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In this paper, we perform an empirical comparison of the classification error of several ensemble methods based on classification trees. This comparison is performed by using 14 data sets that are publicly available and that were used by Lim, Loh and Shih [Lim, T., Loh, W. and Shih, Y.-S., 2000, A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms. Machine Learning , 40, 203–228.]. The methods considered are a single tree, Bagging, Boosting (Arcing) and random forests (RF). They are compared from different perspectives. More precisely, we look at the effects of noise and of allowing linear combinations in the construction of the trees, the differences between some splitting criteria and, specifically for RF, the effect of the number of variables from which to choose the best split at each given node. Moreover, we compare our results with those obtained by Lim et al . [Lim, T., Loh, W. and Shih, Y.-S., 2000, A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms. Machine Learning , 40, 203–228.]. In this study, the best overall results are obtained with RF. In particular, RF are the most robust against noise. The effect of allowing linear combinations and the differences between splitting criteria are small on average, but can be substantial for some data sets. [ABSTRACT FROM AUTHOR]

Exact inference for the location and scale parameters as well as prediction intervals for K -sample exponential case under general Type-II censored samples are derived using an algorithm of Huffer and Lin [Huffer, F. W. and Lin, C. T. (2001). Computing the joint distribution of general linear combinations of spacings or exponential variates. Stat. Sin. , 11 , 1141-1157.]. This approach provides a simple way to determine the exact percentage points of the pivotal quantities based on the best linear unbiased estimators in order to develop exact inference for the location and scale parameters as well as to construct exact prediction intervals for failure times unobserved in the i th sample. Similarly, exact prediction intervals for failure times of units from a future sample can also be easily obtained. A comparison is then made with the approximate inference based on the maximum likelihood estimators. Finally, we present an example to illustrate all the methods of inference developed in this paper. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms are heuristic stochastic search and optimization techniques with principles taken from natural genetics. They are procedures mimicking the evolution process of an initial population through genetic transformations. This paper is concerned with the problem of finding A-optimal incomplete block designs for multiple treatment comparisons represented by a matrix of contrasts. An evolutionary algorithm for searching optimal, or nearly optimal, incomplete block designs is described in detail. Various examples regarding the application of the algorithm to some well-known problems illustrate the good performance of the algorithm [ABSTRACT FROM AUTHOR]

Kaufman and Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this paper, we propose to partition around medoids by maximizing a criteria "Average Silhouette" defined by Kaufman and Rousseeuw (1990). We also propose a fast-to-compute approximation of "Average Silhouette". We implement these two new partitioning around medoids algorithms and illustrate their performance relative to existing partitioning methods in simulations. [ABSTRACT FROM AUTHOR]

This paper introduces practical methods of parameter and standard error estimation for adaptive robust regression where errors are assumed to be from a normal/independent family of distributions. In particular, generalized EM algorithms (GEM) are considered for the two cases of t and slash families of distributions. For the t family, one step method is proposed to estimate the degree of freedom parameter. Use of empirical information is suggested for standard error estimation. It is shown that this choice leads to standard errors that can be obtained as a by-product of the GEM algorithm. The proposed methods, as discussed, can be implemented in most available nonlinear regression programs. Details of implementation in SAS NLIN are given using two specific examples. [ABSTRACT FROM AUTHOR]

The calculation of the permanent of a matrix is an extremely difficult task. Indeed it belongs to the class of hard counting problems denoted #P complete and hence any algorithm to compute the permanent must run in exponential time in the order of the matrix. Attention, therefore, has concentrated on Monte Carlo algorithms to estimate permanents with considerable emphasis on deriving randomised polynomial time algorithms. Interest in this area has largely stemmed from problems in combinatorial enumeration, for instance the permanent of a square (0, 1) matrix gives the number of perfect matchings in a bipartite graph. In this paper we have a different motivation: results in communications theory have recently used permanents to bound the performance of certain digital mobile radio systems. Here the matrix involved is rectangular with strictly positive elements and a high degree of structure. Our approach to estimating permanents is more heuristic and we develop simple algorithms based on treating the permanent as a sum of a finite population. We derive both Monte Carlo and Importance Sampling estimators using this framework and compare our results to existing algorithms. Results show that for a wide variety of matrices our estimators are more precise and hence offer shorter runtimes for a fixed precision or increased precision for a fixed run time. For matrices which are not highly sparse the run time savings are typically 1-2 orders of magnitude. [ABSTRACT FROM AUTHOR]