Markov Conditional Random Fields Research Articles

CO-OCCURRENCE OF MOSQUITO COMMUNITIES IN DISTURBED ENVIRONMENTS USING MARKOV RANDOM FIELDS (MRFs) IN ST. JOHNS COUNTY, FLORIDA

The distribution of mosquito communities is predicted by complex micro- and macrohabitat systems. While macrohabitat variables are significant in modeling the distribution of individual mosquito species, the distribution of mosquito communities in disturbed urban and semi-urban environmental gradients was overlooked in most of the previous models. In our study, we used conditional Markov Random Fields (CRF) to evaluate spatial co-occurrence patterns between mosquito vectors of eastern equine encephalitis (EEEV) and west Nile virus (WNV) in a disturbed urban environment in Saint John’s County, Florida. We aimed to 1) quantify the strength and direction of spatial unconditional and conditional correlations between mosquito assemblages in disturbed environments, and 2) evaluate whether the strength of correlations between mosquito assemblages is conditional on landscape or climate variables. We leveraged the longitudinal surveillance effort using Biogents sentinel traps (BGS) conducted by Anastasia Mosquito Control Districts in disturbed urban environments during 2017-2020. The distribution of high mosquito abundance, especially Aedes albopictus, Ae. aegypti, Ae. vexans, Ae. taeniorhynchus, Culex nigripalpus, Cx. salinarius, and Cx. quinquefasciatus, were conditionally correlated with other EEEV and WNV vector species in reduced woody and herbaceous wetlands and evergreen forests (-54.44%), and in urban developed landscapes (3.44%) during 2019 and 2020. Moreover, conditional correlations between mosquito species pairs were positively associated with increased total precipitation and in areas with high average minimum and maximum temperatures. Our results show that the micro- and macrohabitat characteristics demonstrated spatial effects on distribution and correlations between species pairs of EEEV and WNV mosquito vectors across disturbed environments. Our findings could be used to better understand the joint effects of drivers on mosquito diversity at a specific locality, interspecific interactions among mosquito assemblages, and how this diversity changes across environmental gradients.

Refinements of Approximation Results of Conditional Restricted Boltzmann Machines.

Conditional restricted Boltzmann machines (CRBMs) are the conditional variant of restricted Boltzmann machines (RBMs), which are used to simulate conditional probability distributions. While promising for practical applications, there is a lack of theoretical studies on the approximation ability of CRBMs. In this article, by contributing analysis tools, especially designed for the conditional models, we improve the results of the representational power of CRBMs based on existing work on RBMs. We first study the properties of CRBMs to approximate conditional Markov random fields. On this basis, a universal approximation result is obtained by deriving upper bounds on the minimal number of hidden units, which improves the previous result. Furthermore, the result about maximal approximation errors of CRBMs is also improved by reducing the number of hidden units that can guarantee approximations within a given error tolerance. Furthermore, the representational efficiency of CRBMs in computing deterministic conditional distributions is investigated. Specifically, we show that there are exponentially many deterministic conditional distributions that cannot be computed by CRBMs whose size does not exponentially grow with the number of input units. Some specific examples of these hard-to-present deterministic conditional distributions are provided. Finally, some numerical experiments are carried out to verify the theoretical results of the properties of CRBMs to approximate conditional Markov random fields and the universal approximation of CRBMs.

Co-occurrence probabilities between mosquito vectors of West Nile and Eastern equine encephalitis viruses using Markov Random Fields (MRFcov)

Mosquito vectors of eastern equine encephalitis virus (EEEV) and West Nile virus (WNV) in the USA reside within broad multi-species assemblages that vary in spatial and temporal composition, relative abundances and vector competence. These variations impact the risk of pathogen transmission and the operational management of these species by local public health vector control districts. However, most models of mosquito vector dynamics focus on single species and do not account for co-occurrence probabilities between mosquito species pairs across environmental gradients. In this investigation, we use for the first time conditional Markov Random Fields (CRF) to evaluate spatial co-occurrence patterns between host-seeking mosquito vectors of EEEV and WNV around sampling sites in Manatee County, Florida. Specifically, we aimed to: (i) quantify correlations between mosquito vector species and other mosquito species; (ii) quantify correlations between mosquito vectors and landscape and climate variables; and (iii) investigate whether the strength of correlations between species pairs are conditional on landscape or climate variables. We hypothesized that either mosquito species pairs co-occur in patterns driven by the landscape and/or climate variables, or these vector species pairs are unconditionally dependent on each other regardless of the environmental variables. Our results indicated that landscape and bioclimatic covariates did not substantially improve the overall model performance and that the log abundances of the majority of WNV and EEEV vector species were positively dependent on other vector and non-vector mosquito species, unconditionally. Only five individual mosquito vectors were weakly dependent on environmental variables with one exception, Culiseta melanura, the primary vector for EEEV, which showed a strong correlation with woody wetland, precipitation seasonality and average temperature of driest quarter. Our analyses showed that majority of the studied mosquito species’ abundance and distribution are insignificantly better predicted by the biotic correlations than by environmental variables. Additionally, these mosquito vector species may be habitat generalists, as indicated by the unconditional correlation matrices between species pairs, which could have confounded our analysis, but also indicated that the approach could be operationalized to leverage species co-occurrences as indicators of vector abundances in unsampled areas, or under scenarios where environmental variables are not informative.Graphical

Development of Texture Mapping Approaches for Additively Manufacturable Surfaces

Additive manufacturing (AM) technologies have been recognized for their capability to build complex components and hence have offered more freedom to designers for a long time. The ability to directly use a computer-aided design (CAD) model has allowed for fabricating and realizing complicated components, monolithic design, reducing the number of components in an assembly, decreasing time to market, and adding performance or comfort-enhancing functionalities. One of the features that can be introduced for boosting a component functionality using AM is the inclusion of surface texture on a given component. This inclusion is usually a difficult task as creating a CAD model resolving fine details of a given texture is difficult even using commercial software packages. This paper develops a methodology to include texture directly on the CAD model of a target surface using a patch-based sampling texture synthesis algorithm, which can be manufactured using AM. Input for the texture generation algorithm can be either a physical sample or an image with heightmap information. The heightmap information from a physical sample can be obtained by 3D scanning the sample and using the information from the acquired point cloud. After obtaining the required inputs, the patches are sampled for texture generation according to non-parametric estimation of the local conditional Markov random field (MRF) density function, which helps avoid mismatched features across the patch boundaries. While generating the texture, a design constraint to ensure AM producibility is considered, which is essential when manufacturing a component using, e.g., Fused Deposition Melting (FDM) or Laser Powder Bed Fusion (LPBF). The generated texture is then mapped onto the surface using the developed distance and angle preserving mapping algorithms. The implemented algorithms can be used to map the generated texture onto a mathematically defined surface. This paper maps the textures onto flat, curved, and sinusoidal surfaces for illustration. After the texture mapping, a stereolithography (STL) model is generated with the desired texture on the target surface. The generated STL model is printed using FDM technology as a final step.

Graphical Model Selection for Gaussian Conditional Random Fields in the Presence of Latent Variables

ABSTRACT We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random field into the sum of a sparse and a low-rank matrix. We derive convergence bounds for this estimator and show that it is well-behaved in the high-dimensional regime as well as “sparsistent” (i.e., capable of recovering the graph structure). We then show how proximal gradient algorithms and semi-definite programming techniques can be employed to fit the model to thousands of variables. Through extensive simulations, we illustrate the conditions required for identifiability and show that there is a wide range of situations in which this model performs significantly better than its counterparts, for example, by accommodating more latent variables. Finally, the suggested method is applied to two datasets comprising individual level data on genetic variants and metabolites levels. We show our results replicate better than alternative approaches and show enriched biological signal. Supplementary materials for this article are available online.

Learning Depth from Single Images with Deep Neural Network Embedding Focal Length.

Learning depth from a single image, as an important issue in scene understanding, has attracted a lot of attention in the past decade. The accuracy of the depth estimation has been improved from conditional Markov random fields, non-parametric methods, to deep convolutional neural networks most recently. However, there exist inherent ambiguities in recovering 3D from a single 2D image. In this paper, we first prove the ambiguity between the focal length and monocular depth learning, and verify the result using experiments, showing that the focal length has a great influence on accurate depth recovery. In order to learn monocular depth by embedding the focal length, we propose a method to generate synthetic varying-focal-length dataset from fixed-focal-length datasets, and a simple and effective method is implemented to fill the holes in the newly generated images. For the sake of accurate depth recovery, we propose a novel deep neural network to infer depth through effectively fusing the middle-level information on the fixed-focal-length dataset, which outperforms the state-of-the-art methods built on pretrained VGG. Furthermore, the newly generated varying-focallength dataset is taken as input to the proposed network in both learning and inference phases. Extensive experiments on the fixed- and varying-focal-length datasets demonstrate that the learned monocular depth with embedded focal length is significantly improved compared to that without embedding the focal length information.

Fast depth extraction from a single image

Predicting depth from a single image is an important problem for understanding the 3-D geometry of a scene. Recently, the nonparametric depth sampling (DepthTransfer) has shown great potential in solving this problem, and its two key components are a Scale Invariant Feature Transform (SIFT) flow–based depth warping between the input image and its retrieved similar images and a pixel-wise depth fusion from all warped depth maps. In addition to the inherent heavy computational load in the SIFT flow computation even under a coarse-to-fine scheme, the fusion reliability is also low due to the low discriminativeness of pixel-wise description nature. This article aims at solving these two problems. First, a novel sparse SIFT flow algorithm is proposed to reduce the complexity from subquadratic to sublinear. Then, a reweighting technique is introduced where the variance of the SIFT flow descriptor is computed at every pixel and used for reweighting the data term in the conditional Markov random fields. Our proposed depth transfer method is tested on the Make3D Range Image Data and NYU Depth Dataset V2. It is shown that, with comparable depth estimation accuracy, our method is 2–3 times faster than the DepthTransfer.

Phase transitions in nonlinear filtering

It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture of classical filtering models, many infinite-dimensional problems are outside its scope. Far from being a technical issue, the infinite-dimensional setting gives rise to surprising phenomena and new questions in filtering theory. The aim of this paper is to discuss some elementary examples, conjectures, and general theory that arise in this setting, and to highlight connections with problems in statistical mechanics and ergodic theory. In particular, we exhibit a simple example of a uniformly ergodic model in which ergodicity of the filter undergoes a phase transition, and we develop some qualitative understanding as to when such phenomena can and cannot occur. We also discuss closely related problems in the setting of conditional Markov random fields.

Modeling the spread of plant disease using a sequence of binary random fields with absorbing states

The presence or absence of some event at locations on a spatial lattice can often be modeled using a binary Markov random field model. If observations are repeated over time at the same locations this model structure can be extended to include neighbors in both space and time, as long as conditions sufficient to allow the construction of a joint distribution from the set of specified conditionals are satisfied. One of those conditions involves the relation between the support of the joint distribution and the individual supports of marginal distributions at each location. When a sequence of binary random fields involves an absorbing state and more than two points in time, the support conditions needed to construct a model for the entire sequence as a Markov random field are not satisfied. An application involving the spread of a soybean disease across a field motivates development of a model that avoids the difficulties caused by absorbing states over time, by formulating the overall model as a sequence of conditional Markov random fields which themselves follow a Markov property in time.

Semantic Segmentation with Same Topic Constraints

A popular approach to semantic segmentation problems is to construct a pair wise Conditional Markov Random Field (CRF) over image pixels where the pair wise term encodes a preference for smoothness within pixel neighborhoods. Recently, researchers have considered higher-order models that encode local region or soft non-local constraints (e.g., label consistency or co-occurrence statistics). These new models with higher-order terms have significantly pushed the state-of-the-art for semantic segmentation problems. In this study, we consider a novel non- local constraint that enforces consistent pixel labels among those image regions having the same topic. These topics are discovered by Probabilistic Latent Semantic Analysis model (PLSA). We encode this constraint as a robust Pn higher-order potential among all the image regions of the same topic in a unified CRF model. We experimentally demonstrate quantitative and qualitative improvements over a refined baseline unary and pair wise CRF models.

High-throughput and accurate segmentation of lateral ventricles using combined single atlas propagation and tissue classification: Application to ADNI and IBSR data

Ventricular volume measures have been proposed as a useful biomarker of AD progression as they distinguish disease from normality with a high effect size (Carmichael et al., 2007). In vivo quantification of lateral ventricular volumes is performed using automated techniques. In this work, we proposed a new high-throughput segmentation technique combining single-atlas propagation and tissue-type classification (GM, WM and CSF) for ventricular volume measurement in multicenter studies. The baseline scans of 90 subjects (30 HC, 30 MCI and 30 AD, age matched) from the ADNI database (http://adni.loni.ucla.edu) and 18 subjects from the IBSR database (http://www.cma.mgh.harvard.edu/ibsr/) were analysed. Lateral ventricular volumes were automatically estimated for all scans using the proposed segmentation strategy. An atlas including ventricular labels taken from a randomly selected reference AD patient was propagated to the subject space. In parallel, the subject's brain was classified into grey matter, white matter and CSF using a statistical technique based on Iterated Conditional Mode, Bayesian classification and Markov random field (Pachai et al., 2001). The propagated labels were then made consistent with tissue type using a classification-based nearest neighbour distance transform. The proposed scheme allowed error correction introduced by either the segmentation propagation technique or the atlas itself. The performance of the proposed technique was compared to a manual gold standard segmentation using the Dice similarity index (Dice) and D, the percent volume difference. Dice measured “anatomical precision” while D measured “volumetric accuracy”, which is the important parameter in terms of power for clinical trials. Main results (mean and SD) were summarized in Table 1. Anatomical precision was the same for ADNI and IBSR data, with high Dice value of 96.0 %. This result demonstrated the robustness of the proposed technique when processing image datasets of variable quality. Volumetric accuracy was very similar for both datasets, with low D values of 2.7 (2.5) % and 3.4 (2.0) % for ADNI and IBSR dataset, respectively. Dice and D values were very high and very low, respectively, as expected for an accurate segmentation technique. We have proposed a high-throughput automated technique for accurate segmentation of lateral ventricles in multicenter clinical trials.

Simultaneous Motion Detection and Background Reconstruction with a Conditional Mixed-State Markov Random Field

In this work we present a new way of simultaneously solving the problems of motion detection and background image reconstruction. An accurate estimation of the background is only possible if we locate the moving objects. Meanwhile, a correct motion detection is achieved if we have a good available background model. The key of our joint approach is to define a single random process that can take two types of values, instead of defining two different processes, one symbolic (motion detection) and one numeric (background intensity estimation). It thus allows to exploit the (spatio-temporal) interaction between a decision (motion detection) and an estimation (intensity reconstruction) problem. Consequently, the meaning of solving both tasks jointly, is to obtain a single optimal estimate of such a process. The intrinsic interaction and simultaneity between both problems is shown to be better modeled within the so-called mixed-state statistical framework, which is extended here to account for symbolic states and conditional random fields. Experiments on real sequences and comparisons with existing motion detection methods support our proposal. Further implications for video sequence inpainting will be also discussed.

Information-theoretic characterizations of conditional mutual independence and Markov random fields

We take the point of view that a Markov random field is a collection of so-called full conditional mutual independencies. Using the theory of I-measure, we have obtained a number of fundamental characterizations related to conditional mutual independence and Markov random fields. We show that many aspects of conditional mutual independence and Markov random fields have very simple set-theoretic descriptions. New insights into the structure of conditional mutual independence and Markov random fields are obtained. Our results have immediate applications in the implication problem of probabilistic conditional independency and relational database. We obtain a hypergraph characterization of a Markov random field which makes it legitimate to view a Markov random field as a hypergraph. Based on this result, we naturally employ the Graham reduction, a tool from relational database theory, to recognize a Markov forest. This connection between Markov random fields and hypergraph sheds some light on the possible role of hypergraph theory in the study of Markov random fields.

Using circulant symmetry to model featureless objects

Grenander & Miller (1994) describe a model for representing amorphous two-dimensional objects with no obvious landmark. Each object is represented by n vertices around its perimeter, and is described by deforming an n-sided regular polygon using edge transformations. A multivariate normal distribution with a block circulant covariance matrix is used to model these edge transformations. The purpose of this paper is to describe in detail the statistical properties of this multivariate model and the eigenstructure of the covariance matrix. Various special cases of the model are considered, including articulated models and conditional Markov random field models. We consider maximum likelihood based inference and the model is applied to some datasets to explore shape variability.

Conditional cyclic Markov random fields

Grenander et al. (1991) proposed a conditional cyclic Gaussian Markov random field model for the edges of a closed outline in the plane. In this paper the model is recast as an improper cyclic Gaussian Markov random field for the vertices. The limiting behaviour of this model when the vertices become closely spaced is also described and in particular its relationship with the theory of ‘snakes' (Kass et al. 1987) is established. Applications are given in Grenander et al. (1991), Mardia et al. (1991) and Kent et al. (1992).

Conditional cyclic Markov random fields

Grenander et al. (1991) proposed a conditional cyclic Gaussian Markov random field model for the edges of a closed outline in the plane. In this paper the model is recast as an improper cyclic Gaussian Markov random field for the vertices. The limiting behaviour of this model when the vertices become closely spaced is also described and in particular its relationship with the theory of ‘snakes' (Kass et al. 1987) is established. Applications are given in Grenander et al. (1991), Mardia et al. (1991) and Kent et al. (1992).

Discussion of the Paper by Grenander and Miller

Discussion of the Paper by Grenander and Miller