Optimal designs for conjoint experiments

In conjoint experiments, each respondent receives a set of profiles to rate. Sometimes, the profiles are expensive prototypes that respondents have to test before rating them. Designing these experiments involves determining how many and which profiles each respondent has to rate and how many respondents are needed. To that end, the set of profiles offered to a respondent is treated as a separate block in the design and a random respondent effect is used in the model because profile ratings from the same respondent are correlated. Optimal conjoint designs are then obtained by means of an adapted version of an algorithm for finding D-optimal split-plot designs. A key feature of the design construction algorithm is that it returns the optimal number of respondents and the optimal number of profiles each respondent has to evaluate for a given number of profiles. The properties of the optimal designs are described in detail and some practical recommendations are given.     

A simple and efficient method for variable ranking according to their usefulness for learning

The selection of a subset of input variables is often based on the previous construction of a ranking to order the variables according to a given criterion of relevancy. The objective is then to linearize the search, estimating the quality of subsets containing the topmost ranked variables. An algorithm devised to rank input variables according to their usefulness in the context of a learning task is presented. This algorithm is the result of a combination of simple and classical techniques, like correlation and orthogonalization, which allow the construction of a fast algorithm that also deals explicitly with redundancy. Additionally, the proposed ranker is endowed with a simple polynomial expansion of the input variables to cope with nonlinear problems. The comparison with some state-of-the-art rankers showed that this combination of simple components is able to yield high-quality rankings of input variables. The experimental validation is made on a wide range of artificial data sets and the quality of the rankings is assessed using a ROC-inspired setting, to avoid biased estimations due to any particular learning algorithm.     

A comparison of design and model selection methods for supersaturated experiments

Various design and model selection methods are available for supersaturated designs having more factors than runs but little research is available on their comparison and evaluation. Simulated experiments are used to evaluate the use of E(s²)-optimal and Bayesian D-optimal designs and to compare three analysis strategies representing regression, shrinkage and a novel model-averaging procedure. Suggestions are made for choosing the values of the tuning constants for each approach. Findings include that (i) the preferred analysis is via shrinkage; (ii) designs with similar numbers of runs and factors can be effective for a considerable number of active effects of only moderate size; and (iii) unbalanced designs can perform well. Some comments are made on the performance of the design and analysis methods when effect sparsity does not hold.     

Incorporating historical control information into quantal bioassay with Bayesian approach

A Bayesian approach with an iterative reweighted least squares is used to incorporate historical control information into quantal bioassays to estimate the dose-response relationship, where the logit of the historical control responses are assumed to have a normal distribution. The parameters from this normal distribution are estimated from both empirical and full Bayesian approaches with a marginal likelihood function being approximated by Laplace’s Method. A comparison is made using real data between estimates that include the historical control information and those that do not. It was found that the inclusion of the historical control information improves the efficiency of the estimators. In addition, this logit-normal formulation is compared with the traditional beta-binomial for its improvement in parameter estimates. Consequently the estimated dose-response relationship is used to formulate the point estimator and confidence bands for ED(100p) for various values of risk rate p and the potency for any dose level.     

Extended rate, more GFUN

We present a software package that guesses formulae for sequences of, for example, rational numbers or rational functions, given the first few terms. We implement an algorithm due to Bernhard Beckermann and George Labahn, together with some enhancements to render our package efficient. Thus we extend and complement Christian Krattenthaler’s program Rate.m, the parts concerned with guessing of Bruno Salvy and Paul Zimmermann’s GFUN, the univariate case of Manuel Kauers’ Guess.m and Manuel Kauers’ and Christoph Koutschan’s qGeneratingFunctions.m.     

Robust model selection with flexible trimming

The forward search provides data-driven flexible trimming of a C_p statistic for the choice of regression models that reveals the effect of outliers on model selection. An informed robust model choice follows. Even in small samples, the statistic has a null distribution indistinguishable from an F distribution. Limits on acceptable values of the C_p statistic follow. Two examples of widely differing size are discussed. A powerful graphical tool is the generalized candlestick plot, which summarizes the information on all forward searches and on the choice of models. A comparison is made with the use of M-estimation in robust model choice.     

Penalized cluster analysis with applications to family data

The goal of cluster analysis is to assign observations into clusters so that observations in the same cluster are similar in some sense. Many clustering methods have been developed in the statistical literature, but these methods are inappropriate for clustering family data, which possess intrinsic familial structure. To incorporate the familial structure, we propose a form of penalized cluster analysis with a tuning parameter controlling the tradeoff between the observation dissimilarity and the familial structure. The tuning parameter is selected based on the concept of clustering stability. The effectiveness of the method is illustrated via simulations and an application to a family study of asthma.     

Robust observers for neutral jumping systems with uncertain information

In this paper, the problem of designing observer for a class of uncertain neutral systems. The uncertainties are parametric and norm-bounded. Both robust observation and robust H_∞ observation methods are developed by using linear state-delayed observers. In case of robust observation, sufficient conditions are established for asymptotic stability of the system, which is independent of time delay. The results are then extended to robust H_∞ observation which renders the augmented system asymptotically stable independent of delay with a guaranteed performance measure. Furthermore, a memoryless state-estimate feedback is designed to stabilize the closed-loop neutral system. In all cases, the gain matrices are determined by linear matrix inequality approach. Two numerical examples are presented to illustrate the validity of the theoretical results.     

A new type of fuzzy n-ary hyperstructures

The aim of this paper is to consider and study a new kind of fuzzy n-ary hyperstructures, such as fuzzy n-ary hypergroups and fuzzy (m,n)-ary hyperrings.     

Geometric visualization of clusters obtained from fuzzy clustering algorithms

Fuzzy-clustering methods, such as fuzzy k-means and expectation maximization, allow an object to be assigned to multiple clusters with different degrees of membership. However, the memberships that result from fuzzy-clustering algorithms are difficult to be analyzed and visualized. The memberships, usually converted to 0-1 values, are visualized using parallel coordinates or different color shades. In this paper, we propose a new approach to visualize fuzzy-clustered data. The scheme is based on a geometric visualization, and works by grouping the objects with similar cluster memberships towards the vertices of a hyper-tetrahedron. The proposed method shows clear advantages over the existing methods, demonstrating its capabilities for viewing and navigating inter-cluster relationships in a spatial manner.     

A class of aggregation functions encompassing two-dimensional OWA operators

In this paper we prove that, under suitable conditions, Atanassov’s K_α operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from K_α operators. On the other hand, by analyzing the properties of Atanassov’s operators, we can generalize them. In this way, we introduce a class of aggregation functions - the generalized Atanassov operators - that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.     

State feedback control of continuous-time T-S fuzzy systems via switched fuzzy controllers

This paper studies the problem of state feedback control of continuous-time T-S fuzzy systems. Switched fuzzy controllers are exploited in the control design, which are switched based on the values of membership functions, and the control scheme is an extension of the parallel distributed compensation (PDC) scheme. Sufficient conditions for designing switched state feedback controllers are obtained with meeting an H_∞ norm bound requirement and quadratic D stability constraints. It is shown that the new control design method provides less conservative results than the corresponding ones via the parallel distributed compensation (PDC) scheme. A numerical example is given to illustrate the effectiveness of the proposed method.     

Threshold-based clustering with merging and regularization in application to network intrusion detection

Signature-based intrusion detection systems look for known, suspicious patterns in the input data. In this paper we explore compression of labeled empirical data using threshold-based clustering with regularization. The main target of clustering is to compress training dataset to the limited number of signatures, and to minimize the number of comparisons that are necessary to determine the status of the input event as a result. Essentially, the process of clustering includes merging of the clusters which are close enough. As a consequence, we will reduce original dataset to the limited number of labeled centroids. In a complex with k-nearest-neighbor (kNN) method, this set of centroids may be used as a multi-class classifier. The experiments on the KDD-99 intrusion detection dataset have confirmed effectiveness of the above procedure.     

Fitting finite mixtures of generalized linear regressions in R

R package flexmix provides flexible modelling of finite mixtures of regression models using the EM algorithm. Several new features of the software such as fixed and nested varying effects for mixtures of generalized linear models and multinomial regression for a priori probabilities given concomitant variables are introduced. The use of the software in addition to model selection is demonstrated on a logistic regression example.     

Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data

Penalized B-splines combined with the composite link model are used to estimate a bivariate density from a histogram with wide bins. The goals are multiple: they include the visualization of the dependence between the two variates, but also the estimation of derived quantities like Kendall’s tau, conditional moments and quantiles. Two strategies are proposed: the first one is semiparametric with flexible margins modeled using B-splines and a parametric copula for the dependence structure; the second one is nonparametric and is based on Kronecker products of the marginal B-spline bases. Frequentist and Bayesian estimations are described. A large simulation study quantifies the performances of the two methods under different dependence structures and for varying strengths of dependence, sample sizes and amounts of grouping. It suggests that Schwarz’s BIC is a good tool for classifying the competing models. The density estimates are used to evaluate conditional quantiles in two applications in social and in medical sciences.     

Detecting change-points in Markov chains

Markov chains provide a flexible model for dependent random variables with applications in such disciplines as physics, environmental science and economics. In the applied study of Markov chains, it may be of interest to assess whether the transition probability matrix changes during an observed realization of the process. If such changes occur, it would be of interest to estimate the transitions where the changes take place and the probability transition matrix before and after each change. For the case when the number of changes is known, standard likelihood theory is developed to address this problem. The bootstrap is used to aid in the computation of p-values. When the number of changes is unknown, the AIC and BIC measures are used for model selection. The proposed methods are studied empirically and are applied to example sets of data.     

Three results on frequency assignment in linear cellular networks

In the frequency assignment problem we are given a graph representing a wireless network and a sequence of requests, where each request is associated with a vertex. Each request has two more attributes: its arrival and departure times, and it is considered active from the time of arrival to the time of departure. We want to assign frequencies to all requests so that at each time step any two active requests associated with the same or adjacent vertices use different frequencies. The objective is to minimize the number of frequencies used.We focus exclusively on the special case of the problem when the underlying graph is a linear network (path). For this case, we consider both the offline and online versions of the problem, and we present three results. First, in the incremental online case, where the requests arrive over time, but never depart, we give an algorithm with an optimal (asymptotic) competitive ratio . Second, in the general online case, where the requests arrive and depart over time, we improve the current lower bound on the (asymptotic) competitive ratio to . Third, we prove that the offline version of this problem is NP-complete.