Search Results for « Ensemble »

To understand visual consciousness, we must understand how the brain represents ensembles of objects at many levels of perceptual analysis. Ensemble perception refers to the visual system's ability to extract summary statistical information from groups of similar objects-often in a brief glance. It defines foundational limits on cognition, memory, and behavior. In this review, we provide an operational definition of ensemble perception and demonstrate that ensemble perception spans across multiple levels of visual analysis, incorporating both low-level visual features and high-level social information. Further, we investigate the functional usefulness of ensemble perception and its efficiency, and we consider possible physiological and cognitive mechanisms that underlie an individual's ability to make accurate and rapid assessments of crowds of objects.

The impact of ensemble size on the performance of the European Centre for Medium-Range Weather Forecasts ensemble prediction system (EPS) is analyzed. The skill of ensembles generated using 2, 4, 8, 16, and 32 perturbed ensemble members are compared for a period of 45 days—from 1 October to 15 November 1996. For each ensemble configuration, the skill is compared with the potential skill, measured by randomly choosing one of the 32 ensemble members as verification (idealized ensemble). Results are based on the analyses of the prediction of the 500-hPa geopotential height field. Various measures of performance are applied: skill of the ensemble mean, spread–skill relationship, skill of most accurate ensemble member, Brier score, ranked probability score, relative operating characteristic, and the outlier statistic. The relation between ensemble spread and control error is studied using L2, L8, and L∞ norms to measure distances between ensemble members and the control forecast or the verification. It is argued that the supremum norm is a more suitable measure of distance, given the strategy for constructing ensemble perturbations from rapidly growing singular vectors. Results indicate that, for the supremum norm, any increase of ensemble size within the range considered in this paper is strongly beneficial. With the smaller ensemble sizes, ensemble spread does not provide a reliable bound on control error in many cases. By contrast, with 32 members, spread provides a bound on control error in nearly all cases. It could be anticipated that further improvement could be achieved with higher ensemble size still. On the other hand, spread–skill relationship was not consistently improved with higher ensemble size using the L2 norm. The overall conclusion is that the extent to which an increase of ensemble size (particularly from 8 to 16, and 16 to 32 members) improves EPS performance, is strongly dependent on the measure used to assess performance. In addition to the spread–skill relationship, the measures most sensitive to ensemble size are shown to be the skill of the best ensemble member (particularly when evaluated on a point-wise basis) and the outlier statistic.

The idea of ensemble methodology is to build a predictive model by integrating multiple models. It is well-known that ensemble methods can be used for improving prediction performance. Researchers from various disciplines such as statistics and AI considered the use of ensemble methodology. This paper, review existing ensemble techniques and can be served as a tutorial for practitioners who are interested in building ensemble based systems.

Several means for improving the performance and training of neural networks for classification are proposed. Crossvalidation is used as a tool for optimizing network parameters and architecture. It is shown that the remaining residual generalization error can be reduced by invoking ensembles of similar networks.>

The ensemble transform Kalman filter (ETKF) ensemble forecast scheme is introduced and compared with both a simple and a masked breeding scheme.Instead of directly multiplying each forecast perturbation with a constant or regional rescaling factor as in the simple form of breeding and the masked breeding schemes, the ETKF transforms forecast perturbations into analysis perturbations by multiplying by a transformation matrix.This matrix is chosen to ensure that the ensemble-based analysis error covariance matrix would be equal to the true analysis error covariance if the covariance matrix of the raw forecast perturbations were equal to the true forecast error covariance matrix and the data assimilation scheme were optimal.For small ensembles (ϳ100), the computational expense of the ETKF ensemble generation is only slightly greater than that of the masked breeding scheme.Version 3 of the Community Climate Model (CCM3) developed at National Center for Atmospheric Research (NCAR) is used to test and compare these ensemble generation schemes.The NCEP-NCAR reanalysis data for the boreal summer in 2000 are used for the initialization of the control forecast and the verifications of the ensemble forecasts.The ETKF and masked breeding ensemble variances at the analysis time show reasonable correspondences between variance and observational density.Examination of eigenvalue spectra of ensemble covariance matrices demonstrates that while the ETKF maintains comparable amounts of variance in all orthogonal and uncorrelated directions spanning its ensemble perturbation subspace, both breeding techniques maintain variance in few directions.The growth of the linear combination of ensemble perturbations that maximizes energy growth is computed for each of the ensemble subspaces.The ETKF maximal amplification is found to significantly exceed that of the breeding techniques.The ETKF ensemble mean has lower root-meansquare errors than the mean of the breeding ensemble.New methods to measure the precision of the ensembleestimated forecast error variance are presented.All of the methods indicate that the ETKF estimates of forecast error variance are considerably more accurate than those of the breeding techniques.

Ensemble methods that train multiple learners and then combine them to use, with Boosting and Bagging as representatives, are well-known machine learning approaches. It has become common sense that an ensemble is usually significantly more accurate than a single learner, and ensemble methods have already achieved great success in various real-world tasks. Twelve years have passed since the publication of the first edition of the book in 2012 (Japanese and Chinese versions published in 2017 and 2020, respectively). Many significant advances in this field have been developed. First, many theoretical issues have been tackled, for example, the fundamental question of why AdaBoost seems resistant to overfitting gets addressed, so that now we understand much more about the essence of ensemble methods. Second, ensemble methods have been well developed in more machine learning fields, e.g., isolation forest in anomaly detection, so that now we have powerful ensemble methods for tasks beyond conventional supervised learning. Third, ensemble mechanisms have also been found helpful in emerging areas such as deep learning and online learning. This edition expands on the previous one with additional content to reflect the significant advances in the field, and is written in a concise but comprehensive style to be approachable to readers new to the subject.

Statistical considerations suggest that 1) even for a perfect ensemble (one in which all sources of forecast error are sampled correctly) there need not be a high correlation between spread and skill, 2) the correlation between spread and skill should be larger where the day-to-day variability of spread is large, and 3) the spread is likely to be most useful as a predictor of skill when it is “extreme,” that is, when it is either very large or very small compared to its climatological mean value. The authors investigate the relationship between spread and skill in an operational setting by analyzing ensemble predictions produced by the National Centers for Environmental Prediction. The geographical dependence of the spread–skill relationship is found to be related to the geographical dependence of day-to-day variability of spread. Dynamical mechanisms for spread variability are investigated using a linear quasigeostrophic model. Problems associated with the sample size needed to define what constitutes an extreme value of spread at a given location are discussed.

One object of interest in random matrix theory is a family of point ensembles (ramdom point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one-parametric deformation of these ensembles, which is defined in terms of the biorthogonal polynomials of Jacobi, Laguerre and Hermite type. Our main result is a series of explicit expressions for the correlation functions in the scaling limit (as the number of points goes to infinity). As in the classical case, the correlation functions have determinatal form. They are given by certain new kernels which are described in terms of Wright's generalized Bessel function and can be viewed as a generalization of the well-known sine and Bessel kernels. In contrast to the conventional kernels, the new kernels are non-symmetric. However, they possess other, rather surprising, symmetry properties. Our approach to finding the limit kernel also differs from the conventional one, because of lack of a simple explicit Christoffel-Darboux formula for the biorthogonal polynomials.