Dependency Tree Research Articles

A simplified method for evaluating time dependent fault-trees, using Weibull distribution

A new formula for calculating the failure rate of the mode failure for a time dependent fault tree is derived. The time-to-failure distribution for each component (primary failure) is assumed to be Weibull model with different values of parameters for each component. By using this formula, the TOP failure rate for the fault tree can be easily calculated. By appropriate choice of the two parameters of the Weibull model, a wide range of hazard curves can be approximated. The equations are derived by applying the “Kinetic Tree Theory” mentioned by Vesely [1]. The assumptions of the methodology are the independence of the primary failures and that the mode failures are previously known.

Classification of discrete data with feature space transformation

A newly developed classification scheme for samples with discrete valued features is presented in this paper. In it, we first map the discrete feature space into a Euclidean space called logarithm of likelihood ratio (LLR) space. The likelihood ratios are formed from the estimated distributions based on the dependence tree structure obtained through minimizing the error probability. By discriminant analysis, we then transform the LLR space into one-dimensional space on which classification is conducted. We have applied this new scheme to several sets of biomedical data and have obtained significantly high classification rates.

A Decision-Directed Clustering Algorithm for Discrete Data

This article presents a decision-directed approach for classifying discrete data. In the clustering algorithm, probable clusters are initiated through the use of a sorting scheme based on the estimated probability distribution of the data and an arbitrary distance measure. The subsequent iterative reclassification procedures are directed by the estimated distribution of each class. The distribution estimation adopted is modified from the dependence tree procedure. The algorithm performance is then evaluated through the use of simulated and clinical data. Finally, the algorithm is applied to disease categorization and to signs and symptoms extraction for each disease class.

Pattern Detection of Multivariate Hormonal Systems

A method of data analysis which aims at the detection of the significant periodicities as well as of the irregular high frequency oscillations (perturbations) in biological time series (TS) is proposed. The significant frequency modes are detected by application of a statistical significance criterion on the periodogram derived from the given TS; they are used to construct the significant periodic series. The latter is then subtracted from the original TS in order to obtain the detrended TS defined as the perturbation series which is considered as the outcome of a stochastic process. Under the assumption of Gaussian characteristics for the stochastic process, evidence of which is available, a probabilistic basis for both univariate and bivariate analysis is provided. A ``surprisal'' measure defined as the reciprocal of the probability for an outcome of a stochastic process (or a pair of correlated porcesses) is introduced to account for both the average as well as the localized perturbation of the TS (or the correlation between the pair of TS). A dependence tree configuration that maximizes the overall mutual information or dependence among branches is proposed as an optimal representation of a multivariate system. Lag-correlation analysis and cospectrum tests are adopted for validation and modification of the configuration generated. Simulated systems are employed to test the extent of linear approximation of various nonlinear functions as well as the sensitivity of the proposed method when the simulated system is subject to disturbances of varied type and degree.

Case, category, and configuration

ABSTRACTRepresentation of syntactic relations by dependency trees with nodes labelled by categories of lexical morphemes and with branches effectively labelled by relational morphemes reveals the relationships of elements to which selectional restrictions apply more directly than do current phrase structure characterizations and avoids certain defects of a configurational definition of relationships. The relations are those of CASE as defined by Fillmore and more generally those of HEAD-OF and COMPLEMENT-OF. Adoption of the view that SUBJECT-OF is a surface rather than a deep structure relation eliminates the need to distinguish strict subcategorization rules from selectional rules.

Approximating discrete probability distributions

The method of minimum discrimination information estimation is applied to the problem of estimating an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -dimensional discrete probability distribution in terms of lower order marginal distributions. The procedure provides a convergent iterative algorithm. The method yields regular best asymptotically normal (RBAN) estimates. The general procedure includes as a particular case that proposed by a method using dependence trees. An example is given.

Approximating discrete probability distributions with dependence trees

A method is presented to approximate optimally an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n - 1</tex> first order dependence relationship among the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> variables. It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information. It is further shown that when this procedure is applied to empirical observations from an unknown distribution of tree dependence, the procedure is the maximum-likelihood estimate of the distribution.

Analyzing English syntax with a pattern-learning parser

Abstract : A dependency analysis system based on pattern recognition and learning logic was developed to infer word-classes and rules of syntactic combination from experience with text which had been analyzed. The characteristics used to form word-classes are the depth in the dependency tree of each word, the direction of its governor, and the same features for each of its immediate neighbors. Syntactic rules of combination show the relation of a word to its governor in the depth pattern of the sentence. The system was tested on 400 elementary Basic English sentences including 300 used earlier by Knowlton in a different learning parser. The Pattern Learning Parser was able to derive a grammar which in a second pass allowed completely correct parsing of all 400 sentences. After experience with 300 sentences it was able to generalize with 77% accuracy to the next 100. In accumulative learning trials after the first 200 sentences it averaged a probability of .9 for accurately parsing each new sentence it encountered. It was concluded that the system was adequate for learning to parse the bulk of Basic English but that further development is required before conclusions about its application to ordinary English can be stated. The system is operational and available on the ARPA/SDC time-shared Q-32 computing system. (Author)