ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

An Interpolation Method for Karhunen-Loève Expansion of Random Field Discretization

In the context of global mean square error concerning the number of random variables in the representation,the Karhunen–Loève(KL)expansion is the optimal series expansion method for random field discretization.The computational efficiency and accuracy of the KL expansion are contingent upon the accurate resolution of the Fredholm integral eigenvalue problem(IEVP).The paper proposes an interpolation method based on different interpolation basis functions such as moving least squares(MLS),least squares(LS),and finite element method(FEM)to solve the IEVP.Compared with the Galerkin method based on finite element or Legendre polynomials,the main advantage of the interpolation method is that,in the calculation of eigenvalues and eigenfunctions in one-dimensional random fields,the integral matrix containing covariance function only requires a single integral,which is less than a two-folded integral by the Galerkin method.The effectiveness and computational efficiency of the proposed interpolation method are verified through various one-dimensional examples.Furthermore,based on theKL expansion and polynomial chaos expansion,the stochastic analysis of two-dimensional regular and irregular domains is conducted,and the basis function of the extended finite element method(XFEM)is introduced as the interpolation basis function in two-dimensional irregular domains to solve the IEVP.

Semantic role labeling based on conditional random fields

Due to the fact that semantic role labeling （SRL） is very necessary for deep natural language processing, a method based on conditional random fields （CRFs） is proposed for the SRL task. This method takes shallow syntactic parsing as the foundation, phrases or named entities as the labeled units, and the CRFs model is trained to label the predicates＇ semantic roles in a sentence. The key of the method is parameter estimation and feature selection for the CRFs model. The L-BFGS algorithm was employed for parameter estimation, and three category features： features based on sentence constituents, features based on predicate, and predicate-constituent features as a set of features for the model were selected. Evaluation on the datasets of CoNLL-2005 SRL shared task shows that the method can obtain better performance than the maximum entropy model, and can achieve 80. 43 % precision and 63. 55 % recall for semantic role labeling.

Prestack inversion based on anisotropic Markov random field-maximum posterior probability inversion and its application to identify shale gas sweet spots

Economic shale gas production requires hydraulic fracture stimulation to increase the formation permeability. Hydraulic fracturing strongly depends on geomechanical parameters such as Young＇s modulus and Poisson＇s ratio. Fracture-prone sweet spots can be predicted by prestack inversion, which is an ill-posed problem; thus, regularization is needed to obtain unique and stable solutions. To characterize gas-bearing shale sedimentary bodies, elastic parameter variations are regarded as an anisotropic Markov random field. Bayesian statistics are adopted for transforming prestack inversion to the maximum posterior probability. Two energy functions for the lateral and vertical directions are used to describe the distribution, and the expectation-maximization algorithm is used to estimate the hyperparameters of the prior probability of elastic parameters. Finally, the inversion yields clear geological boundaries, high vertical resolution, and reasonable lateral continuity using the conjugate gradient method to minimize the objective function. Antinoise and imaging ability of the method were tested using synthetic and real data.

TONE MODELING BASED ON HIDDEN CONDITIONAL RANDOM FIELDS AND DISCRIMINATIVE MODEL WEIGHT TRAINING

The use of hidden conditional random fields （HCRFs） for tone modeling is explored. The tone recognition performance is improved using HCRFs by taking advantage of intra-syllable dynamic, inter-syllable dynamic and duration features. When the tone model is integrated into continuous speech recognition, the discriminative model weight training （DMWT） is proposed. Acoustic and tone scores are scaled by model weights discriminatively trained by the minimum phone error （MPE） criterion. Two schemes of weight training are evaluated and a smoothing technique is used to make training robust to overtraining problem. Experiments show that the accuracies of tone recognition and large vocabulary continuous speech recognition （LVCSR） can be improved by the HCRFs based tone model. Compared with the global weight scheme, continuous speech recognition can be improved by the discriminative trained weight combinations.

CONVERGENCERATESIN THESTRONG LAWSOFASYMPTOTICALLY NEGATIVELY ASSOCIATEDRANDOM FIELDS

In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields.

An extended stochastic response surface method for random field problems

An efficient and accurate uncertainty propagation methodology for mechanics problems with random fields is developed in this paper. This methodology is based on the stochastic response surface method （SRSM） which has been previously proposed for problems dealing with random variables only. This paper extends SRSM to problems involving random fields or random processes fields. The favorable property of SRSM lies in that the deterministic computational model can be treated as a black box, as in the case of commercial finite element codes. Numerical examples are used to highlight the features of this technique and to demonstrate the accuracy and efficiency of the proposed method. A comparison with Monte Carlo simulation shows that the proposed method can achieve numerical results close to those from Monte Carlo simulation while dramatically reducing the number of deterministic finite element runs.

Fast segmentation approach for SAR image based on simple Markov random field

Traditional image segmentation methods based on MRF converge slowly and require pre-defined weight. These disadvantages are addressed, and a fast segmentation approach based on simple Markov random field （MRF） for SAR image is proposed. The approach is firstly used to perform coarse segmentation in blocks. Then the image is modeled with simple MRF and adaptive variable weighting forms are applied in homogeneous and heterogeneous regions. As a result, the convergent speed is accelerated while the segmentation results in homogeneous regions and boarders are improved. Simulations with synthetic and real SAR images demonstrate the effectiveness of the proposed approach.

CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARYρ~*-MIXING RANDOM FIELDS

By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.

Optimization by Estimation of Distribution with DEUM Framework Based on Markov Random Fields

This paper presents a Markov random field （MRP） approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields （DEUM）. DEUM is a subclass of estimation of distribution algorithms （EDAs） where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are： 1） use of MRF models, 2） fitness modeling approach to estimating the parameter of the model and 3） Monte Carlo approach to sampling from the model.

Rockhead profile simulation using an improved generation method of conditional random field

Rockhead profile is an important part of geological profiles and can have significant impacts on some geotechnical engineering practice,and thus,it is necessary to establish a useful method to reverse the rockhead profile using site investigation results.As a general method to reflect the spatial distribution of geo-material properties based on field measurements,the conditional random field(CRF)was improved in this paper to simulate rockhead profiles.Besides,in geotechnical engineering practice,measurements are generally limited due to the limitations of budget and time so that the estimation of the mean value can have uncertainty to some extent.As the Bayesian theory can effectively combine the measurements and prior information to deal with uncertainty,CRF was implemented with the aid of the Bayesian framework in this study.More importantly,this simulation procedure is achieved as an analytical solution to avoid the time-consuming sampling work.The results show that the proposed method can provide a reasonable estimation about the rockhead depth at various locations against measurement data and as a result,the subjectivity in determining prior mean can be minimized.Finally,both the measurement data and selection of hyper-parameters in the proposed method can affect the simulated rockhead profiles,while the influence of the latter is less significant than that of the former.

Image Dehazing by Incorporating Markov Random Field with Dark Channel Prior

As one of the most simple and effective single image dehazing methods, the dark channel prior(DCP) algorithm has been widely applied. However, the algorithm does not work for pixels similar to airlight(e.g., snowy ground or a white wall), resulting in underestimation of the transmittance of some local scenes. To address that problem, we propose an image dehazing method by incorporating Markov random field(MRF) with the DCP. The DCP explicitly represents the input image observation in the MRF model obtained by the transmittance map. The key idea is that the sparsely distributed wrongly estimated transmittance can be corrected by properly characterizing the spatial dependencies between the neighboring pixels of the transmittances that are well estimated and those that are wrongly estimated. To that purpose, the energy function of the MRF model is designed. The estimation of the initial transmittance map is pixel-based using the DCP, and the segmentation on the transmittance map is employed to separate the foreground and background, thereby avoiding the block effect and artifacts at the depth discontinuity. Given the limited number of labels obtained by clustering, the smoothing term in the MRF model can properly smooth the transmittance map without an extra refinement filter. Experimental results obtained by using terrestrial and underwater images are given.

Power entity recognition based on bidirectional long short-term memory and conditional random fields

With the application of artificial intelligence technology in the power industry,the knowledge graph is expected to play a key role in power grid dispatch processes,intelligent maintenance,and customer service response provision.Knowledge graphs are usually constructed based on entity recognition.Specifically,based on the mining of entity attributes and relationships,domain knowledge graphs can be constructed through knowledge fusion.In this work,the entities and characteristics of power entity recognition are analyzed,the mechanism of entity recognition is clarified,and entity recognition techniques are analyzed in the context of the power domain.Power entity recognition based on the conditional random fields (CRF) and bidirectional long short-term memory (BLSTM) models is investigated,and the two methods are comparatively analyzed.The results indicated that the CRF model,with an accuracy of 83%,can better identify the power entities compared to the BLSTM.The CRF approach can thus be applied to the entity extraction for knowledge graph construction in the power field.

A User Participation Behavior Prediction Model of Social Hotspots Based on Influence and Markov Random Field

Hotspot topic trends can be captured by analyzing user attributes and historical behavior in social network. In this paper, we propose a user participation behavior prediction model for social hotspots, based on user behavior and relationship data, to predict user participation behavior and topic development trends. Firstly, for the complex factors of user behavior, three dynamic influence factor functions are defined, including individual, peer and community influence. These functions take timeliness into account using a time discretization method. Secondly, to determine laws of individual behavior and group behavior within a social topic, a hotspot user participation behavior prediction model is proposed and associated with the basic concepts of randora field and Markov property in information diffusion. The experimental results show that the model can not only dynamically predict the individual behavior, but also grasp the development trends of topics.

Reservoir lithology stochastic simulation based on Markov random fields

Markov random fields(MRF) have potential for predicting and simulating petroleum reservoir facies more accurately from sample data such as logging, core data and seismic data because they can incorporate interclass relationships. While, many relative studies were based on Markov chain, not MRF, and using Markov chain model for 3D reservoir stochastic simulation has always been the difficulty in reservoir stochastic simulation. MRF was proposed to simulate type variables(for example lithofacies) in this work. Firstly, a Gibbs distribution was proposed to characterize reservoir heterogeneity for building 3-D(three-dimensional) MRF. Secondly, maximum likelihood approaches of model parameters on well data and training image were considered. Compared with the simulation results of MC(Markov chain), the MRF can better reflect the spatial distribution characteristics of sand body.

A CONDITIONAL RANDOM FIELDS APPROACH TO BIOMEDICAL NAMED ENTITY RECOGNITION

Named entity recognition is a fundamental task in biomedical data mining. In this letter, a named entity recognition system based on CRFs （Conditional Random Fields） for biomedical texts is presented. The system makes extensive use of a diverse set of features, including local features, full text features and external resource features. All features incorporated in this system are described in detail, and the impacts of different feature sets on the performance of the system are evaluated. In order to improve the performance of system, post-processing modules are exploited to deal with the abbreviation phenomena, cascaded named entity and boundary errors identification. Evaluation on this system proved that the feature selection has important impact on the system performance, and the post-processing explored has an important contribution on system performance to achieve better resuits.

Conditional Random Field Tracking Model Based on a Visual Long Short Term Memory Network

In dense pedestrian tracking,frequent object occlusions and close distances between objects cause difficulty when accurately estimating object trajectories.In this study,a conditional random field tracking model is established by using a visual long short term memory network in the three-dimensional(3D)space and the motion estimations jointly performed on object trajectory segments.Object visual field information is added to the long short term memory network to improve the accuracy of the motion related object pair selection and motion estimation.To address the uncertainty of the length and interval of trajectory segments,a multimode long short term memory network is proposed for the object motion estimation.The tracking performance is evaluated using the PETS2009 dataset.The experimental results show that the proposed method achieves better performance than the tracking methods based on the independent motion estimation.

Coherence-coefficient-based Markov random field approach for building segmentation from high-resolution SAR images

Building segmentation from high-resolution synthetic aperture radar (SAR) images has always been one of the important research issues. Due to the existence of speckle noise and multipath effect, the pixel values change drastically, causing the large intensity differences in pixels of building areas. Moreover, the geometric structure of buildings can cause strong scattering spots, which brings difficulties to the segmentation and extraction of buildings. To solve of these problems, this paper presents a coherence-coefficient-based Markov random field (CCMRF) approach for building segmentation from high-resolution SAR images. The method introduces the coherence coefficient of interferometric synthetic aperture radar (InSAR) into the neighborhood energy based on traditional Markov random field (MRF), which makes interferometric and spatial contextual information more fully used in SAR image segmentation. According to the Hammersley-Clifford theorem, the problem of maximum a posteriori (MAP) for image segmentation is transformed into the solution of minimizing the sum of likelihood energy and neighborhood energy. Finally, the iterative condition model (ICM) is used to find the optimal solution. The experimental results demonstrate that the proposed method can segment SAR building effectively and obtain more accurate results than the traditional MRF method and K-means clustering.

HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS

Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are established.As an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations.

Adaptive foreground and shadow segmentation using hidden conditional random fields

Video object segmentation is important for video surveillance, object tracking, video object recognition and video editing. An adaptive video segmentation algorithm based on hidden conditional random fields (HCRFs) is proposed, which models spatio-temporal constraints of video sequence. In order to improve the segmentation quality, the weights of spatio-temporal con- straints are adaptively updated by on-line learning for HCRFs. Shadows are the factors affecting segmentation quality. To separate foreground objects from the shadows they cast, linear transform for Gaussian distribution of the background is adopted to model the shadow. The experimental results demonstrated that the error ratio of our algorithm is reduced by 23% and 19% respectively, compared with the Gaussian mixture model (GMM) and spatio-temporal Markov random fields (MRFs).