Lagged queue-length correlations in two-node networks

Lagged correlations between the queue lengths in two-node queueing networks are considered. These can be calculated easily by the randomization method. It is shown that the lagged correlation between node 1 and node 2 is exactly proportional to that between node 2 and node 1. The effect of feedback speed on correlations at a single node is also considered.     

Lagged correlations in simple queueing networks

The correlations between the queue lengths at nodes in simple Jackson networks are investigated by the randomization numerical method. Although at a fixed point in time these queue lengths are well known to be independent when we compare values at slightly different time points substantial correlation patterns show up. Several classes of systems turn out to have either identical or closely related correlation patterns.     

Inferring Boolean functions via higher-order correlations

Both the Walsh transform and a modified Pearson correlation coefficient can be used to infer the structure of a Boolean network from time series data. Unlike the correlation coefficient, the Walsh transform is also able to represent higher-order correlations. These correlations of several combined input variables with one output variable give additional information about the dependency between variables, but are also more sensitive to noise. Furthermore computational complexity increases exponentially with the order. We first show that the Walsh transform of order 1 and the modified Pearson correlation coefficient are equivalent for the reconstruction of Boolean functions. Secondly, we also investigate under which conditions (noise, number of samples, function classes) higher-order correlations can contribute to an improvement of the reconstruction process. We present the merits, as well as the limitations, of higher-order correlations for the inference of Boolean networks.     

Combining dissimilarity matrices by using rank correlations

Recently there has been increased interest in methods for aggregating multiple matrices observed on a fixed set of entities, where each matrix expresses a particular notion of the dissimilarity of one entity from another. An optimization-based procedure is developed, which returns a global dissimilarity matrix in the form of a weighted average of the partial matrices. The weights are determined with the goal of overcoming conflicts and overlaps that inevitably arise when different sources of data become part of the same representational structure. One important aspect in this context is the coefficient used to measure the degree of association between matrices. Here, it is normal to adopt the vector correlation proposed by Escoufier, but this has the drawback of depending on the Pearson’s correlation, which is highly prone to the effects of outliers. The solution that we propose to mitigate this problem is the substitution of the Pearson coefficient with rank correlations that are less affected by errors of measurement, nonlinearity or outliers. The results obtained with real and simulated data confirm that applying vector rank correlations attenuates the adverse effects of anomalies and, in the case of clean and faultless data, yields weights which basically conform to those obtained using the Escoufier coefficient.     

Robust canonical correlations: A comparative study

Summary  Several approaches for robust canonical correlation analysis will be presented and discussed. A first method is based on the definition of canonical correlation analysis as looking for linear combinations of two sets of variables having maximal (robust) correlation. A second method is based on alternating robust regressions. These methods are discussed in detail and compared with the more traditional approach to robust canonical correlation via covariance matrix estimates. A simulation study compares the performance of the different estimators under several kinds of sampling schemes. Robustness is studied as well by breakdown plots.     

Some properties of canonical correlations and variates in infinite dimensions

In this paper the notion of functional canonical correlation as a maximum of correlations of linear functionals is explored. It is shown that the population functional canonical correlation is in general well defined, but that it is a supremum rather than a maximum, so that a pair of canonical variates may not exist in the spaces considered. Also the relation with the maximum eigenvalue of an associated pair of operators and the corresponding eigenvectors is not in general valid. When the inverses of the operators involved are regularized, however, all of the above properties are restored. Relations between the actual population quantities and their regularized versions are also established. The sample functional canonical correlations can be regularized in a similar way, and consistency is shown at a fixed level of the regularization parameter.     

Normalizing and variance stabilizing transformations for intraclass correlations

Summary A concept of normalizing transformations of statistics is constructed on the basis of the rate of convergence to normality. The concept is applied to derive a normalizing transformation of a maximum likelihood estimate of intraclass correlation coefficient in ap-variate normal sample. Numerical comparisons are made to examine whether the proposed transformation is efficient to achieve normality. The relationship between normalization and variance stabilization is also considered. The Institute of Statistical Mathematics     

Parameterizing correlations: a geometric interpretation

^** Email: francesco.rapisarda{at}ubs.com In this paper, we present a new interpretation of the parameterizationof a correlation matrix proposed earlier by some authors (Jäckel& Rebonato, 1999). This interpretation is based on viewingany correlation matrix as the result of the scalar productsof a suitable set of unit vectors in a multidimensional space,each rotated from all the others by generalized Euler angles.It is possible to exploit the intuitive nature of this approachin order to obtain more efficient optimization schemes whencalibrating a reduced-form model to a desired correlation structure.     

Fitting correlated arrival and service times and related queueing performance

In this paper, we consider a queue where the inter-arrival times are correlated and, additionally, service times are also correlated with inter-arrival times. We show that the resulting model can be interpreted as an MMAP[K]/PH[K]/1 queue for which matrix geometric solution algorithms are available. The major result of this paper is the presentation of approaches to fit the parameters of the model, namely the MMAP, the PH distribution and the parameters introducing correlation between inter-arrival and service times, according to some trace of inter-arrival and corresponding service times. Two different algorithms are presented. The first algorithm is based on available methods to compute a MAP from the inter-arrival times and a PH distribution from the service times. Afterward, the correlation between inter-arrival and service times is integrated by solving a quadratic programming problem over some joint moments. The second algorithm is of the expectation maximization type and computes all parameters of the MAP and the PH distribution in an iterative way. It is shown that both algorithms yield sufficiently accurate results with an acceptable effort.     

A practical non-parametric copula algorithm for system reliability with correlations

System reliability analysis involving correlated random variables is challenging because the failure probability cannot be uniquely determined under the given probability information. This paper proposes a system reliability evaluation method based on non-parametric copulas. The approximated joint probability distribution satisfying the constraints specified by correlations has the maximal relative entropy with respect to the joint probability distribution of independent random variables. Thus the reliability evaluation is unbiased from the perspective of information theory. The estimation of the non-parametric copula parameters from Pearson linear correlation, Spearman rank correlation, and Kendall rank correlation are provided, respectively. The approximated maximum entropy distribution is then integrated with the first and second order system reliability method. Four examples are adopted to illustrate the accuracy and efficiency of the proposed method. It is found that traditional system reliability method encodes excessive dependence information for correlated random variables and the estimated failure probability can be significantly biased.     

Chained correlations for feature selection

Advances in Data Analysis and Classification - Data-driven algorithms stand and fall with the availability and quality of existing data sources. Both can be limited in high-dimensional settings (...     

Combinatorics on partial word correlations

Partial words are strings over a finite alphabet that may contain a number of “do not know” symbols. In this paper, we consider the period and weak period sets of partial words of length n over a finite alphabet, and study the combinatorics of specific representations of them, called correlations, which are binary and ternary vectors of length n indicating the periods and weak periods. We characterize precisely which vectors represent the period and weak period sets of partial words and prove that all valid correlations may be taken over the binary alphabet. We show that the sets of all such vectors of a given length form distributive lattices under suitably defined partial orderings. We show that there is a well-defined minimal set of generators for any binary correlation of length n and demonstrate that these generating sets are the primitive subsets of {1,2,…,n−1}. We also investigate the number of partial word correlations of length n. Finally, we compute the population size, that is, the number of partial words sharing a given correlation, and obtain recurrences to compute it. Our results generalize those of Guibas, Odlyzko, Rivals and Rahmann.     

A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices

This paper studies the performance of two stochastic local search algorithms for the biobjective Quadratic Assignment Problem with different degrees of correlation between the flow matrices. The two algorithms follow two fundamentally different ways of tackling multiobjective combinatorial optimization problems. The first is based on the component-wise ordering of the objective value vectors of neighboring solutions, while the second is based on different scalarizations of the objective function vector. Our experimental results suggest that the performance of the algorithms with respect to solution quality and computation time depends strongly on the correlation between the flow matrices. In addition, some variants of these stochastic local search algorithms obtain very good solutions in short computation time.     

Pair correlations in lower-dimensional systems

We consider a system consisting of separate fibers weakly coupled to each other. Each fiber is characterized by a scalar order parameter. We study the correlation of order parameter fluctuations depending on the number of fibers in the system. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 129–136, April, 2006.     

On testing equality of pairwise rank correlations in a multivariate random vector

Spearman’s rank-correlation coefficient (also called Spearman’s rho) represents one of the best-known measures to quantify the degree of dependence between two random variables. As a copula-based dependence measure, it is invariant with respect to the distribution’s univariate marginal distribution functions. In this paper, we consider statistical tests for the hypothesis that all pairwise Spearman’s rank correlation coefficients in a multivariate random vector are equal. The tests are nonparametric and their asymptotic distributions are derived based on the asymptotic behavior of the empirical copula process. Only weak assumptions on the distribution function, such as continuity of the marginal distributions and continuous partial differentiability of the copula, are required for obtaining the results. A nonparametric bootstrap method is suggested for either estimating unknown parameters of the test statistics or for determining the associated critical values. We present a simulation study in order to investigate the power of the proposed tests. The results are compared to a classical parametric test for equal pairwise Pearson’s correlation coefficients in a multivariate random vector. The general setting also allows the derivation of a test for stochastic independence based on Spearman’s rho.     

Universality and scaling of correlations between zeros on complex manifolds

We study the limit as N→∞ of the correlations between simultaneous zeros of random sections of the powers L ^N of a positive holomorphic line bundle L over a compact complex manifold M, when distances are rescaled so that the average density of zeros is independent of N. We show that the limit correlation is independent of the line bundle and depends only on the dimension of M and the codimension of the zero sets. We also provide some explicit formulas for pair correlations. In particular, we prove that Hannay’s limit pair correlation function for SU(2) polynomials holds for all compact Riemann surfaces. Oblatum 17-VI-1999 & 31-III-2000?Published online: 5 June 2000     

Fitness landscape analysis for the no-wait flow-shop scheduling problem

The fitness landscape of the no-wait (continuous) flow-shop scheduling problem is investigated by examining the ruggedness of the landscape and the correlation between the quality of a solution and its distance to an optimal solution. The results confirm the presence of a big valley structure as known from other combinatorial optimization problems. The suitability of the landscape for search with evolutionary computation and local search methods is discussed. The observations are validated by experiments with two evolutionary algorithms.     

Special algorithms for the simulation of homogeneous random fields

In this paper, two new algorithms for the simulation of homogeneous random fields are proposed. Both algorithms are based on the well-known algorithm of rows and columns for the simulation of Gaussian fields with special correlation functions. The algorithms make it possible to efficiently simulate homogeneous random fields with nonconvex correlation functions.     

The search for correlations in polymer adhesion

The parameters suitable for correlation with the end result of adhesion interaction are considered and the need to use surface energies is demonstrated with reference to the conventional σ₀ and theoretical σ_e strengths of polyvinyl-butyral-metal bonds [12].     

Wiener Chaos and Nonlinear Filtering

The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. The paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering.