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.

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 Remote Sensing Image Semantic Segmentation Method by Combining Deformable Convolution with Conditional Random Fields

Currently,deep convolutional neural networks have made great progress in the field of semantic segmentation.Because of the fixed convolution kernel geometry,standard convolution neural networks have been limited the ability to simulate geometric transformations.Therefore,a deformable convolution is introduced to enhance the adaptability of convolutional networks to spatial transformation.Considering that the deep convolutional neural networks cannot adequately segment the local objects at the output layer due to using the pooling layers in neural network architecture.To overcome this shortcoming,the rough prediction segmentation results of the neural network output layer will be processed by fully connected conditional random fields to improve the ability of image segmentation.The proposed method can easily be trained by end-to-end using standard backpropagation algorithms.Finally,the proposed method is tested on the ISPRS dataset.The results show that the proposed method can effectively overcome the influence of the complex structure of the segmentation object and obtain state-of-the-art accuracy on the ISPRS Vaihingen 2D semantic labeling dataset.

CONVERGENCE RATES IN THE STRONG LAWS FOR A CLASS OF DEPENDENT RANDOM FIELDS

By using a Rosenthal type inequality established in this paper,the complete convergence rates in the strong laws for a class of dependent random fields are discussed.And the result obtained extends those for ρ --mixing random fields,ρ *-mixing random fields and negatively associated fields.

Enhanced Identifying Gene Names from Biomedical Literature with Conditional Random Fields

Identifying gene names is an attractive research area of biology computing. However, accurate extraction of gene names is a challenging task with the lack of conventions for describing gene names. We devise a systematical architecture and apply the model using conditional random fields （CRFs） for extracting gene names from Medline. In order to improve the performance, biomedical ontology features are inserted into the model and post processing including boundary adjusting and word filter is presented to solve name overlapping problem and remove false positive single words. Pure string match method, baseline CRFs, and CRFs with our methods are applied to human gene names and HIV gene names extraction respectively in 1100 abstracts of Medline and their performances are contrasted. Results show that CRFs are robust for unseen gene names. Furthermore, CRFs with our methods outperforms other methods with precision 0.818 and recall 0.812.

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.

Segmentation of MS lesions using entropy-based EM algorithm and Markov random fields

This paper presents an approach for fully automatic segmentation of MS lesions in fluid attenuated inversion recovery (FLAIR) Magnetic Resonance (MR) images. The proposed method estimates a gaussian mixture model with three kernels as cerebrospinal fluid (CSF), normal tissue and Multiple Sclerosis lesions. To estimate this model, an automatic Entropy based EM algorithm is used to find the best estimated Model. Then, Markov random field (MRF) model and EM algorithm are utilized to obtain and upgrade the class conditional probability density function and the apriori probability of each class. After estimation of Model parameters and apriori probability, brain tissues are classified using bayesian classification. To evaluate the result of the proposed method, similarity criteria of different slices related to 20 MS patients are calculated and compared with other methods which include manual segmentation. Also, volume of segmented lesions are computed and compared with gold standard using correlation coefficient. The proposed method has better performance in comparison with previous works which are reported here.

Fast Chinese syntactic parsing method based on conditional random fields

A fast method for phrase structure grammar analysis is proposed based on conditional ran- dom fields （CRF）. The method trains several CRF classifiers for recognizing the phrase nodes at dif- ferent levels, and uses the bottom-up to connect the recognized phrase nodes to construct the syn- tactic tree. On the basis of Beijing forest studio Chinese tagged corpus, two experiments are de- signed to select the training parameters and verify the validity of the method. The result shows that the method costs 78. 98 ms and 4. 63 ms to train and test a Chinese sentence of 17. 9 words. The method is a new way to parse the phrase structure grammar for Chinese, and has good generalization ability and fast speed.

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.

Rosenthal type inequalities for B-valued strong mixing random fields and their applications

Some inequalities for moments of partial sums of a B valued strong mixing field are established and their applications to the weak and strong laws of large numbers and the complete convergences are discussed.

Iterated Conditional Modes to Solve Simultaneous Localization and Mapping in Markov Random Fields Context

This paper models the complex simultaneous localization and mapping（SLAM） problem through a very flexible Markov random field and then solves it by using the iterated conditional modes algorithm. Markovian models allow to incorporate： any motion model; any observation model regardless of the type of sensor being chosen; prior information of the map through a map model; maps of diverse natures; sensor fusion weighted according to the accuracy. On the other hand, the iterated conditional modes algorithm is a probabilistic optimizer widely used for image processing which has not yet been used to solve the SLAM problem. This iterative solver has theoretical convergence regardless of the Markov random field chosen to model. Its initialization can be performed on-line and improved by parallel iterations whenever deemed appropriate. It can be used as a post-processing methodology if it is initialized with estimates obtained from another SLAM solver. The applied methodology can be easily implemented in other versions of the SLAM problem, such as the multi-robot version or the SLAM with dynamic environment. Simulations and real experiments show the flexibility and the excellent results of this proposal.

Extracting 3D model feature lines based on conditional random fields

We propose a 3D model feature line extraction method using templates for guidance. The 3D model is first projected into a depth map, and a set of candidate feature points are extracted. Then, a conditional random fields (CRF) model is established to match the sketch points and the candidate feature points. Using sketch strokes, the candidate feature points can then be connected to obtain the feature lines, and using a CRF-matching model, the 2D image shape similarity features and 3D model geometric features can be effectively integrated. Finally, a relational metric based on shape and topological similarity is proposed to evaluate the matching results, and an iterative matching process is applied to obtain the globally optimized model feature lines. Experimental results showed that the proposed method can extract sound 3D model feature lines which correspond to the initial sketch template.

Scaling Conditional Random Fields by One-Against-the-Other Decomposition

As a powerful sequence labeling model, conditional random fields （CRFs） have had successful applications in many natural language processing （NLP） tasks. However, the high complexity of CRFs training only allows a very small tag （or label） set, because the training becomes intractable as the tag set enlarges. This paper proposes an improved decomposed training and joint decoding algorithm for CRF learning. Instead of training a single CRF model for all tags, it trains a binary sub-CRF independently for each tag. An optimal tag sequence is then produced by a joint decoding algorithm based on the probabilistic output of all sub-CRFs involved. To test its effectiveness, we apply this approach to tackling Chinese word segmentation （CWS） as a sequence labeling problem. Our evaluation shows that it can reduce the computational cost of this language processing task by 40-50% without any significant performance loss on various large-scale data sets.

Packing Dimension of Space-time Anisotropic Gaussian Random Fields

Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian random field whose components are independent and satisfy some mild conditions.We study the packing dimension of range X(E)under the anisotropic(time variable)metric space(R^(N),ρ)and(space variable)metric space(R^(d),τ),where E⊂R^(N) is a Borel set.Our results generalize the corresponding results of Estrade,Wu and Xiao(Commun.Stoch.Anal.,5,41-64(2011))for time-anisotropic Gaussian random fields to space-time anisotropic Gaussian fields.

Hausdorff-type Measures of the Sample Path of Gaussian Random Fields

Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X（t）（t ∈ R^N） be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX（[0, 1]N）, and evaluate the exact φ - mA measure of the image and graph set of X（t）. A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X（[0, 1] ^N） and GrX（[0, 1]^N） are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite （ φ A）-Hausdorff measure for X（[0, 1]^N） and GrX（[0, 1]N）.

2D Correlative-Chain Conditional Random Fields for Semantic Annotation of Web Objects

Semantic annotation of Web objects is a key problem for Web information extraction. The Web contains an abundance of useful semi-structured information about real world objects, and the empirical study shows that strong two-dimensional sequence characteristics and correlative characteristics exist for Web information about objects of the same type across different Web sites. Conditional Random Fields （CRFs） are the state-of-the-art approaches taking the sequence characteristics to do better labeling. However, as the appearance of correlative characteristics between Web object elements, previous CRFs have their limitations for semantic annotation of Web objects and cannot deal with the long distance dependencies between Web object elements efficiently. To better incorporate the long distance dependencies, on one hand, this paper describes long distance dependencies by correlative edges, which are built by making good use of structured information and the characteristics of records from external databases; and on the other hand, this paper presents a two-dimensional Correlative-Chain Conditional Random Fields （2DCC-CRFs） to do semantic annotation of Web objects. This approach extends a classic model, two-dimensional Conditional Random Fields （2DCRFs）, by adding correlative edges. Experimental results using a large number of real-world data collected from diverse domains show that the proposed approach can significantly improve the semantic annotation accuracy of Web objects.

Multi-Label Markov Random Fields as an Efficient and Effective Tool for Image Segmentation, Total Variations and Regularization

One of the classical optimization models for image segmentation is the well known Markov Random Fields(MRF)model.This model is a discrete optimization problem,which is shown here to formulate many continuous models used in image segmentation.In spite of the presence of MRF in the literature,the dominant perception has been that the model is not effective for image segmentation.We show here that the reason for the non-effectiveness is due to the lack of access to the optimal solution.Instead of solving optimally,heuristics have been engaged.Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm.Worse still,heuristics do not link directly the input functions and parameters to the output thus obscuring what would be ideal choices of parameters and functions which are to be selected by users in each particular application context.We describe here how MRF can model and solve efficiently several known continuous models for image segmentation and describe briefly a very efficient polynomial time algorithm,which is provably fastest possible,to solve optimally the MRF problem.The MRF algorithm is enhanced here compared to the algorithm in Hochbaum(2001)by allowing the set of assigned labels to be any discrete set.Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time.Several new theoretical results on the properties of the algorithm are proved here and are demonstrated for images in the context of medical and biological imaging.An interactive implementation tool for MRF is described,and its performance and flexibility in practice are demonstrated via computational experiments.We conclude that many continuous models common in image segmentation have discrete analogs to various special cases of MRF and as such are solved optimally and efficiently,rather than with the use of continuous techniques,such as PDE methods,that restrict the type of functions used and furthermore,can only guarantee convergence to a local minimum.

WEAK CONVERGENCE FOR NON-UNIFORMφ-MIXING RANDOM FIELDS

Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),A E A}to converge to Brownian motion.By a direct calculation,the author ahows that the result holds for a more general class of set index A,where A is assurned only to have the metric entropy exponentr,0<r<1.and the rate of nonuniform p-mixing is weakened.The result obtained essentially improve those given by Chen[1)and Goldie,Greenwood[6],etc.

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.