Large-scale kernel methods for independence testing

Zhang, Qinyi; Filippi, Sarah; Gretton, Arthur; Sejdinović, Dino

doi:10.1007/s11222-016-9721-7

Cited by 76 publications

(80 citation statements)

References 27 publications

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“…6. It might be possible to reduce computational complexity by using linear time approximation methods as described by Zhang et al (2017) for the pairwise HSIC. (We thank one of the referees for pointing this out.…”

Section: Run Time Analysismentioning

confidence: 99%

Kernel-Based Tests for Joint Independence

Pfister

Bühlmann

Schoelkopf

et al. 2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

146

197

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Summary.We investigate the problem of testing whether d possibly multivariate random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two-variable Hilbert-Schmidt independence criterion but allows for an arbitrary number of variables. We embed the joint distribution and the product of the marginals in a reproducing kernel Hilbert space and define the d-variable Hilbert-Schmidt independence criterion dHSIC as the squared distance between the embeddings. In the population case, the value of dHSIC is 0 if and only if the d variables are jointly independent, as long as the kernel is characteristic. On the basis of an empirical estimate of dHSIC, we investigate three nonparametric hypothesis tests: a permutation test, a bootstrap analogue and a procedure based on a gamma approximation. We apply non-parametric independence testing to a problem in causal discovery and illustrate the new methods on simulated and real data sets.

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Section: Run Time Analysismentioning

confidence: 99%

Kernel-Based Tests for Joint Independence

Pfister

Bühlmann

Schoelkopf

et al. 2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

146

197

View full text Add to dashboard Cite

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“…Block HSIC Lasso employs the block HSIC estimator (Zhang et al, 2018) instead of the V-statistics estimator of Equation (2). More specifically, to compute the block HSIC, we first partition the training…”

Section: Block Hsic Lassomentioning

confidence: 99%

“…In this paper, we propose block HSIC Lasso: a simple yet effective nonlinear feature selection algorithm based on HSIC Lasso. The key idea is to use the recently proposed block HSIC estimator (Zhang et al, 2018) to estimate the HSIC terms. By splitting the data in blocks of size B ⌧ n, the memory complexity of HSIC Lasso goes from O(dn 2 ) down to O(dnB).…”

Section: Introductionmentioning

confidence: 99%

Block HSIC Lasso: model-free biomarker detection for ultra-high dimensional data

Climente-González

Azencott

Kaski

et al. 2019

Preprint

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Motivation: Finding nonlinear relationships between biomolecules and a biological outcome is computationally expensive and statistically challenging. Existing methods have important drawbacks, including among others lack of parsimony, non-convexity, and computational overhead. Here we propose block HSIC Lasso, a nonlinear feature selector that does not present the previous drawbacks. Results: We compare block HSIC Lasso to other state-of-the-art feature selection techniques in both synthetic and real data, including experiments over three common types of genomic data: gene-expression microarrays, single-cell RNA sequencing, and genome-wide association studies. In all cases, we observe that features selected by block HSIC Lasso retain more information about the underlying biology than those selected by other techniques. As a proof of concept, we applied block HSIC Lasso to a single-cell RNA sequencing experiment on mouse hippocampus. We discovered that many genes linked in the past to brain development and function are involved in the biological differences between the types of neurons. Availability: Block HSIC Lasso is implemented in the Python 2/3 package pyHSICLasso, available on PyPI. Source code is available on GitHub (https://

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“…Non-parametric tests have no restrictions in the sample inference process. The test used here employs a statistical permutation (Collingridge, 2013;Konietschke and Pauly, 2014;Koopman et al, 2015;Zhang et al, 2017;Pauly et al, 2018;Derrick et al 2018).…”

Section: Validation Of the Simulationsmentioning

confidence: 99%

Seasonal Climate Forecast For The Alcântara Launch Center - Brazil

Corrêa

Reboita

Camillo

et al. 2019

Rev. Bras. Geog. Fis.

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Este trabalho analisou o desempenho de três esquemas de parametrização de convecção cumulus (Kain-Fritsch, Emanuel e Grell/Emanuel) na previsão do clima sazonal, durante a transição do período chuvoso para seco (junho a julho de 2017), no Centro de Lançamento de Alcântara (CLA) -Maranhão -Brasil. Para tanto, os resultados do sistema global de previsão climática do National Centers for Environmental Prediction (NCEP-CFSv2) foram usados como condições inicial e de fronteira no Regional Climate Model (RegCM4.4). Os resultados enfocam principalmente a intensidade do vento na baixa atmosfera no CLA. As previsões desta variável foram validadas através de comparações com a reanálise ERA-Interim e com dados registrados por uma torre micrometeorológica localizada no CLA. De forma geral, as simulações com o esquema de Kain-Fritsch e Grell/Emanuel tiveram boa performance na região de estudo. Palavras-chave: modelo climático regional (RegCM4.4), inicialização global, condições iniciais do CFSv2 A B S T R A C TThis work analyzed the performance of three cumulus convection parameterization schemes (Kain-Fritsch, Emanuel and Grell/Emanuel) in forecasting the seasonal climate during the transition from rainy to dry period (June to July 2017) in Alcântara Launch Center (ALC) located in Maranhão State-Brazil. For this reason, the outputs from the global NCEP Climate Forecast System (CFSv2) were used as initial and boundary conditions in the Regional Climate Model (RegCM4.4). The results focused on the wind intensity in the lower atmosphere in the ALC. The forecasts of this variable were validated with comparisons with ERA-Interim reanalysis and measured data by a micrometeorological tower in ALC. In general, the simulations with Kain-Fritsch and Grell-Emanuel convective schemes had good performance in the studied region.

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Large-scale kernel methods for independence testing

Cited by 76 publications

References 27 publications

Kernel-Based Tests for Joint Independence

Kernel-Based Tests for Joint Independence

Block HSIC Lasso: model-free biomarker detection for ultra-high dimensional data

Seasonal Climate Forecast For The Alcântara Launch Center - Brazil

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