Markov networks

The article examines the influence of Markov processes on computations in Bayesian networks (BN), an important area of research within probabilistic graphical models. The concept of Bayesian Markov networks (BMN) is introduced, an extension of traditional Bayesian networks with the addition of a Markov constraint, according to which the probability in a node can only depend on the state of neighboring nodes. This constraint makes the model more realistic for many practical tasks, as most graphical models that reflect real-world processes possess the Markov property. The article also discusses that Bayesian networks, in the absence of evidence, actually exhibit the Markov property. However, when evidence (additional information) is introduced into the model, challenges arise that require more complex computational methods. In response, the article proposes algorithms adapted for working with Bayesian Markov networks in the presence of evidence. These algorithms are aimed at optimizing computations and reducing computational complexity. Additionally, a comparative analysis of calculations in Bayesian networks without Markov constraints and with them is conducted, highlighting the advantages and disadvantages of each approach. Special attention is paid to the practical applications of the proposed methods and their effectiveness in various scenarios.

Abstract. We introduce in this work a set of strategies for improving the piecing-together step in Local-to-global Markov networks structure learning algorithms. For Markov networks, Local-to-global algorithms decompose the problem of learning a complete independence structure with n variables into n independent Markov blanket learning problems. On a second step these algorithms piece-together all the learned Markov blankets into a global structure using an “OR rule”. Insufficient data may result in incorrect learning of Markov ...

We present a new parallel algorithm for probabilistic graphical model optimization. The algorithm relies on data-parallel primitives (DPPs), which provide portable performance over hardware architecture. We evaluate results on CPUs and GPUs for an image segmentation problem. Compared to a serial baseline, we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare our performance to a reference, OpenMP-based algorithm, and find speedups of up to 7X (CPU).

We present a new parallel algorithm for probabilistic graphical model optimization. The algorithm relies on data-parallel primitives (DPPs), which provide portable performance over hardware architecture. We evaluate results on CPUs and GPUs for an image segmentation problem. Compared to a serial baseline, we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare our performance to a reference, OpenMP-based algorithm, and find speedups of up to 7X (CPU).

This work focuses on learning the structure of Markov networks. Markov networks are parametric models for compactly representing complex probability distributions. These models are composed by: a structure and numerical weights. The structure describes independences that hold in the distribution. Depending on the goal of learning intended by the user, structure learning algorithms can be divided into: density estimation algorithms, focusing on learning structures for answering inference queries; and knowledge discovery algorithms, focusing on learning structures for describing independences qualitatively. The latter algorithms present an important limitation for describing independences as they use a single graph, a coarse grain representation of the structure. However, many practical distributions present a flexible type of independences called context-specific independences, which cannot be described by a single graph. This work presents an approach for overcoming this limitation by proposing an alternative representation of the structure that named canonical model; and a novel knowledge discovery algorithm called CSPC for learning canonical models by using as constraints context-specific independences present in data. On an extensive empirical evaluation, CSPC learns more accurate structures than state-of-the-art density estimation and knowledge discovery algorithms. Moreover, for answering inference queries, our approach obtains competitive results against density estimation algorithms, significantly outperforming knowledge discovery algorithms.

This work focuses on learning the structure of Markov networks from data. Markov networks are parametric models for compactly representing complex probability distributions. These models are composed by: a structure and numerical weights, where the structure describes independences that hold in the distribution. Depending on which is the goal of structure learning, learning algorithms can be divided into: density estimation algorithms, where structure is learned for answering inference queries; and knowledge discovery algorithms, where structure is learned for describing independences qualitatively. The latter algorithms present an important limitation for describing independences because they use a single graph; a coarse grain structure representation which cannot represent flexible independences. For instance, context-specific independences cannot be described by a single graph. To overcome this limitation, this work proposes a new alternative representation named canonical model ...

This work presents a region-growing image segmentation approach based on superpixel decomposition. From an initial contour-constrained over-segmentation of the input image, the image segmentation is achieved by iteratively merging similar superpixels into regions. This approach raises two key issues: (1) how to compute the similarity between superpixels in order to perform accurate merging and (2) in which order those superpixels must be merged together. In this perspective, we firstly introduce a robust adaptive multi-scale superpixel similarity in which region comparisons are made both at content and common border level. Secondly, we propose a global merging strategy to efficiently guide the region merging process. Such strategy uses an adpative merging criterion to ensure that best region aggregations are given highest priorities. This allows to reach a final segmentation into consistent regions with strong boundary adherence. We perform experiments on the BSDS500 image dataset to highlight to which extent our method compares favorably against other well-known image segmentation algorithms. The obtained results demonstrate the promising potential of the proposed approach.

This work presents a region-growing image segmentation approach based on superpixel decomposition. From an initial contour-constrained over-segmentation of the input image, the image segmentation is achieved by iteratively merging similar superpixels into regions. This approach raises two key issues: (1) how to compute the similarity between superpixels in order to perform accurate merging and (2) in which order those superpixels must be merged together. In this perspective, we firstly introduce a robust adaptive multi-scale superpixel similarity in which region comparisons are made both at content and common border level. Secondly, we propose a global merging strategy to efficiently guide the region merging process. Such strategy uses an adpative merging criterion to ensure that best region aggregations are given highest priorities. This allows to reach a final segmentation into consistent regions with strong boundary adherence. We perform experiments on the BSDS500 image dataset to highlight to which extent our method compares favorably against other well-known image segmentation algorithms. The obtained results demonstrate the promising potential of the proposed approach.

Phase-Type distributions are a powerful tool in stochastic modeling of real systems. In this paper, we describe an object-oriented tool used to represent and manipulate these distributions as computational objects. It allows the computation of multiple closure properties that can be used when modeling large systems with multiple interactions. The tool also includes procedures for fitting the parameter of a distribution from a data set and capabilities for generating random numbers from a specified distribution. This framework is built in a flexible and expandable way, and, therefore, it is not limited to the algorithms provided.

Codon is the basic unit for biological message transmission during synthesis of proteins in an organism. Codon Usage Bias is preferential usage among synonymous codons, in an organisms. This preferential use of a synonymous codon was found not only among species but also occurs among genes within the same genome of a species. This variation of codon usage patterns are controlled by natural processes such as mutation, drift and pressure. In this study, we have used computational as well as statistical techniques for finding codon usage bias and codon context pattern of Salinibacter ruber (extreme halophilic), Chromohalobacter salexigens (moderate halophilic) and Rhizobium etli (nonhalophilic). In addition to this, compositional variation in translated amino acid frequency, effective number of codons and optimal codons were also studied. A plot of EN c versus GC 3s suggests that both mutation bias and translational selection contribute to these differences of codon bias. However, mutation bias is the driving force of the synonymous codon usage patterns in halophilic bacteria (Salinibacter ruber and Chromohalobacter salexigens) and translational selection seems to affect codon usage pattern in non-halophilic bacteria (Rhizobium etli). Correspondence analysis of Relative Synonymous Codon Usage revealed different clusters of genes varying in numbers in the bacteria under study. Moreover, codon context pattern was also seen variable in these bacteria. These results clearly indicate the variation in the codon usage pattern in these bacterial genomes.

Markov blanket (Mb) and Markov boundary (MB) are two key concepts in Bayesian networks (BNs). In this paper, we study the problem of Mb and MB for multiple variables. First, we show that Mb possesses the additivity property under the local intersection assumption, that is, an Mb of multiple targets can be constructed by simply taking the union of Mbs of the individual targets and removing the targets themselves. MB is also proven to have additivity under the local intersection assumption. Second, we analyze the cases of violating additivity of Mb and MB and then put forward the notions of Markov blanket supplementary (MbS) and Markov boundary supplementary (MBS). The properties of MbS and MBS are studied in detail. Third, we build two MB discovery algorithms and prove their correctness under the local composition assumption. We also discuss the ways of practically doing conditional independence tests and analyze the complexities of the algorithms. Finally, we make a benchmarking study based on six synthetic BNs and then apply MB discovery to multi-class prediction based on a real data set. The experimental results reveal our algorithms have higher accuracies and lower complexities than existing algorithms.

In this paper, we focus on the reliability, or data efficiency, problem of the existing Markov blanket learning algorithms. We first define as well as demonstrate the seriousness of this problem. Secondly, we review eleven published algorithms ranging from 1996 to 2010, including their design and the reliability problem. Then, we discuss the challenge to improve this performance for different strategy as taken in existing works. Finally, we point out IPC-MB [1, 2] is the one with best data efficiency among published works, but it is still only sub-optimal. This work can be a reference for future effort aiming at a more reliable solution, though we conclude here that the best solution may not exist if an optimal output is expected.

Traditional security analyses are often geared towards cryptographic primitives or protocols. Although such analyses are absolutely necessary, they do not provide much insight for answering an equally important question: What is the security assurance of a physically or logically networked system when we consider it as a whole? This question is known to be notoriously difficult, and the state-of-the-art is that we know very little about it. In this paper, we make a step towards resolving it with a new modeling approach. 2 System Setting and Notations A system is modeled as G = (V, E), a finite graph with V = {1, 2,. .. , n} the set of nodes (i.e., users or vertices) and E the set of edges. We stress, however, that an edge (u, v) ∈ E does not necessarily correspond to the physical link between nodes u and v. Instead, it could be a logical concept that captures, for instance, that the compromise of

Image segmentation is the task of assigning a label to each image pixel. When the number of labels is greater than two (multi-label) the segmentation can be modelled as a multi-cut problem in graphs. In the general case, finding the minimum cut in a graph is an NP-hard problem, in which improving the results concerning time and quality is a major challenge. This paper addresses the multi-label problem applied in interactive image segmentation. The proposed approach makes use of dynamic programming to initialize an α-expansion, thus reducing its runtime, while keeping the Dice-score measure in an interactive segmentation task. Over BSDS data set, the proposed algorithm was approximately 51.2% faster than its standard counterpart, 36.2% faster than Fast Primal-Dual (FastPD) and 10.5 times faster than quadratic pseudo-boolean optimization (QBPO) optimizers, while preserving the same segmentation quality.

The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii) its significance level. These parameters are usually set to values recommended by an expert. Nevertheless, such an approach can suffer from human bias, leading to suboptimal reconstruction results. In this paper we consider a more principled approach for choosing these parameters in an automatic way. For this we optimize a reconstruction score evaluated on a set of different Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a closed-form expression, which means that Bayesian optimization (BO) is a natural choice. BO methods use a model to guide the search and are hence able to exploit smoothness properties of the objective surface. We show that the parameters found by a BO method outperform those found by a random search strategy and the expert recommendation. Importantly, we have found that an often overlooked statistical test provides the best overall reconstruction results.

In this paper, we propose the efficient approach to tackle the multi-label interactive image segmentation issue by applying the higher order Conditional Random Fields model which associates superpixel as higher order energy. People did take advantage of CRF model for unsupervised segmentation for years, but it requires training set for providing neccessary information. Therefore, unsupervised strategy is fairly restrictive for the variety of image contexts and categorizations. For this reason, the user interaction seems inevitable to help us address the multilabel segmentation's riddle in accordance with exploiting CRF perspectives. The promising experiments are conducted in MSRC and Berkeley dataset comparing with the original Conditional Random Fields framework.

In this paper, we propose the efficient approach to tackle the multi-label interactive image segmentation issue by applying the higher order Conditional Random Fields model which associates superpixel as higher order energy. People did take advantage of CRF model for unsupervised segmentation for years, but it requires training set for providing neccessary information. Therefore, unsupervised strategy is fairly restrictive for the variety of image contexts and categorizations. For this reason, the user interaction seems inevitable to help us address the multilabel segmentation's riddle in accordance with exploiting CRF perspectives. The promising experiments are conducted in MSRC and Berkeley dataset comparing with the original Conditional Random Fields framework.

In Video Instance Segmentation (VIS), current approaches either focus on the quality of the results, by taking the whole video as input and processing it offline; or on speed, by handling it frame by frame at the cost of competitive performance. In this work, we propose an online method that is on par with the performance of the offline counterparts. We introduce a message-passing graph neural network that encodes objects and relates them through time. We additionally propose a novel module to fuse features from the feature pyramid network with residual connections. Our model, trained end-to-end, achieves state-of-the-art performance on the YouTube-VIS dataset within the online methods. Further experiments on DAVIS demonstrate the generalization capability of our model to the video object segmentation task.

Semantic image segmentation is a fundamental yet challenging problem, which can be viewed as an extension of the conventional object detection with close relation to image segmentation and classification. It aims to partition images into non-overlapping regions that are assigned predefined semantic labels. Most of the existing approaches utilize and integrate lowlevel local features and high-level contextual cues, which are fed into an inference framework such as, the conditional random field (CRF). However, the lack of meaning in the primitives (i.e., pixels or superpixels) and the cues provides low discriminatory capabilities, since they are rarely object-consistent. Moreover, blind combinations of heterogeneous features and contextual cues exploitation through limited neighborhood relations in the CRFs tend to degrade the labeling performance. This paper proposes an ontology-based semantic image segmentation (OBSIS) approach that jointly models image segmentation and object detection. In particular, a Dirichlet process mixture model transforms the low-level visual space into an intermediate semantic space, which drastically reduces the feature dimensionality. These features are then individually weighed and independently learned within the context, using multiple CRFs. The segmentation of images into object parts is hence reduced to a classification task, where object inference is passed to an ontology model. This model resembles the way by which humans understand the images through the combination of different cues, context models, and rule-based learning of the ontologies. Experimental evaluations using the MSRC-21 and PASCAL VOC'2010 data sets show promising results.

We propose a cooperative-coevolution-Parisian trend-algorithm, IMPEA (Independence Model based Parisian EA), to the problem of Bayesian networks structure estimation. It is based on an intermediate stage which consists of evaluating an independence model of the data to be modelled. The Parisian cooperative coevolution is particularly well suited to the structure of this intermediate problem, and allows to represent an independence model with help of a whole population, each individual being an independence statement, i.e. a component of the independence model. Once an independence model is estimated, a Bayesian network can be built. This two level resolution of the complex problem of Bayesian network structure estimation has the major advantage to avoid the difficult problem of direct acyclic graph representation within an evolutionary algorithm, which causes many troubles related to constraints handling and slows down algorithms.Comparativeresultswithadeterministicalgorithm, PC, on two test cases (including the Insurance BN benchmark), prove the efficiency of IMPEA, which provides better results than PC in a comparable computation time, and which is able to tackle more complex issues than PC.