeling (SGPPSL), which encodes uncertainty in the prediction and does not need extra effort for model selection and hyperparameter learning. The model employs factor-as-piece approximation that divides the linear-chain graph structure into the set of pieces, which preserves the basic Markov random field structure and effectively avoids handling a large number of candidate output sequences generated by partially annotated data. Then, confidence measure is introduced in the model to address different contributions of candidate labels, which enables the ground-truth label information to be utilized in parameter learning. Based on the derived lower bound of the variational lower bound of the proposed model, variational parameters and confidence measures are estimated in the framework of alternating optimization. Moreover, a weighted Viterbi algorithm is proposed to incorporate confidence measures to sequence prediction, which considers label ambiguity arose from multiple annotations in the training data and thus helps improve the performance. SGPPSL is evaluated on several sequence labeling tasks and the experimental results show the effectiveness of the proposed model.

A Multi-Scale Graph Based on Spatio-Temporal-Radiometric Interaction for SAR Image Change Detection

Change detection (CD) in remote sensing imagery has found broad applications in ecosystem service assessment, disaster evaluation, urban planning, land utilization, etc. In this paper, we propose a novel graph model-based method for synthetic aperture radar (SAR) image CD. To mitigate the influence of speckle noise on SAR image CD, we opt for comparing the structures of multi-temporal images instead of the conventional approach of directly comparing pixel values, which is more robust to the speckle noise. Specifically, we first segment the multi-temporal images into square patches at multiple scales and construct multi-scale K-nearest neighbor (KNN) graphs for each image, and then develop an effective graph fusion strategy, facilitating the exploitation of multi-scale information within SAR images, which offers an enhanced representation of the complex relationships among features in the images. Second, we accomplish the interaction of spatio-temporal-radiometric information between graph models through graph mapping, which can efficiently uncover the connections between multi-temporal images, leading to a more precise extraction of changes between the images. Finally, we use the Markov random field (MRF) based segmentation method to obtain the binary change map. Through extensive experimentation on real datasets, we demonstrate the remarkable superiority of our methodologies by comparing with some current state-of-the-art methods.

A computational model of circRNA-associated diseases based on a graph neural network: prediction and case studies for follow-up experimental validation

BackgroundCircular RNAs (circRNAs) have been confirmed to play a vital role in the occurrence and development of diseases. Exploring the relationship between circRNAs and diseases is of far-reaching significance for studying etiopathogenesis and treating diseases. To this end, based on the graph Markov neural network algorithm (GMNN) constructed in our previous work GMNN2CD, we further considered the multisource biological data that affects the association between circRNA and disease and developed an updated web server CircDA and based on the human hepatocellular carcinoma (HCC) tissue data to verify the prediction results of CircDA.ResultsCircDA is built on a Tumarkov-based deep learning framework. The algorithm regards biomolecules as nodes and the interactions between molecules as edges, reasonably abstracts multiomics data, and models them as a heterogeneous biomolecular association network, which can reflect the complex relationship between different biomolecules. Case studies using literature data from HCC, cervical, and gastric cancers demonstrate that the CircDA predictor can identify missing associations between known circRNAs and diseases, and using the quantitative real-time PCR (RT-qPCR) experiment of HCC in human tissue samples, it was found that five circRNAs were significantly differentially expressed, which proved that CircDA can predict diseases related to new circRNAs.ConclusionsThis efficient computational prediction and case analysis with sufficient feedback allows us to identify circRNA-associated diseases and disease-associated circRNAs. Our work provides a method to predict circRNA-associated diseases and can provide guidance for the association of diseases with certain circRNAs. For ease of use, an online prediction server (http://server.malab.cn/CircDA) is provided, and the code is open-sourced (https://github.com/nmt315320/CircDA.git) for the convenience of algorithm improvement.

Causal inference over stochastic networks.

Claiming causal inferences in network settings necessitates careful consideration of the often complex dependency between outcomes for actors. Of particular importance are treatment spillover or outcome interference effects. We consider causal inference when the actors are connected via an underlying network structure. Our key contribution is a model for causality when the underlying network is endogenous; where the ties between actors and the actor covariates are statistically dependent. We develop a joint model for the relational and covariate generating process that avoids restrictive separability and fixed network assumptions, as these rarely hold in realistic social settings. While our framework can be used with general models, we develop the highly expressive class of Exponential-family Random Network models (ERNM) of which Markov random fields and Exponential-family Random Graph models are special cases. We present potential outcome-based inference within a Bayesian framework and propose a modification to the exchange algorithm to allow for sampling from ERNM posteriors. We present results of a simulation study demonstrating the validity of the approach. Finally, we demonstrate the value of the framework in a case study of smoking in the context of adolescent friendship networks.

Graph signal recovery using variational Bayes in Fourier pairs with Cramér–Rao bounds

In this paper, the graph signal recovery problem is addressed by employing an aggregation of samples in the vertex domain and the Fourier graph transform domain. The statistical graph signal is modeled using a Gaussian Markov Random Field (GMRF). The reconstruction process involves employing a variational Bayes (VB) algorithm, which is a fully Bayesian method that iteratively estimates all unknown parameters by computing the posteriors in a closed-form. Furthermore, the closed-form of the Cramér–Rao lower bound (CRLB) for graph signal estimation is also derived. Simulation results demonstrate the superiority of the proposed algorithm over some of state-of-the-art algorithms in the literature.

Efficient 3D real-time adaptive AUV sampling of a river plume front

The coastal environment faces multiple challenges due to climate change and human activities. Sustainable marine resource management necessitates knowledge, and development of efficient ocean sampling approaches is increasingly important for understanding the ocean processes. Currents, winds, and freshwater runoff make ocean variables such as salinity very heterogeneous, and standard statistical models can be unreasonable for describing such complex environments. We employ a class of Gaussian Markov random fields that learns complex spatial dependencies and variability from numerical ocean model data. The suggested model further benefits from fast computations using sparse matrices, and this facilitates real-time model updating and adaptive sampling routines on an autonomous underwater vehicle. To justify our approach, we compare its performance in a simulation experiment with a similar approach using a more standard statistical model. We show that our suggested modeling framework outperforms the current state of the art for modeling such spatial fields. Then, the approach is tested in a field experiment using two autonomous underwater vehicles for characterizing the three-dimensional fresh-/saltwater front in the sea outside Trondheim, Norway. One vehicle is running an adaptive path planning algorithm while the other runs a preprogrammed path. The objective of adaptive sampling is to reduce the variance of the excursion set to classify freshwater and more saline fjord water masses. Results show that the adaptive strategy conducts effective sampling of the frontal region of the river plume.

Identifying the latent relationships between factors associated with traffic crashes through graphical models

Traffic safety field has been oriented toward finding the relationships between crash outcomes and predictor variables to understand crash phenomena and/or predict future crashes. In the literature, the main framework established for this purpose is based on constructing a modelling equation in which crash outcome (e.g., frequencies) is examined in relation to explanatory variables chosen based on the problem at hand. Despite the importance and success of this approach, there are two issues that are generally not discussed: 1) the latent relationships between factors associated with crashes are oftentimes not the focus of analysis or not observed; and 2) there are not many tools to make informed decisions on which variables might have an impact on the crash outcome and should be included in a safety model, particularly when observations are limited. To address these issues, this paper proposes the use of graphical models, namely a Markov random field (MRF) modelling, Bayesian network modelling, and a graphical XGBoost approach, to disclose relationship topologies of explanatory variables leading to fatal and incapacitating injury pedestrian crashes. The application of graph learning models in traffic safety has a high potential because they are not only useful to understand the mechanism behind the crash occurrence but also can assist in devising accurate and reliable prevention measures by identifying the true variable structure and essential factors jointly acting towards crash occurrence, similar to a pathological examination.

Automatic detection of myocardial ischaemia using generalisable spatio-temporal hierarchical Bayesian modelling of DCE-MRI

Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) can be used as a non-invasive method for the assessment of myocardial perfusion. The acquired images can be utilised to analyse the spatial extent and severity of myocardial ischaemia (regions with impaired microvascular blood flow). In the present paper, we propose a novel generalisable spatio-temporal hierarchical Bayesian model (GST-HBM) to automate the detection of ischaemic lesions and improve the in silico prediction accuracy by systematically integrating spatio-temporal context information. We present a computational inference procedure with an adequate trade-off between accuracy and computational efficiency, whereby model parameters are sampled from the posterior distribution with Gibbs sampling, while lower-level hyperparameters are selected using model selection strategies based on the Watanabe Akaike information criterion (WAIC). We have assessed our method on both synthetic (in silico) data with known gold-standard and 12 sets of clinical first-pass myocardial perfusion DCE-MRI datasets. We have also carried out a comparative performance evaluation with four established alternative methods: Gaussian mixture model (GMM), opening and closing operations based on Gaussian mixture model (GMMC&Omax), Markov random field constrained Gaussian mixture model (GMM-MRF) and model-based hierarchical Bayesian model (M-HBM). Our results show that the proposed GST-HBM method achieves much higher in silico prediction accuracy than the established alternative methods. Furthermore, this method appears to provide a more robust delineation of ischaemic lesions in datasets affected by spatially variant noise.

MicroNet-MIMRF: a microbial network inference approach based on mutual information and Markov random fields.

The human microbiome, comprises complex associations and communication networks among microbial communities, which are crucial for maintaining health. The construction of microbial networks is vital for elucidating these associations. However, existing microbial networks inference methods cannot solve the issues of zero-inflation and non-linear associations. Therefore, necessitating novel methods to improve the accuracy of microbial networks inference. In this study, we introduce the Microbial Network based on Mutual Information and Markov Random Fields (MicroNet-MIMRF) as a novel approach for inferring microbial networks. Abundance data of microbes are modeled through the zero-inflated Poisson distribution, and the discrete matrix is estimated for further calculation. Markov random fields based on mutual information are used to construct accurate microbial networks. MicroNet-MIMRF excels at estimating pairwise associations between microbes, effectively addressing zero-inflation and non-linear associations in microbial abundance data. It outperforms commonly used techniques in simulation experiments, achieving area under the curve values exceeding 0.75 for all parameters. A case study on inflammatory bowel disease data further demonstrates the method's ability to identify insightful associations. Conclusively, MicroNet-MIMRF is a powerful tool for microbial network inference that handles the biases caused by zero-inflation and overestimation of associations. The MicroNet-MIMRF is provided at https://github.com/Fionabiostats/MicroNet-MIMRF.

Synthetic aperture radar image segmentation with quantum annealing

AbstractIn image processing, image segmentation is the process of partitioning a digital image into multiple image segments. Among state‐of‐the‐art methods, Markov random fields can be used to model dependencies between pixels and achieve a segmentation by minimising an associated cost function. Currently, finding the optimal set of segments for a given image modelled as a Markov random fields appears to be NP‐hard. The authors aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of synthetic aperture radar images. For that purpose, the authors propose a hybrid quantum annealing classical optimisation expectation maximisation algorithm to obtain optimal sets of segments. After proposing suitable formulations, the authors discuss the performances and the scalability of authors’ approach on the D‐Wave quantum computer. The authors also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimisation problems.

Identifying Latent Groups in Spatial Panel Data Using a Markov Random Field Constrained Product Partition Model

Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.

Sensitivity analysis of the PC hyperprior for range and standard deviation components in Bayesian Spatiotemporal high-resolution prediction: An application to PM2.5 prediction in Jakarta, Indonesia

The Gaussian Markov Random Field (GMRF) is widely acknowledged for its remarkable flexibility, especially in the realm of high-resolution prediction, when compared to conventional Kriging methods. Rooted in the fundamental principles of Bayesian estimation, this methodology underscores the importance of a meticulous examination of prior and hyperprior distributions, along with their corresponding parameter values. Sensitivity analyses are crucial for evaluating the potential impact of these distributions and parameter values on prediction results. To determine the most effective values for hyperprior parameters, an iterative trial-and-error approach is commonly employed. In our research, we systematically assessed a variety of parameter values through exhaustive cross-validation. Our study is focused on optimizing hyperprior parameter values, with a particular emphasis on Penalized Complexity (PC). We applied our method to conduct spatiotemporal high-resolution predictions of PM2.5 concentrations in Jakarta province, Indonesia. Achieving accurate predictive modeling of PM2.5 concentrations in Jakarta is contingent upon this optimization. We identified that the optimal values for PC hyperprior parameters, with a range of less than 2,000 and a hyperprior standard deviation greater than 1 with a 0.1 probability, yield the most accurate predictions. These parameter values result in the minimum mean absolute percentage error (MAPE) of 19.35393, along with a deviation information criterion (DIC) of -154.23. Our findings highlight that the standard deviation parameter significantly influences model fit compared to the relatively insignificant impact of the range parameter. When coupled with high-resolution mapping, these optimized parameters facilitate a comprehensive understanding of distribution patterns. This process aids in detecting areas particularly susceptible to risks, thereby enhancing decision-making efficacy regarding air quality management.

GCN-Based Encoder-Decoder Networks With Markov Random Field for Unsupervised Community Detection

GCN-Based Encoder-Decoder Networks With Markov Random Field for Unsupervised Community Detection

Coastline Detection in Polarimetric SAR Images Based on Freeman Decomposition and Three-Region Markov Random Field Segmentation

Coastline Detection in Polarimetric SAR Images Based on Freeman Decomposition and Three-Region Markov Random Field Segmentation

Power Line Detection for Aerial Images Using Object-Based Markov Random Field With Discrete Multineighborhood System

Power Line Detection for Aerial Images Using Object-Based Markov Random Field With Discrete Multineighborhood System

Hierarchical Self-Learning Knowledge Inference Based on Markov Random Field for Semantic Segmentation of Remote Sensing Images

Hierarchical Self-Learning Knowledge Inference Based on Markov Random Field for Semantic Segmentation of Remote Sensing Images