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Building Undirected Influence Ontologies Using Pairwise Similarity Functions
Abstract
The recovery of influence ontology structures is a useful tool within knowledge discovery, allowing for an easy and intuitive method of graphically representing the influences between concepts or variables within a system. The focus of this research is to develop a method by which undirected influence structures, here in the form of undirected Bayesian network skeletons, can be recovered from observations by means of some pairwise similarity function, either a statistical measure of correlation or some problem-specific measure. In this research, we present two algorithms to construct undirected influence structures from observations. The first makes use of a threshold value to filter out relations denoting weak influence, and the second constructs a maximum weighted spanning tree over the complete set of relations. In addition, we present a modification to the minimum graph edit distance (GED), which we refer to as the modified scaled GED, in order to evaluate the performance of these algorithms in reconstructing known structures. We perform a number of experiments in reconstructing known Bayesian network structures, including a real-world medical network. Our analysis shows that these algorithms outperform a random reconstruction (modified scaled GED ≈ 0.5), and can regularly achieve modified scaled GED scores better than 0.3 in sparse cases and 0.45 in dense cases. We argue that, while these methods cannot replace traditional Bayesian network structure-learning techniques, they are useful as computationally cheap data exploration tools and in knowledge discovery over structures which cannot be modelled as Bayesian networks.
... Bayesian networks, as graphical probabilistic models have been developed to compactly represent and reason over linked complex phenomena using computation techniques [29], [30]. Various attempts to integrate dynamic systems models, ontology engineering methods and Bayesian networks to model CAS are detailed in [16], [31], [32]. ...
Abstract—Wicked problems are a specific class of complex problems that emerge from complex adaptive systems (CAS) and stakeholder disagreements on the definition and charac- ter of these problems and their possible resolution. Attempts at resolving wicked problems through integration and use of formal methods such as ontologies, Bayesian networks (BN), and complex systems dynamic (CSD) models have been attempted recently but wicked problems continue to defy resolution. This paper argues that this is the result of a lack of ontologically precise causal Bayesian models that adequately represent the hierarchical, dynamic, emergent characteristics and multiple perceptions of CAS and their emergent wicked problems. This paper’s contribution is the incorporation of complexity systems theory concepts, namely: perspective, granularity and context, as explicit ontological constructs in a high precision ontolog- ical causal BN model, the Granular Contextual Perspectives (GCP) causal Bayesian Network model, using Hidden Markov Model (HMM) formalism to address this shortcoming. Using an illustrative example this conceptual paper shows that the (GCP) causal Bayesian Network model performs better than baseline Bayesian Network models at the visual representation, compact and retractable inference, and machine learning of CAS and their emergent wicked problems. The model is useful at supporting the exploration of possible effects of proposed alternative interventions or prototypical design strategies for resolving a given wicked problem.
Index Terms—Hidden Markov Models, Causal Hierarchical Dynamic Bayesian Networks , Ontology engineering, Wicked problems, Complex Adaptive Systems, Design Science strategies
Cramér's V and Tschuprow's T are closely related nominal variable association mea-sures, which are usually estimated by their empirical values. Although these estimators are consistent, they can have large bias for finite samples, making interpretation difficult. We propose a new and simple bias correction and show via simulations that, for larger than 2 × 2 tables, the newly obtained estimators outperform the classical (empirical) ones. For 2 × 2 tables performance is comparable. The larger the table and the smaller the sample size, the greater the superiority of the new estimators.
An efficient graph matching algorithm based on optimizing the graph edit distance is presented. The graph edit distance is expressed as a linear function of a permutation matrix and a sequence of edit matrices which represent graph edit operations. This allows the development of a linear program that is solved using an interior point method. The linear optimization produces a continuous analog to the permutation matrix that is used as a weight matrix for an instance of the well-known assignment problem. The assignment problem is solved as usual with the Hungarian method to produce a permutation matrix. A standard recognition problem of matching a sample input graph to a database of known prototype graphs is presented as an application of the new method. The costs associated with various edit operations are chosen using a minimum variance criterion applied to pairwise distances between nearest neighbors in the database of prototypes. The new approach is shown to provide significant reduction in classification ambiguity.
We review recent developments in applying Bayesian probabilistic and statistical ideas to expert systems. Using a real, moderately complex, medical example we illustrate how qualitative and quantitative knowledge can be represented within a directed graphical model, generally known as a belief network in this context. Exact probabilistic inference on individual cases is possible using a general propagation procedure. When data on a series of cases are available, Bayesian statistical techniques can be used for updating the original subjective quantitative inputs, and we present a set of diagnostics for identifying conflicts between the data and the prior specification. A model comparison procedure is explored, and a number of links made with mainstream statistical methods. Details are given on the use of Dirichlet prior distributions for learning about parameters and the process of transforming the original graphical model to a junction tree as the basis for efficient computation.
We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption oflikelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user''s priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—aprior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at mostk=1 parent. For the general case (k>1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches.
Motivation:
Bayesian network methods have shown promise in gene regulatory network reconstruction because of their capability of capturing causal relationships between genes and handling data with noises found in biological experiments. The problem of learning network structures, however, is NP hard. Consequently, heuristic methods such as hill climbing are used for structure learning. For networks of a moderate size, hill climbing methods are not computationally efficient. Furthermore, relatively low accuracy of the learned structures may be observed. The purpose of this article is to present a novel structure learning method for gene network discovery.
Results:
In this paper, we present a novel structure learning method to reconstruct the underlying gene networks from the observational gene expression data. Unlike hill climbing approaches, the proposed method first constructs an undirected network based on mutual information between two nodes and then splits the structure into substructures. The directional orientations for the edges that connect two nodes are then obtained by optimizing a scoring function for each substructure. Our method is evaluated using two benchmark network datasets with known structures. The results show that the proposed method can identify networks that are close to the optimal structures. It outperforms hill climbing methods in terms of both computation time and predicted structure accuracy. We also apply the method to gene expression data measured during the yeast cycle and show the effectiveness of the proposed method for network reconstruction.
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate
descent procedure for the lasso, we develop a simple algorithm—the graphical lasso—that is remarkably fast: It solves a 1000-node problem (∼500000 parameters) in at most a minute and is 30–4000 times faster
than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen
and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.
Recent work in Artificial Intelligence (AI) is exploring the use of formal ontologies as a way of specifying content-specific agreements for the sharing and reuse of knowledge among software entities. We take an engineering perspective on the development of such ontologies. Formal ontologies are viewed as designed artifacts, formulated for specific purposes and evaluated against objective design criteria. We describe the role of ontologies in supporting knowledge sharing activities, and then present a set of criteria to guide the development of ontologies for these purposes. We show how these criteria are applied in case studies from the design of ontologies for engineering mathematics and bibliographic data. Selected design decisions are discussed, and alternative representation choices are evaluated against the design criteria.
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a computationally attractive alternative to standard covariance selection for sparse high-dimensional graphs. Neighborhood selection estimates the conditional independence restrictions separately for each node in the graph and is hence equivalent to variable selection for Gaussian linear models. We show that the proposed neighborhood selection scheme is consistent for sparse high-dimensional graphs. Consistency hinges on the choice of the penalty parameter. The oracle value for optimal prediction does not lead to a consistent neighborhood estimate. Controlling instead the probability of falsely joining some distinct connectivity components of the graph, consistent estimation for sparse graphs is achieved (with exponential rates), even when the number of variables grows as the number of observations raised to an arbitrary power.
Note:
Republished in: Am J Psychol. 100(3-4) 441-71 (1987).
Republished in: Int J Epidemiol. 39(5):1137-50 (2010).
Consider a population in which sexual selection and natural selection may or may not be taking place. Assume only that the deviations from the mean in the case of any organ of any generation follow exactly or closely the normal law of frequency, then the following expressions may be shown to give the law of inheritance of the population.
A method to determine a distance measure between two nonhierarchical attributed relational graphs is presented. In order to apply this distance measure, the graphs are characterised by descriptive graph grammars (DGG). The proposed distance measure is based on the computation of the minimum number of modifications required to transform an input graph into the reference one. Specifically, the distance measure is defined as the cost of recognition of nodes plus the number of transformations which include node insertion, node deletion, branch insertion, branch deletion, node label substitution and branch label substitution. The major difference between the proposed distance measure and the other ones is the consideration of the cost of recognition of nodes in the distance computation. In order to do this, the principal features of the nodes are described by one or several cost functions which are used to compute the similarity between the input nodes and the reference ones. Finally, an application of this distance measure to the recognition of lower case handwritten English characters is presented.
This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.
The relation between topological ordering and adjacency matrix in digraphs
- T Rastad
- N Delfan