Independence test and canonical correlation analysis based on the alignment between kernel matrices for multivariate functional data

Górecki, Tomasz; Krzyśko, Mirosław; Wołyński, Waldemar

doi:10.1007/s10462-018-9666-7

Cited by 22 publications

(17 citation statements)

References 29 publications

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“…[15] have developed a two-sample test for distributions based on generalisations of a finite-dimensional test by utilising functional principal component analysis, and [16] have derived kernels over functions to be used with MMD for the two-sample test. Independence testing for functional data using kernels was recently proposed in [17] but assumes the samples lie on a finite-dimensional subspace of the function space-an assumption not required in our work. Moreover, ref.…”

Section: Related Workmentioning

confidence: 99%

Kernel Two-Sample and Independence Tests for Nonstationary Random Processes

Laumann

Kügelgen

Barahona

2021

The 7th International Conference on Time Series and Forecasting

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Two-sample and independence tests with the kernel-based mmd and hsic have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to nonstationary random processes, a prevalent form of data in many scientific disciplines. In this work, we extend the application of mmd and hsic to nonstationary settings by assuming access to independent realisations of the underlying random process. These realisations—in the form of nonstationary time-series measured on the same temporal grid—can then be viewed as i.i.d. samples from a multivariate probability distribution, to which mmd and hsic can be applied. We further show how to choose suitable kernels over these high-dimensional spaces by maximising the estimated test power with respect to the kernel hyperparameters. In experiments on synthetic data, we demonstrate superior performance of our proposed approaches in terms of test power when compared to current state-of-the-art functional or multivariate two-sample and independence tests. Finally, we employ our methods on a real socioeconomic dataset as an example application.

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Section: Related Workmentioning

confidence: 99%

Kernel Two-Sample and Independence Tests for Nonstationary Random Processes

Laumann

Kügelgen

Barahona

2021

The 7th International Conference on Time Series and Forecasting

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“…Other studies aim at expanding and utilizing the measures in a general manner. They proposed methods based on the measures for the following: statistical tests [44]- [46], robustness improvement [47]- [49], algorithmic strategies for multi dependence detection [50], [51], feature selection [52]- [56], and feature extraction [57], [58]. The other studies are to utilize the measures in specific domains, the applications in short, which are as given in Section I-A.…”

Section: Cc(x Y) =mentioning

confidence: 99%

NNR-GL: A Measure to Detect Co-Nonlinearity Based on Neural Network Regression Regularized by Group Lasso

et al. 2021

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For finding keys to understand and elucidate a phenomenon, it is essential to detect dependences among variables, and so measures for that have been proposed. Correlation coefficient and its variants are most common, but they only detect a linear dependence (co-linearity) between two variables. Some recent measures can detect a nonlinear dependence (co-nonlinearity) by means of kernelization or segmentation. They are supposed to handle two variables only and open to discussion with regard to performance in detection and difficulty in setup. There is room for a novel measure based on Neural Networks (NNs), since usual NNs aim at prediction but not at variable dependence detection. For the high-performance detection of co-nonlinearities among multi variables, we propose a measure called NNR-GL based on Neural Network Regression (NNR) regularized by Group Lasso (GL). NNR-GL embodies the detection through multi-input single-output regression by NNR and regularization on the input layer by GL. NNR-GL then calculates how strong the detected co-nonlinearities are by unifying the regression performance and the weights on input variables. We conducted experiments using artificial data to examine the behaviors and fundamental effectiveness of NNR-GL. The performance was estimated by a comprehensive detection performance criterion (CDP-AUC in short), which is the mean of area under curves representing true positive and true negative detections. NNR-GL achieved the values of CDP-AUC from 0.7472 to 0.9681, where 0 means complete failure and 1 means complete success in detection. These values were consistently higher than those from 0.5972 to 0.9259 of the conventional measures for all the different conditions of dependence, data size, and noise rate. Consequently, the effectiveness and robustness of NNR-GL were clearly confirmed.

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“…However, Pomann et al [2016] have developed a two-sample test for distributions based on generalisations of a finite-dimensional test by utilising functional principal component analysis, and Wynne and Duncan [2020] have derived kernels over functions to be used with MMD for the two-sample test. Independence testing for functional data using kernels was recently proposed in Górecki et al [2018], but assumes the samples lie on a finite-dimensional subspace of the function space-an assumption not required in our work. Moreover, Zhang et al [2018] have developed computationally efficient methods to test for independence on high-dimensional distributions and large sample sizes by using eigenvalues of centred kernel matrices to approximate the distribution under the null hypothesis H 0 instead of simulating a large number of permutations.…”

Section: Related Workmentioning

confidence: 99%

Kernel Two-Sample and Independence Tests for Non-Stationary Random Processes

Laumann¹,

Kügelgen²,

Barahona³

2020

Preprint

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Two-sample and independence tests with the kernel-based maximum mean discrepancy (MMD) and Hilbert-Schmidt independence criterion (HSIC) have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to non-stationary random processes, a prevalent form of data in many scientific disciplines. In this work, we extend the application of MMD and HSIC to non-stationary settings by assuming access to independent realisations of the underlying random process. These realisations-in the form of non-stationary timeseries measured on the same temporal grid-can then be viewed as i.i.d. samples from a multivariate probability distribution, to which MMD and HSIC can be applied. We further show how to choose suitable kernels over these high-dimensional spaces by maximising the estimated test power with respect to the kernel hyper-parameters. In experiments on synthetic data, we demonstrate superior performance of our proposed approaches in terms of test power when compared to current stateof-the-art functional or multivariate two-sample and independence tests. Finally, we employ our methods on a real socio-economic dataset as an example application.

show abstract

Independence test and canonical correlation analysis based on the alignment between kernel matrices for multivariate functional data

Cited by 22 publications

References 29 publications

Kernel Two-Sample and Independence Tests for Nonstationary Random Processes

Kernel Two-Sample and Independence Tests for Nonstationary Random Processes

NNR-GL: A Measure to Detect Co-Nonlinearity Based on Neural Network Regression Regularized by Group Lasso

Kernel Two-Sample and Independence Tests for Non-Stationary Random Processes

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