Least-squares estimation of a class of frequency functions: A finite sample variance expression

A new expression for the variance of scalar frequency functions estimated using the least-squares method is presented. The expression is valid for finite sample size and for a class of model structures, which includes finite impulse response, Laguerre and Kautz models, when the number of estimated parameters coincides with the number of excitation frequencies of the input. The expression gives direct insight into how excitation frequencies and amplitudes affect the accuracy of frequency function estimates. With the help of this expression, a severe sensitivity of the accuracy with respect to the excitation frequencies is exposed. The relevance of the expression when more excitation frequencies are used is also discussed.     

An adaptive B-spline representation of piecewise polynomial functions for multilevel approximation

Let I be some real interval endowed with an arbitrary partition τ. The aim of this work is to establish a new B-spline representation of the piecewise polynomial functions (p.p.f.) defined on I which can be used for a multilevel approximation. First, we show that any p.p.f. S can be written in terms of B-splines having τ as sequence of simple knots and the same smoothness order as S. This new family of B-splines has interesting properties similar to those of the well known B-splines. In order to illustrate the interest of this representation, we establish two methods which allow to approximate or project a given p.p.f. S in spaces with high smoothness order. At the end of this paper, we use this representation for constructing quasi-interpolants based on these methods.     

Comparing perceptual judgment and subjective measures of spatial awareness

Spatial awareness is important in domains where safety hinges on human operators keeping track of the relative locations of objects in the environment. While a variety of subjective and judgment-based measures have been used to evaluate spatial awareness, none have probed all three of its levels: (1) identification of environmental objects, (2) their current locations relative to the operator, and (3) their relative positions over time. This work compares new judgment-based measures of spatial awareness that probe all three levels of spatial awareness to conventional subjective measures. In the evaluation of 14 configurations of Synthetic Vision Systems head down displays (seven terrain textures and two Geometric Fields of View (GFOVs)), 18 pilots made four types of judgments (relative angle, distance, height, and abeam time) regarding the location of terrain points displayed in 112 5-s, non-interactive simulations. They also provided subjective demand, awareness, clutter, SA-SWORD, and preferred GFOV measures. Correlation analyses revealed that displays that received higher awareness and SA-SWORD subjective ratings were associated with smaller errors in abeam time judgments and, for SA-SWORD, smaller errors in relative distance judgments. Thus SA-SWORD provides insight into level 2 spatial awareness and both SA-SWORD and awareness provide insight into level 3 spatial awareness. ANOVA and χ² analyses revealed comparable results between display configurations that produced the minimum error in judgments and those recommended by the awareness, SA-SWORD, and preferred GFOV measures.     

Prediction error method for identification of LPV models

This paper is concerned with identification of linear parameter varying (LPV) systems in an input-output setting with Box-Jenkins (BJ) model structure. Classical linear time invariant prediction error method (PEM) is extended to the LPV PEM. Under the new LPV framework, identification of two types of input-output LPV models is considered: one is based on parameter interpolation and the other is based on model interpolation. The effectiveness of the proposed solution is validated by comparison with other existing LPV identification approaches through simulation examples and demonstrated by experiment studies.     

Effectiveness of error correcting output coding methods in ensemble and monolithic learning machines

Abstract Error Correcting Output Coding (ECOC) methods for multiclass classification present several open problems ranging from the trade-off between their error recovering capabilities and the learnability of the induced dichotomies to the selection of proper base learners and to the design of well-separated codes for a given multiclass problem. We experimentally analyse some of the main factors affecting the effectiveness of ECOC methods. We show that the architecture of ECOC learning machines influences the accuracy of the ECOC classifier, highlighting that ensembles of parallel and independent dichotomic Multi-Layer Perceptrons are well-suited to implement ECOC methods. We quantitatively evaluate the dependence among codeword bit errors using mutual information based measures, experimentally showing that a low dependence enhances the generalisation capabilities of ECOC. Moreover we show that the proper selection of the base learner and the decoding function of the reconstruction stage significantly affects the performance of the ECOC ensemble. The analysis of the relationships between the error recovering power, the accuracy of the base learners, and the dependence among codeword bits show that all these factors concur to the effectiveness of ECOC methods in a not straightforward way, very likely dependent on the distribution and complexity of the data.An erratum to this article can be found at     

数据协调中测量数据方差–协方差估计及过失误差序列补偿算法

数据协调测量误差的方差-协方差矩阵(也称Q矩阵)通常是由操作人员根据仪表的精度事先给定的,由于没有考虑仪表精度的变化,很可能会造成数据的不一致或不准确.基于空间冗余的约束残差,本文提出了一种测量方差-协方差Q矩阵的估计方法,有效地减少了对Q矩阵先验知识的依赖.针对常见非线性或双线性问题,提出了估计方法的应用方案.并给出了侦破过失误差的序列补偿法.最后,某焦化厂的应用示例表明.该方法对于获得Q矩阵的最初估计和侦破过失误差是有效的.     

An approximation method for high-order fractional derivatives of algebraically singular functions

The fractional derivative D^qf(s) (0≤s≤1) of a given function f(s) with a positive non-integer q is defined in terms of an indefinite integral. We propose a uniform approximation scheme to D^qf(s) for algebraically singular functions f(s)=s^αg(s) (α>−1) with smooth functions g(s). The present method consists of interpolating g(s) at sample points t_j in [0,1] by a finite sum of the Chebyshev polynomials. We demonstrate that for the non-negative integer m such that m<q<m+1, the use of high-order derivatives g⁽ⁱ⁾(0) and g⁽ⁱ⁾(1) (0≤i≤m) at both ends of [0,1] as well as g(t_j), t_j∈[0,1] in interpolating g(s), is essential to uniformly approximate D^q{s^αg(s)} for 0≤s≤1 when α≥q−m−1. Some numerical examples in the simplest case 1<q<2 are included.     

Automated error analysis for the agilization of feature modeling

Software Product Lines (SPL) and agile methods share the common goal of rapidly developing high-quality software. Although they follow different approaches to achieve it, some synergies can be found between them by (i) applying agile techniques to SPL activities so SPL development becomes more agile; and (ii) tailoring agile methodologies to support the development of SPL. Both options require an intensive use of feature models, which are usually strongly affected by changes on requirements. Changing large-scale feature models as a consequence of changes on requirements is a well-known error-prone activity. Since one of the objectives of agile methods is a rapid response to changes in requirements, it is essential an automated error analysis support in order to make SPL development more agile and to produce error-free feature models.

As a contribution to find the intended synergies, this article sets the basis to provide an automated support to feature model error analysis by means of a framework which is organized in three levels: a feature model level, where the problem of error treatment is described; a diagnosis level, where an abstract solution that relies on Reiter’s theory of diagnosis is proposed; and an implementation level, where the abstract solution is implemented by using Constraint Satisfaction Problems (CSP).

To show an application of our proposal, a real case study is presented where the Feature-Driven Development (FDD) methodology is adapted to develop an SPL. Current proposals on error analysis are also studied and a comparison among them and our proposal is provided. Lastly, the support of new kinds of errors and different implementation levels for the proposed framework are proposed as the focus of our future work.     

Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation

In this paper we present rigorous a posteriori L ² error bounds for reduced basis approximations of the unsteady viscous Burgers’ equation in one space dimension. The a posteriori error estimator, derived from standard analysis of the error-residual equation, comprises two key ingredients—both of which admit efficient Offline-Online treatment: the first is a sum over timesteps of the square of the dual norm of the residual; the second is an accurate upper bound (computed by the Successive Constraint Method) for the exponential-in-time stability factor. These error bounds serve both Offline for construction of the reduced basis space by a new POD-Greedy procedure and Online for verification of fidelity. The a posteriori error bounds are practicable for final times (measured in convective units) T≈O(1) and Reynolds numbers ν ⁻¹≫1; we present numerical results for a (stationary) steepening front for T=2 and 1≤ν ⁻¹≤200. This work was supported by AFOSR Grants FA9550-05-1-0114 and FA-9550-07-1-0425 and the Singapore-MIT Alliance. We acknowledge many helpful discussions with Professor Yvon Maday of University of Paris VI and Dr. Paul Fischer of Argonne National Laboratory and University of Chicago.     

布尔函数和伪布尔函数多项式表示的快速实现算法

布尔函数和伪布尔函数在不同的领域有着广泛的应用,利用多项式表示有利于刻划它们的一些特征属性。论文首先在已知输入都能得到输出的条件下给出了布尔函数多项式表示的快速实现算法,该算法仅用到模2加运算,运算次数少,具有简洁、易于编程实现、准确而快速的特点,而且该算法很易推广为伪布尔函数多项式表示的快速实现算法,只需把模2加运算换成实数加运算即可。接着通过比较说明了伪布尔函数多项式表示的快速实现算法,同时指出任何伪布尔函数都能通过多项式形式表示出来。最后通过实例进一步验证了算法的正确性。     

Will the PLS criterion for order estimation work with AML and a posteriori prediction error?

The general formula of the PLS (Predictive Least Squares) criterion for order estimation is worked out under the assumption that the parameter estimates are calculated via the AML (Approximate Maximum Likelihood). A particular case is then carefully analysed and it is shown that depending on the system generating the data the PLS critetion using the a posteriori prediction error can, surprisingly, almost surely overestimate the true order.     

Testing and estimation of purely nonparametric effects in repeated measures designs

The several sample case of the so-called nonparametric Behrens-Fisher problem in repeated measures designs is considered. That is, even under the null hypothesis, the marginal distribution functions in the different groups may have different shapes, and are not assumed to be equal. Moreover, the continuity of the marginal distribution functions is not required so that data with ties and, particularly, ordered categorical data are covered by this model. A multiple relative treatment effect is defined which can be estimated by using the mid-ranks of the observations within pairwise samples. The asymptotic distribution of this estimator is derived, along with a consistent estimator of its asymptotic covariance matrix. In addition, a multiple contrast test and related simultaneous confidence intervals for the relative marginal effects are derived and compared to rank-based Wald-type and ANOVA-type statistics. Simulations show that the ANOVA-type statistic and the multiple contrast test appear to maintain the pre-assigned level of the test quite accurately (even for rather small sample sizes) while the Wald-type statistic leads, as expected, to somewhat liberal decisions. Regarding the power, none of the statistics is uniformly superior. A real data set illustrates the application.     

Chebyshev approximation of functions by the sum of a polynomial and an expression with a nonlinear parameter and endpoint interpolation

Sufficient existence conditions are established for the uniform Chebyshev (minimax) approximation of a function by the sum of a polynomial and an expression with a nonlinear parameter with the minimum absolute error and interpolation at the interval endpoints. An algorithm for determining the parameters of such an approximation using the Remez algorithm is proposed. The application of the iterative method to calculating the nonlinear parameter is substantiated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 64–75, January–February 2009.     

Conditional mean estimation under asymmetric and heteroscedastic error by linear combination of quantile regressions

In this paper we propose a new estimator for regression problems in the form of the linear combination of quantile regressions. The proposed estimator is helpful for the conditional mean estimation when the error distribution is asymmetric and heteroscedastic.It is shown that the proposed estimator has the consistency under heteroscedastic regression model: Y=μ(X)+σ(X)·e, where X is a vector of covariates, Y is a scalar response, e is a zero mean random variable independent of X and σ(X) is a positive value function. When the error term e is asymmetric, we show that the proposed estimator yields better conditional mean estimation performance than the other estimators. Numerical experiments both in synthetic and real data are shown to illustrate the usefulness of the proposed estimator.     

On looseness of error bounds provided by the generalized separability measures of Lissack and Fu

An expression is obtained for maximum difference between the upper and the lower bounds to Bayesian probability of error in terms of the generalized separability measures of Lissack and Fu (L. The expression gives the magnitude of looseness of error bounds for different values of .     

Simultaneous estimation of odor classes and concentrations using an electronic nose with function approximation model ensembles

This paper sets up a practical electronic nose for simultaneously estimating many kinds of odor classes and concentrations. Mathematically, such simultaneous estimation problems can be regarded as multi-input/multi-output (MIMO) function approximation problems. After decomposing an MIMO approximation task into multiple many-to-one tasks, we can use multiple many-to-one approximation model ensembles to implement them one after another. A single approximation model may be a multivariate logarithmic regression, a quadratic multivariate logarithmic regression, a multilayer perceptron, or a support vector machine. An ensemble is made up of the above four models, represents a special kind of odor, and realizes the relationship between sensor array responses and the represented odor concentrations. Naturally, all members in the ensemble are trained only by the samples from the represented odor. The real outputs of ensembles are the average predicted concentrations and the relative standard deviations (R.S.D.s). The ensemble with the smallest R.S.D. finally gives the label and concentration of an odor sample, which can be looked upon as the use of the average and the minimum combination rules. The predicted results for four kinds of fragrant materials, ethanol, ethyl acetate, ethyl caproate, and ethyl lactate, 21 concentrations in total, show that the proposed approximation model ensembles and combination strategies with the electronic nose are effective for simultaneously estimating many kinds of odor classes and concentrations.     

Explicit A-Priori error bounds and Adaptive error control for approximation of nonlinear initial value differential systems

This paper develops and demonstrates a guaranteed a-priori error bound for the Taylor polynomial approximation of any degree to the solution of initial value ordinary differential equations. The error bound is explicit and does not require upper bounds on the potentially complicated and intrinsically unknown right-hand side nor on any of its higher-order derivatives as with existing bounds, and thus it provides a valuable tool for the numerous applications in which initial value ode problems arise and for which approximate solutions must be sought.     

A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets

Ranking methods, similarity measures and uncertainty measures are very important concepts for interval type-2 fuzzy sets (IT2 FSs). So far, there is only one ranking method for such sets, whereas there are many similarity and uncertainty measures. A new ranking method and a new similarity measure for IT2 FSs are proposed in this paper. All these ranking methods, similarity measures and uncertainty measures are compared based on real survey data and then the most suitable ranking method, similarity measure and uncertainty measure that can be used in the computing with words paradigm are suggested. The results are useful in understanding the uncertainties associated with linguistic terms and hence how to use them effectively in survey design and linguistic information processing.