Undirected Models Research Articles

Psychological mechanisms connected to dissociation: Generating hypotheses using network analyses

A large number of mechanisms, many relating to the processing of affect, have been proposed to cause dissociation. The aim of this study was to use network analyses to identify psychological processes most closely connected with ‘felt sense of anomaly’ dissociative experiences. Both an undirected model and a partially directed network model were estimated using data from 6161 general population respondents collected online. The networks were used to identify relationships between dissociation and ten candidate mechanisms: cognitive appraisals, behavioural responses to dissociation, affect intolerance, alexithymia, attentional control, body vigilance, anxiety sensitivity, general self-efficacy, perseverative thinking, and beliefs regarding stress. Both models indicated a highly connected network in which dissociation had direct connections with six psychological processes: cognitive appraisals, behavioural responses, perseverative thinking, alexithymia, general self-efficacy, and beliefs about being overwhelmed. The strongest connection in both networks was between dissociation and cognitive appraisals (causal effect 0.73). The causal direction of connections could not be statistically determined with confidence, apart from the strong probability that dissociation causes meta-cognitions about being overwhelmed (98.54% of 50,000 sampled directed acyclic graphs). Both networks suggest that cognitive appraisals and factors relating to heightened (negative) sensitivity to affect are closely connected to dissociation. Dissociative experiences may arise from a high sensitivity to affect leading to threat-based appraisals that are ruminated upon and maintained by unhelpful behaviours such as avoidance. Investigation of these relationships in clinical groups, and direct causal tests, are required.

A directed graph convolutional neural network for edge-structured signals in link-fault detection

The growing interest in graph deep learning has led to a surge of research focusing on learning various characteristics of graph-structured data. Directed graphs have generally been treated as incidental to definitions on the more general class of undirected graphs. The implicit class imbalance in some graph problems also proves difficult to tackle. Moreover, a body of work has begun to grow that considers how to learn signals structured on the edges of graphs. In this paper, we propose the directed graph convolutional neural network (DGCNN), and describe a simple way to mitigate the inherent class imbalance in graphs. The model is applied to edge-structured signals from datacenter simulations using the structure of a directed linegraph to represent the second-order structure of its underlying graph. We demonstrate that the DGCNN’s improves over undirected models and other directed models by applying our model to locating link-faults in a datacenter simulation.

Minimum redundancy maximal relevance gene selection of apoptosis pathway genes in peripheral blood mononuclear cells of HIV-infected patients with antiretroviral therapy-associated mitochondrial toxicity

BackgroundWe previously identified differentially expressed genes on the basis of false discovery rate adjusted P value using empirical Bayes moderated tests. However, that approach yielded a subset of differentially expressed genes without accounting for redundancy between the selected genes.MethodsThis study is a secondary analysis of a case–control study of the effect of antiretroviral therapy on apoptosis pathway genes comprising of 16 cases (HIV infected with mitochondrial toxicity) and 16 controls (uninfected). We applied the maximum relevance minimum redundancy (mRMR) algorithm on the genes that were differentially expressed between the cases and controls. The mRMR algorithm iteratively selects features (genes) that are maximally relevant for class prediction and minimally redundant. We implemented several machine learning classifiers and tested the prediction accuracy of the two mRMR genes. We next used network analysis to estimate and visualize the association among the differentially expressed genes. We employed Markov Random Field or undirected network models to identify gene networks related to mitochondrial toxicity. The Spinglass model was used to identify clusters of gene communities.ResultsThe mRMR algorithm ranked DFFA and TNFRSF1A, two of the upregulated proapoptotic genes, on the top. The overall prediction accuracy was 86%, the two mRMR genes correctly classified 86% of the participants into their respective groups. The estimated network models showed different patterns of gene networks. In the network of the cases, FASLG was the most central gene. However, instead of FASLG, ABL1 and LTBR had the highest centrality in controls.ConclusionThe mRMR algorithm and network analysis revealed a new correlation of genes associated with mitochondrial toxicity.

Dissociation in patients with non-affective psychosis: Prevalence, symptom associations, and maintenance factors

Dissociation is problematic in its own right for patients with psychosis but may also contribute to the occurrence of psychotic experiences. We therefore set out to estimate in a large cohort of patients with psychosis the prevalence of dissociative experiences, and assess using network models the relationships between dissociation, its potential maintenance mechanisms, and mental health symptoms.902 patients with non-affective psychosis attending UK mental health services participated. Both an undirected model and a partially directed network model were estimated to identify potential relationships between ‘felt sense of anomaly’ dissociative experiences, paranoia, hallucinations, psychological wellbeing, sleep, and six potential maintenance mechanisms (affect intolerance, perseverative thinking, general self-efficacy, alexithymia, cognitive appraisals, and cognitive-behavioural responses to dissociation).617 patients (65.4%) had experienced at least one dissociative symptom regularly over the past fortnight, with the average number experienced being 8.9 (SD = 8.0). Dissociation had direct relationships with paranoia, hallucinations, low psychological wellbeing, cognitive appraisals, cognitive-behavioural responses to dissociation, perseverative thinking, and low alexithymia. Dissociation was a probable cause of hallucinations (94.21% of 50,000 sampled directed acyclic graphs), with a trend towards also being a cause of paranoia (86.25% of 50,000 sampled directed acyclic graphs).Approximately two-thirds of patients with psychosis experience regular dissociative experiences. Dissociation is associated with low psychological wellbeing, and it is likely to have a direct causal influence on psychotic symptoms. Catastrophic cognitive appraisals, cognitive-behavioural responses to dissociation, factors related to affect sensitivity, and perseverative thinking may contribute to the occurrence of dissociation.

The diagnosis of amnestic mild cognitive impairment by combining the characteristics of brain functional network and support vector machine classifier

BackgroundAmnestic mild cognitive impairment (aMCI) is an essential stage of early detection and potential intervention for Alzheimer’s disease (AD). Patients with aMCI exhibit partially abnormal functional brain connectivity and it is suggested that these features may represent a new diagnostic marker of early AD. New methodIn this paper, we constructed two brain network models, a phase synchronization index (PSI) undirected network and a directed transfer function (DTF) directed network, to evaluate the cognitive function in patients with aMCI. We then built SVM classification models using the network clustering coefficient, global efficiency and average node degree as features to distinguish between aMCI patients and controls. ResultsOur results reveal a classification accuracy and AUC of 66.6 ± 1.7% and 0.7475 and 80.0 ± 2.2% and 0.7825, respectively, for the two network models (PSI and DTF). As the directed network model performed better than the undirected model, we introduced an improved graph theory feature, efficiency density, which resulted in an increased classification accuracy and AUC value 86.6 ± 2.6% and 0.8295, respectively. Comparison with existing methodsThe analysis of network models and the directionality of information flow is suitable for analysis of nonlinear EEG signals for assessment of the functional state of the brain. Compared with traditional network features, our proposed improved features more comprehensively evaluate transmission efficiency and density of the brain. ConclusionIn this study, we demonstrate that an improved efficiency density feature is helpful for enhancing classification the accuracy of aMCI. Moreover, directed brain network models exhibit better classification for aMCI diagnosis than undirected networks.

Query Training: Learning a Worse Model to Infer Better Marginals in Undirected Graphical Models with Hidden Variables

Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model once, new probabilistic queries can be answered at test time without retraining. However, when using undirected PGMS with hidden variables, two sources of error typically compound in all but the simplest models (a) learning error (both computing the partition function and integrating out the hidden variables is intractable); and (b) prediction error (exact inference is also intractable). Here we introduce query training (QT), a mechanism to learn a PGM that is optimized for the approximate inference algorithm that will be paired with it. The resulting PGM is a worse model of the data (as measured by the likelihood), but it is tuned to produce better marginals for a given inference algorithm. Unlike prior works, our approach preserves the querying flexibility of the original PGM: at test time, we can estimate the marginal of any variable given any partial evidence. We demonstrate experimentally that QT can be used to learn a challenging 8-connected grid Markov random field with hidden variables and that it consistently outperforms the state-of-the-art AdVIL when tested on three undirected models across multiple datasets.

Heterogeneity and Directionality Analysis of the Cyber Physical Power System

A cyber physical power system model based on the weighted tensor product is proposed in this paper to describe the interlayer and intralayer relationships of entities in both systems. The different functional attributes of nodes and the directivity of the energy flow in the system are respectively described as the heterogeneity of nodes and the directionality of edges. During failure propagation, the dynamic topology method is applied to convert the protection strategies and load redistribution measures into system connectivity rebuilding. The simulation results of fault propagation in the cyber physical power system under different initial failure ratios show that, compared with the undirected model, the directional interactions in the proposed approach can significantly improve the system survival rate during cascading failure. In addition, the physical system shows a lower vulnerability due to the protection provided by spare edges and power sources.

Adverse Birth Outcomes as Indicators of Poor Fetal Growth Conditions in a French Newborn Population-A Stratified Analysis by Neighborhood Deprivation Level.

Background: Adverse birth outcomes are related to unfavorable fetal growth conditions. A latent variable, named Favorable Fetal Growth Condition (FFGC), has been defined by Bollen et al., in 2013; he showed that this FFGC latent variable mediates the effects of maternal characteristics on several birth outcomes. Objectives: The objectives of the present study were to replicate Bollen’s approach in a population of newborns in Paris and to investigate the potential differential effect of the FFGC latent variable according to the neighborhood socioeconomic level. Methods: Newborn health data were available from the first birth certificate registered by the Maternal and Child Care department of the City of Paris. All newborns (2008–2011) were geocoded at the mother residential census block. Each census block was assigned a socioeconomic deprivation level. Several mothers’ characteristics were collected from the birth certificates: age, parity, education and occupational status and the occupational status of the father. Three birth outcomes were considered: birth weight (BW), birth length (BL) and gestational age (GA). Results: Using a series of structural equation models, we confirm that the undirected model (that includes the FFGC latent variable) provided a better fit for the data compared with the model where parental characteristics directly affected BW, BL, and/or GA. However, the strength, the direction and statistical significance of the associations between the exogenous variables and the FFGC were different according to the neighborhood deprivation level. Conclusion: Future research should be designed to assess the how robust the FFGC latent variable is across populations and should take into account neighborhood characteristics to identify the most vulnerable group and create better design prevention policies.

BEYOND BLACK-BOXES IN BAYESIAN INVERSE PROBLEMS AND MODEL VALIDATION: APPLICATIONS IN SOLID MECHANICS OF ELASTOGRAPHY

The present paper is motivated by one of the most fundamental challenges in inverse problems, that of quantifying model discrepancies and errors. While significant strides have been made in calibrating model parameters, the overwhelming majority of pertinent methods is based on the assumption of a perfect model. Motivated by problems in solid mechanics which, as all problems in continuum thermodynamics, are described by conservation laws and phenomenological constitutive closures, we argue that in order to quantify model uncertainty in a physically meaningful manner, one should break open the black-box forward model. In particular we propose formulating an undirected probabilistic model that explicitly accounts for the governing equations and their validity. This recasts the solution of both forward and inverse problems as probabilistic inference tasks where the problem's state variables should not only be compatible with the data but also with the governing equations as well. Even though the probability densities involved do not contain any black-box terms, they live in much higher-dimensional spaces. In combination with the intractability of the normalization constant of the undirected model employed, this poses significant challenges which we propose to address with a linearly-scaling, double-layer of Stochastic Variational Inference. We demonstrate the capabilities and efficacy of the proposed model in synthetic forward and inverse problems (with and without model error) in elastography.

Tourism Research Co-authorship Networks in China

The primary objective of this study is to explore the patterns of collaborations in the tourism research community in China. The study reveals that co-authorship is fast-growing over the past 10 years. Using a common binary undirectional network model, this paper explores some network characteristics of the tourism research co-authorship network in China (TRCNC) and discusses the significance of the results. The results show that the TRCNC is typically a complex network with scale-free and small-world properties. The analyses of density and centrality indicate loose collaborations and a clear “leading scholars” phenomenon in the TRCNC. Clique analysis shows that there are lots of academic teams in tourism research in China in which scholars collaborate closely but out of which the scientific collaboration is less. In the TRCNC, those whose networks bridge structural holes are all well-known scholars in China, which is beneficial for making academic factions flourish while maybe incurring sluggish academic innovation ability.

Optimal designs for the proportional interference model

The interference model has been widely used and studied in block experiments where the treatment for a particular plot has effects on its neighbor plots. In this paper, we study optimal circular designs for the proportional interference model, in which the neighbor effects of a treatment are proportional to its direct effect. Kiefer's equivalence theorems for estimating both the direct and total treatment effects are developed with respect to the criteria of A, D, E and T. Parallel studies are carried out for the undirectional model, where the neighbor effects do not depend on whether they are from the left or right. Moreover, the connection between optimal designs for the directional and undiretional models is built. Importantly, one can easily develop a computer program for finding optimal designs based on these theorems.

Representing Aggregators in Relational Probabilistic Models

We consider the problem of, given a probabilistic model on a set of random variables, how to add a new variable that depends on the other variables, without changing the original distribution. In particular, we consider relational models (such as Markov logic networks (MLNs)), where we cannot directly define conditional probabilities. In relational models, there may be an unbounded number of parents in the grounding, and conditional distributions need to be defined in terms of aggregators. The question we ask is whether and when it is possible to represent conditional probabilities at all in various relational models. Some aggregators have been shown to be representable by MLNs, by adding auxiliary variables; however it was unknown whether they could be defined without auxiliary variables. For other aggregators, it was not known whether they can be represented by MLNs at all. We obtained surprisingly strong negative results on the capability of flexible undirected relational models such as MLNs to represent aggregators without affecting the original model's distribution. We provide a map of what aspects of the models, including the use of auxiliary variables and quantifiers, result in the ability to represent various aggregators. In addition, we provide proof techniques which can be used to facilitate future theoretic results on relational models, and demonstrate them on relational logistic regression (RLR).

Community discovery and importance analysis in social network

Social networks are widespread and important in our daily life. Finding communities and reveal node characteristics in community are crucial to understand the network structure and function. Many methods based on Nonnegative matrix factorization NMF are proposed to find communities, while these results appear uncertain with the initial condition especially in weighted directed network. In this paper, firstly we improve the nonnegative matrix factorization NMF method with modeling network as the weighted directed graph and using diagonally dominant matrix as constraint condition to obtain the community membership of each node as well as the interaction among communities. Furthermore, we raise methods to evaluate nodes importance and to discuss node characteristics in community to analyze the network structure. Some experiments on the Zachary club datasets and other real-world datasets have been did to demonstrate the superiority of our methods for community discovery over other related matrix factorization methods. The results demonstrate that our methods are useful and applicable both in weighted directed model and undirected model for community discovery, and the results are more reliable. Experiments also illustrate the meaningful results by discussing the node characteristics in community. All those provide a useful way for analyzing social network.

Coordination Frictions and Job Heterogeneity

We develop a competing auction model of a labor market with a continuum of heterogeneous workers and firms. We estimate this model and compare it to closely related models of price posting using Danish data on wages and productivities. Assuming heterogeneous workers with no comparative advantage, we find that each model gives a reasonable approximation of the statistical moments of both the wage and productivity distribution. A sensitivity analysis then draws out further implications of the theory. We explain how the feasible matchings between workers and firms changes as the worker moves up the job ladder, how the identification of assortative matching is fundamentally different in directed and undirected search models, how our theory accounts for business cycle facts related to inter-temporal changes in job offer distributions, and how our model could also be used to identify the contributions of specific versus general human capital.

Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks

Undirected graphical models are widely used in statistics, physics, and machine vision. However, Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalizing constant. This problem has received much attention, but very little of this has focused on the important practical case where the data consist of noisy or incomplete observations of the underlying hidden structure. This article specifically addresses this problem, comparing two alternate methodologies. In the first of these approaches, particle Markov chain Monte Carlo (Andrieu, Doucet, and Holenstein) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray, Ghahramani, and MacKay) for avoiding the calculation of the intractable normalizing constant (a proof showing that this combination targets the correct distribution is given in Appendix A available in the online supplementary materials). This approach is compared with approximate Bayesian computation (Pritchard et al.). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the article targets an approximation to the true posterior due to the use of Markov chain Monte Carlo method (MCMC) to simulate from the latent graphical model, in lieu of being able to do this exactly, in general. Appendix B (online supplementary materials) also describes the nature of the resulting approximation. Supplementary materials for this article are available online.

Learning directed relational models with recursive dependencies

Recently, there has been an increasing interest in generative models that represent probabilistic patterns over both links and attributes. A common characteristic of relational data is that the value of a predicate often depends on values of the same predicate for related entities. For directed graphical models, such recursive dependencies lead to cycles, which violates the acyclicity constraint of Bayes nets. In this paper we present a new approach to learning directed relational models which utilizes two key concepts: a pseudo likelihood measure that is well defined for recursive dependencies, and the notion of stratification from logic programming. An issue for modelling recursive dependencies with Bayes nets are redundant edges that increase the complexity of learning. We propose a new normal form format that removes the redundancy, and prove that assuming stratification, the normal form constraints involve no loss of modelling power. Empirical evaluation compares our approach to learning recursive dependencies with undirected models (Markov Logic Networks). The Bayes net approach is orders of magnitude faster, and learns more recursive dependencies, which lead to more accurate predictions.

Learning graphical models for relational data via lattice search

Many machine learning applications that involve relational databases incorporate first-order logic and probability. Relational extensions of graphical models include Parametrized Bayes Net (Poole in IJCAI, pp. 985---991, 2003), Probabilistic Relational Models (Getoor et al. in Introduction to statistical relational learning, pp. 129---173, 2007), and Markov Logic Networks (MLNs) (Domingos and Richardson in Introduction to statistical relational learning, 2007). Many of the current state-of-the-art algorithms for learning MLNs have focused on relatively small datasets with few descriptive attributes, where predicates are mostly binary and the main task is usually prediction of links between entities. This paper addresses what is in a sense a complementary problem: learning the structure of a graphical model that models the distribution of discrete descriptive attributes given the links between entities in a relational database. Descriptive attributes are usually nonbinary and can be very informative, but they increase the search space of possible candidate clauses. We present an efficient new algorithm for learning a Parametrized Bayes Net that performs a level-wise search through the table join lattice for relational dependencies. From the Bayes net we obtain an MLN structure via a standard moralization procedure for converting directed models to undirected models. Learning MLN structure by moralization is 200---1000 times faster and scores substantially higher in predictive accuracy than benchmark MLN algorithms on five relational databases.

Two Distributed-State Models For Generating High-Dimensional Time Series

In this paper we develop a class of nonlinear generative models for high-dimensional time series. We first propose a model based on the restricted Boltzmann machine (RBM) that uses an undirected model with binary latent variables and real-valued variables. The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. This conditional RBM (CRBM) makes on-line inference efficient and allows us to use a simple approximate learning procedure. We demonstrate the power of our approach by synthesizing various sequences from a model trained on motion capture data and by performing on-line filling in of data lost during capture. We extend the CRBM in a way that preserves its most important computational properties and introduces multiplicative three-way interactions that allow the effective interaction weight between two variables to be modulated by the dynamic state of a third variable. We introduce a factoring of the implied three-way weight tensor to permit a more compact parameterization. The resulting model can capture diverse styles of motion with a single set of parameters, and the three-way interactions greatly improve its ability to blend motion styles or to transition smoothly among them. Videos and source code can be found at http://www.cs.nyu.edu/~gwtaylor/publications/jmlr2011.

Polyominoes with nearly convex columns: An undirected model

Column-convex polyominoes were introduced in 1950’s by Temperley, a mathematical physicist working on “lattice gases”. By now, columnconvex polyominoes are a popular and well-understood model. There exist several generalizations of column-convex polyominoes; an example is a model called multi-directed animals. In this paper, we introduce a new sequence of supersets of column-convex polyominoes. Our model (we call it level m column-subconvex polyominoes) is defined in a simple way. We focus on the case when cells are hexagons and we compute the area generating functions for the levels one and two. Both of those generating functions are complicated q-series, whereas the area generating function of column-convex polyominoes is a rational function. The growth constants of level one and level two column-subconvex polyominoes are 4.319139 and 4.509480, respectively. For comparison, the growth constants of column-convex polyominoes, multi-directed animals and all polyominoes are 3.863131, 4.587894 and 5.183148, respectively.

Structure Learning for Markov Logic Networks with Many Descriptive Attributes

Many machine learning applications that involve relational databases incorporate first-order logic and probability. Markov Logic Networks (MLNs) are a prominent statistical relational model that consist of weighted first order clauses. Many of the current state-of-the-art algorithms for learning MLNs have focused on relatively small datasets with few descriptive attributes, where predicates are mostly binary and the main task is usually prediction of links between entities. This paper addresses what is in a sense a complementary problem: learning the structure of an MLN that models the distribution of discrete descriptive attributes on medium to large datasets, given the links between entities in a relational database. Descriptive attributes are usually nonbinary and can be very informative, but they increase the search space of possible candidate clauses. We present an efficient new algorithm for learning a directed relational model (parametrized Bayes net), which produces an MLN structure via a standard moralization procedure for converting directed models to undirected models. Learning MLN structure in this way is 200-1000 times faster and scores substantially higher in predictive accuracy than benchmark algorithms on three relational databases.