Classical Ensemble Research Articles

Coupling theK-nearest neighbors and locally weighted linear regression with ensemble Kalman filter for data-driven data assimilation

AbstractMachine learning-based data-driven methods are increasingly being used to extract structures and essences from the ever-increasing pool of geoscience-related big data, which are often used in relation to the atmosphere, oceans, and land surfaces. This study focuses on applying a data-driven forecast model to the classical ensemble Kalman filter process to reconstruct, analyze, and elucidate the model. In this study, a nonparametric sampler from a catalog of historical datasets, namely, a nearest neighbor or analog sampler, is given by numerical simulations. Based on this catalog (sampler), the dynamics physics model is reconstructed using theK-nearest neighbors algorithm. The optimal values of the surrogate model are found, and the forecast step is performed using locally weighted linear regression. Several numerical experiments carried out using the Lorenz-63 and Lorenz-96 models demonstrate that the proposed approach performs as good as the ensemble Kalman filter for larger catalog sizes. This approach is restricted to the ensemble Kalman filter form. However, the basic strategy is not restricted to any particular version of the Kalman filter. It is found that this combined approach can outperform the generally used sequential data assimilation approach when the size of the catalog is substantially large.

Trans-spectral vector beam nonlinear conversion via parametric four-wave mixing in alkali vapor.

Coherent frequency conversion of vector beams (VBs) without distorting their intensity profile or spatial polarization distribution is important for novel applications in quantum and classical regimes. Here, we experimentally and theoretically investigate VB transfer from near-infrared to blue light using a Sagnac interferometer, combining the parametric four-wave mixing process in atomic vapor. The vector probe beam is converted into a completely different wavelength, and the vector mode of the generated blue beam is highly similar to the incident probe beam. These results may provide a feasible solution for communication interfaces in classical and quantum science fields based on atomic ensembles.

Hypertension-Related Drug Activity Identification Based on Novel Ensemble Method.

Hypertension is a chronic disease and major risk factor for cardiovascular and cerebrovascular diseases that often leads to damage to target organs. The prevention and treatment of hypertension is crucially important for human health. In this paper, a novel ensemble method based on a flexible neural tree (FNT) is proposed to identify hypertension-related active compounds. In the ensemble method, the base classifiers are Multi-Grained Cascade Forest (gcForest), support vector machines (SVM), random forest (RF), AdaBoost, decision tree (DT), Gradient Boosting Decision Tree (GBDT), KNN, logical regression, and naïve Bayes (NB). The classification results of nine classifiers are utilized as the input vector of FNT, which is utilized as a nonlinear ensemble method to identify hypertension-related drug compounds. The experiment data are extracted from hypertension-unrelated and hypertension-related compounds collected from the up-to-date literature. The results reveal that our proposed ensemble method performs better than other single classifiers in terms of ROC curve, AUC, TPR, FRP, Precision, Specificity, and F1. Our proposed method is also compared with the averaged and voting ensemble methods. The results reveal that our method could identify hypertension-related compounds more accurately than two classical ensemble methods.

Deep Ensembles for Hyperspectral Image Data Classification and Unmixing

Hyperspectral images capture very detailed information about scanned objects and, hence, can be used to uncover various characteristics of the materials present in the analyzed scene. However, such image data are difficult to transfer due to their large volume, and generating new ground-truth datasets that could be utilized to train supervised learners is costly, time-consuming, very user-dependent, and often infeasible in practice. The research efforts have been focusing on developing algorithms for hyperspectral data classification and unmixing, which are two main tasks in the analysis chain of such imagery. Although in both of them, the deep learning techniques have bloomed as an extremely effective tool, designing the deep models that generalize well over the unseen data is a serious practical challenge in emerging applications. In this paper, we introduce the deep ensembles benefiting from different architectural advances of convolutional base models and suggest a new approach towards aggregating the outputs of base learners using a supervised fuser. Furthermore, we propose a model augmentation technique that allows us to synthesize new deep networks based on the original one by injecting Gaussian noise into the model’s weights. The experiments, performed for both hyperspectral data classification and unmixing, show that our deep ensembles outperform base spectral and spectral-spatial deep models and classical ensembles employing voting and averaging as a fusing scheme in both hyperspectral image analysis tasks.

Computable structural formulas for the distribution of the $$\beta $$-Jacobi edge eigenvalues

The Jacobi ensemble is one of the classical ensembles of random matrix theory. Prominent in applications are properties of the eigenvalues at the spectrum edge, specifically the distribution of the largest (e.g. Roy’s largest root test in multivariate statistics) and smallest (e.g. condition numbers of linear systems) eigenvalues. We identify three ranges of parameter values for which the gap probability determining these distributions is a finite sum with respect to particular bases, and moreover make use of a certain differential–difference system fundamental in the theory of the Selberg integral to provide a recursive scheme to compute the corresponding coefficients.

Laser-subcycle control of electronic excitation across system boundaries

We report on the results of a joint experimental and numerical study on the sub-cycle laser field-driven electron dynamics that underlie the population of highly excited electronic states in multiply ionized argon dimers by electron recapture processes. Our experiments using few-cycle laser pulses with a known carrier-envelope phase (CEP) in combination with reaction microscopy reveal a distinct CEP-dependence of the electron emission and recapture process and, furthermore, a small but significant CEP-offset to the scenario in which no excited argon dimers are produced. With the help of classical ensemble trajectory simulations we trace down these different CEP-dependencies to subtle differences in the laser-driven sub-cycle electron trajectory dynamics that involve in both cases the transfer of an electron from one argon ion across the system boundary to the neighboring ion and its transient capture on this ion.

Asymptotic correlations with corrections for the circular Jacobi [formula omitted]-ensemble

Previous works have considered the leading correction term to the scaled limit of various correlation functions and distributions for classical random matrix ensembles and their β generalisations at the hard and soft edge. It has been found that the functional form of this correction is given by a derivative operation applied to the leading term. In the present work we compute the leading correction term of the correlation kernel at the spectrum singularity for the circular Jacobi ensemble with Dyson indices β=1,2 and 4, and also to the spectral density in the corresponding β-ensemble with β even. The former requires an analysis involving the Routh–Romanovski polynomials, while the latter is based on multidimensional integral formulas for generalised hypergeometric series based on Jack polynomials. In all cases this correction term is found to be related to the leading term by a derivative operation.

POD-based analysis of time-resolved tornado-like vortices

In this study, three representative configurations of tornado-like vortices, i.e., single vortex, vortex breakdown and multi-vortex, are numerically simulated using large-eddy simulation (LES). Proper orthogonal decomposition (POD) is firstly employed to decompose flow-field snapshots into a series of orthogonal flow patterns (POD modes) and time-dependent coefficients. Then, a conditional-average analysis is conducted to obtain the four kinds of conditionally-averaged flow fields, which are then compared with instantaneous and ensemble-averaged flow fields. Next, a quadruple POD analysis is performed to decompose the instantaneous flow field into mean, coherent, transition and noise components. Finally, a qualitative analysis is implemented for unsteady vortex motions in horizontal and vertical planes. Results show that the conditional average shows larger-scale coherent structures than the classical ensemble average, while it loses the small-scale turbulent fluctuations present in instantaneous flow. The tornado vortex structure is controlled by the mean component in the single-vortex stage. With increase in swirl ratio, the tornado vortex evolves from single-vortex, to vortex-breakdown to multi-vortex, companied by kinetic energy transference to coherent and transition components. The horizontal and vertical vortex motions are essentially the results of horizontal and vertical velocity perturbations.

Moments of generalized Cauchy random matrices and continuous-Hahn polynomials

In this paper we prove that, after an appropriate rescaling, the sum of moments of an N × N Hermitian matrix H sampled according to the generalized Cauchy (also known as Hua–Pickrell) ensemble with parameter s > 0 is a continuous-Hahn polynomial in the variable k. This completes the picture of the investigation that began in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) where analogous results were obtained for the other three classical ensembles of random matrices, the Gaussian, the Laguerre and Jacobi. Our strategy of proof is somewhat different from the one in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) due to the fact that the generalized Cauchy is the only classical ensemble which has a finite number of integer moments. Our arguments also apply, with straightforward modifications, to the other three cases studied in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) as well. We finally obtain a differential equation for the one-point density function of the eigenvalue distribution of this ensemble and establish the large N asymptotics of the moments.

Influence of relative phase on the nonsequential double ionization process of CO2 molecules by counter-rotating two-color circularly polarized laser fields

We investigate the nonsequential double ionization (NSDI) of linear triatomic molecules by the counter-rotating two-color circularly polarized (CRTC) laser fields with a classical ensemble method. The results of the simulation reveal that NSDI yield strongly connected with the relative phase. The trajectory tracking method shows that the return time of the electron is controlled by the relative phase. In addition, when we change the CRTC laser wavelengths, the relative phase of the maximum and minimum yield of NSDI also changes. This shows that the influence of the Coulomb potential in the triatomic molecules on the electron return process cannot be ignored. This work will effectively promote the electronic dynamics study of NSDI for the triatomic molecule.

Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulæ for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials.

Manipulating frustrated double ionization by orthogonal two-color laser pulses

Using a three-dimensional classical ensemble method, we theoretically investigated frustrated double ionization (FDI) of atoms driven by the orthogonal two-color (OTC) laser pulses. The numerical results show that the FDI yields could be controlled by changing the relative phase of the OTC fields. Moreover, the relative contribution of the two pathways of FDI, corresponding to the processes wherein the firstly or the secondly ionized electron is finally recaptured when the laser field is over, could also be manipulated by changing the relative phase of the OTC fields. The underlying dynamics for this relative-phase dependence of the FDI pathways is revealed by back-tracing the classical trajectories of the FDI events. Interestingly, the energy distributions of the highly excited states of the atom ions in the FDI events also display a sensitive relative phase dependence.

Research on the Prediction of A-Share "High Stock Dividend" Phenomenon-A Feature Adaptive Improved Multi-Layers Ensemble Model.

Since the “high stock dividend” of A-share companies in China often leads to the short-term stock price increase, this phenomenon’s prediction has been widely concerned by academia and industry. In this study, a new multi-layer stacking ensemble algorithm is proposed. Unlike the classic stacking ensemble algorithm that focused on the differentiation of base models, this paper used the equal weight comprehensive feature evaluation method to select features before predicting the base model and used a genetic algorithm to match the optimal feature subset for each base model. After the base model’s output prediction, the LightGBM (LGB) model was added to the algorithm as a secondary information extraction layer. Finally, the algorithm inputs the extracted information into the Logistic Regression (LR) model to complete the prediction of the “high stock dividend” phenomenon. Using the A-share market data from 2010 to 2019 for simulation and evaluation, the proposed model improves the AUC (Area Under Curve) and F1 score by 0.173 and 0.303, respectively, compared to the baseline model. The prediction results shed light on event-driven investment strategies.

Ordered level spacing distribution in embedded random matrix ensembles

The probability distribution of the closest neighbor and farther neighbor spacings from a given level have been studied for interacting fermion/boson systems with and without spin degree of freedom constructed using an embedded GOE of one plus random two-body interactions. Our numerical results demonstrate a very good consistency with the recently derived analytical expressions using a $3 \times 3$ random matrix model and other related quantities by Srivastava et. al [{\it J. Phys. A: Math. Theor.} {\bf 52} 025101 (2019)]. This establishes conclusively that local level fluctuations generated by embedded ensembles (EE) follow the results of classical Gaussian ensembles.

A Dynamic Ensemble Learning Algorithm based on K-means for ICU mortality prediction

This research proposes a Dynamic Ensemble Learning Algorithm based on K-means (DELAK) for intensive care unit (ICU) mortality prediction. Nowadays, the widely applied traditional scoring systems, which predict the mortality risk with some scores reflecting the severity of disease and physiological states of patients in ICU, have shown insufficient predictive performance when faced with large volume of data. Although taking advantage of large volume of data, single machine learning model and ensemble learning methods show an inadequate ability to make personalized predictions for each new patient. Dynamic ensemble selection (DES) methods which are widely studied in pattern recognition field can make personalized prediction but they only select a single classifier instead of ensemble of the results from a pool of classifiers. To overcome the limitations mentioned above, this research proposes an ensemble learning algorithm based on K-means sampling and distance-based dynamic ensemble. K-means sampling helps to achieve the diversity of base classifiers and the distance-based dynamic ensemble is a flexible fusion method which creates a personalized combination of results from base classifiers for each new test sample. To evaluate the performance for mortality prediction of the proposed algorithm, comprehensive experiments are conducted on MIMIC-III dataset. The experimental results show that DELAK achieves outstanding performance in term of AUROC and AUPRC compared with other six fusion strategies, traditional scoring systems, classical ensemble models, i.e. AdaBoost, Bagging and random forest, and dynamic ensemble selection methods in most mortality prediction tasks.

The principle of modeling as a means of classification of instrumental ensembles with a domra

The present article, developing a comprehensive approach to the classification of instrumental ensembles with a domra, aims at detecting the principles which can serve as a basis for the creation of various models of such objects. The author suggests analyzing the aspects of existence of the phenomenon under study from various positions: as music groups, and from the viewpoint of music compositions created for such groups. The article considers and compares the models of concert groups according to the number of their members and instrumental components, as well as according to the genre and style peculiarities of the repertoire of instrumental ensembles with a domra and their cooperation with composers. This classification method helps to comprehensively cover the work of a large number of musicians, both the members of ensembles and composers. The modeling of various systems of the creation of methods of classification of instrumental ensembles helps to study the peculiarities of the existence of such groups in modern music culture. The author arrives at the conclusion that at present, the music performance spectrum of Russia contains a vast range of ensembles with various instrumental contents and different numbers of members. The diversity of genre and style models of such groups is reflected in their repertoire - from folklore, classical music and modern composers schools to jazz, rock, pop-music and performance.   

Tracy-Widom Distributions for the Gaussian Orthogonal and Symplectic Ensembles Revisited: A Skew-Orthogonal Polynomials Approach

We study the distribution of the largest eigenvalue in the "Pfaffian" classical ensembles of random matrix theory, namely in the Gaussian orthogonal (GOE) and Gaussian symplectic (GSE) ensembles, using semi-classical skew-orthogonal polynomials, in analogue to the approach of Nadal and Majumdar (NM) for the Gaussian unitary ensemble (GUE). Generalizing the techniques of Adler, Forrester, Nagao and van Moerbeke, and using "overlapping Pfaffian" identities due to Knuth, we explicitly construct these semi-classical skew-orthogonal polynomials in terms of the semi-classical orthogonal polynomials studied by NM in the case of the GUE. With these polynomials we obtain expressions for the cumulative distribution functions of the largest eigenvalue in the GOE and the GSE. Further, by performing asymptotic analysis of these skew-orthogonal polynomials in the limit of large matrix size, we obtain an alternative derivation of the Tracy-Widom distributions for GOE and GSE. This asymptotic analysis relies on a certain Pfaffian identity, the proof of which employs the characterization of Pfaffians in terms of perfect matchings and link diagrams.

Quantum eigenstates from classical Gibbs distributions

We discuss how the language of wave functions (state vectors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics by applying the inverse Wigner-Weyl transform to the phase space probability distribution and observables. In this language, the Schr"odinger equation follows from the Liouville equation, with \hbarℏ now a free parameter. Classical stationary distributions can be represented as sums over stationary states with discrete (quantized) energies, where these states directly correspond to quantum eigenstates. Interestingly, it is now classical mechanics which allows for apparent negative probabilities to occupy eigenstates, dual to the negative probabilities in Wigner’s quasiprobability distribution. These negative probabilities are shown to disappear when allowing sufficient uncertainty in the classical distributions. We show that this correspondence is particularly pronounced for canonical Gibbs ensembles, where classical eigenstates satisfy an integral eigenvalue equation that reduces to the Schr"odinger equation in a saddle-point approximation controlled by the inverse temperature. We illustrate this correspondence by showing that some paradigmatic examples such as tunneling, band structures, Berry phases, Landau levels, level statistics and quantum eigenstates in chaotic potentials can be reproduced to a surprising precision from a classical Gibbs ensemble, without any reference to quantum mechanics and with all parameters (including \hbarℏ) on the order of unity.

Adaptive regularisation for ensemble Kalman inversion

We propose a new regularisation strategy for the classical ensemble Kalman inversion (EKI) framework. The strategy consists of: (i) an adaptive choice for the regularisation parameter in the update formula in EKI, and (ii) criteria for the early stopping of the scheme. In contrast to existing approaches, our parameter choice does not rely on additional tuning parameters which often have severe effects on the efficiency of EKI. We motivate our approach using the interpretation of EKI as a Gaussian approximation in the Bayesian tempering setting for inverse problems. We show that our parameter choice controls the symmetrised Kullback–Leibler divergence between consecutive tempering measures. We further motivate our choice using a heuristic statistical discrepancy principle. We test our framework using electrical impedance tomography with the complete electrode model. Parameterisations of the unknown conductivity are employed which enable us to characterise both smooth or a discontinuous (piecewise-constant) fields. We show numerically that the proposed regularisation of EKI can produce efficient, robust and accurate estimates, even for the discontinuous case which tends to require larger ensembles and more iterations to converge. We compare the proposed technique with a standard method of choice and demonstrate that the proposed method is a viable choice to address computational efficiency of EKI in practical/operational settings.

Local eigenvalue statistics of one-dimensional random nonselfadjoint pseudodifferential operators

We consider a class of one-dimensional nonselfadjoint semiclassical pseudodifferential operators, subject to small random perturbations, and study the statistical properties of their (discrete) spectra, in the semiclassical limit h\to 0 . We compare two types of random perturbation: a random potential vs. a random matrix. Hager and Sjöstrand showed that, with high probability, the local spectral density of the perturbed operator follows a semiclassical form of Weyl’s law, depending on the value distribution of the principal symbol of our pseudodifferential operator. Beyond the spectral density, we investigate the full local statistics of the perturbed spectrum, and show that it satisfies a form of universality: the statistics only depends on the local spectral density, and of the type of random perturbation, but it is independent of the precise law of the perturbation. This local statistics can be described in terms of the Gaussian Analytic Function, a classical ensemble of random entire functions.