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.

Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods

A long slope consisting of spatially random soils is a common geographical feature. This paper examined the necessity of three-dimensional(3 D) analysis when dealing with slope with full randomness in soil properties. Although 3 D random finite element analysis can well reflect the spatial variability of soil properties, it is often time-consuming for probabilistic stability analysis. For this reason, we also examined the least advantageous(or most pessimistic) cross-section of the studied slope. The concept of"most pessimistic" refers to the minimal cross-sectional average of undrained shear strength. The selection of the most pessimistic section is achievable by simulating the undrained shear strength as a 3 D random field. Random finite element analysis results suggest that two-dimensional(2 D) plane strain analysis based the most pessimistic cross-section generally provides a more conservative result than the corresponding full 3 D analysis. The level of conservativeness is around 15% on average. This result may have engineering implications for slope design where computationally tractable 2 D analyses based on the procedure proposed in this study could ensure conservative results.

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.

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.

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.

Detection and characterization of regulatory elements using probabilistic conditional random field and hidden Markov models

By altering the electrostatic charge of histones or providing binding sites to protein recognition molecules, Chromatin marks have been proposed to regulate gene expression, a property that has motivated researchers to link these marks to cis-regulatory elements. With the help of next generation sequencing technologies, we can now correlate one specific chromatin mark with regulatory elements (e.g. enhancers or promoters) and also build tools, such as hidden Markov models, to gain insight into mark combinations. However, hidden Markov models have limitation for their character of generative models and assume that a current observation depends only on a current hidden state in the chain. Here, we employed two graphical probabilistic models, namely the linear conditional random field model and multivariate hidden Markov model, to mark gene regions with different states based on recurrent and spatially coherent character of these eight marks. Both models revealed chromatin states that may correspond to enhancers and promoters, transcribed regions, transcriptional elongation, and low-signal regions. We also found that the linear conditional random field model was more effective than the hidden Markov model in recognizing regulatory elements, such as promoter-, enhancer-, and transcriptional elongation-associated regions, which gives us a better choice.

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.

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.

Spin-1 Blume-Capel model with longitudinal random crystal and transverse magnetic fields:A mean-field approach

The spin-1 Blume–Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ=Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.

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.

Neumann stochastic finite element method for calculating temperature field of frozen soil based on random field theory

To study the effect of uncertain factors on the temperature field of frozen soil, we propose a method to calculate the spatial average variance from just the point variance based on the local average theory of random fields. We model the heat transfer coefficient and specific heat capacity as spatially random fields instead of traditional random variables. An analysis for calculating the random temperature field of seasonal frozen soil is suggested by the Neumann stochastic finite element method, and here we provide the computational formulae of mathematical expectation, variance and variable coefficient. As shown in the calculation flow chart, the stochastic finite element calculation program for solving the random temperature field, as compiled by Matrix Laboratory （MATLAB） sottware, can directly output the statistical results of the temperature field of frozen soil. An example is presented to demonstrate the random effects from random field parameters, and the feasibility of the proposed approach is proven by compar- ing these results with the results derived when the random parameters are only modeled as random variables. The results show that the Neumann stochastic finite element method can efficiently solve the problem of random temperature fields of frozen soil based on random field theory, and it can reduce the variability of calculation results when the random parameters are modeled as spatial- ly random fields.

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.

Prediction of Potential Disease-Associated MicroRNAs Based on Hidden Conditional Random Field

MicroRNAs( miRNAs) are reported to be associated with various diseases. The identification of disease-related miRNAs would be beneficial to the disease diagnosis and prognosis. However,in contrast with the widely available expression profiling, the limited knowledge of molecular function restrict the development of previous methods based on network similarity measure. To construct reliable training data,the decision fusion method is used to prioritize the results of existing methods. After that,the performance of decision fusion method is validated. Furthermore,in consideration of the long range dependencies of successive expression values,Hidden Conditional Random Field model( HCRF) is selected and applied to miRNA expression profiling to infer disease-associated miRNAs. The results show that HCRF achieves superior performance and outperforms the previous methods. The results also demonstrate the power of using expression profiling for discovering disease-associated miRNAs.

Some Limit Theorems for Weighted Sums of Random Variable Fields

Let{Xn^-,n^-∈N^d}be a field of Banach space valued random variables, 0 〈r〈p≤2 and{an^-,k^-, （n^-,k^-） ∈ N^d × N^d ,k^-≤n^-} a triangular array of real numhers, where N^d is the d-dimensional lattice （d≥1 ）. Under the minimal condition that {｜｜Xn^-｜｜ r,n^- ∈N^d} is {｜an^-,k^-｜^r,（n^-,k^-）} ∈ N^d ×N^d,k^-≤n^-}-uniformly integrable, we show that ∑（k^-≤n^-）an^-,k^-,Xk^-^（L^r（or a,s,）→0 as ｜n^-｜→∞ In the above, if 0〈r〈1, the random variables are not needed to be independent. If 1≤r〈p≤2, and Banach space valued random variables are independent with mean zero we assume the Banaeh space is of type p. If 1≤r≤p≤2 and Banach space valued random variables are not independent we assume the Banach space is p-smoothable.

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 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.