mlsanityData to 14 Oct 2026

Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysis

arXiv 2105.12778 ↗First posted 26 May 2021math.ST stat.ML stat.THcited by 6

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Abstract (arXiv)

Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied and with much experimental success, little theoretical progress has been made in analysing functional depths. This article highlights how the common h-depth and related statistical depths for functional data can be viewed as a kernel mean embedding, a technique used widely in statistical machine learning. This connection facilitates answers to open questions regarding statistical properties of functional depths, as well as it provides a link between the depth and empirical characteristic function based procedures for functional data.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 22 of its 120 references that are in the map. First posted on arXiv 26 May 2021.

Builds on

22 of 120 references.

References · 22

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 364
  2. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  3. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 192
  4. 2016A Kernel Test of Goodness of Fitcited by 143
  5. 2016A Primer on the Signature Method in Machine Learningcited by 104
  6. 2016Generative Models and Model Criticism via Optimized Maximum Mean Discrepancycited by 100
  7. 2020The Random Feature Model for Input-Output Maps between Banach Spacescited by 90
  8. 2015Operator-valued Kernels for Learning from Functional Response Datacited by 60
  9. 2018Signature moments to characterize laws of stochastic processescited by 56
  10. 2016Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributionscited by 40
  11. 2019Stein Point Markov Chain Monte Carlocited by 29
  12. 2020A Kernel Two-Sample Test for Functional Datacited by 28
10 more
  1. 2015Probabilistic Integration: A Role in Statistical Computation?cited by 26
  2. 2020Choosing among notions of multivariate depth statisticscited by 14
  3. 2014Exact computation of the halfspace depthcited by 11
  4. 2016Lens depth function and k-relative neighborhood graph: versatile tools for ordinal data analysiscited by 5
  5. 2018On Mahalanobis distance in functional settingscited by 5
  6. 2021Post-Processing of MCMCcited by 5
  7. 2014On data depth in infinite dimensional spacescited by 2
  8. 2015The DDG-classifier in the functional settingcited by 2
  9. 2016Classification with the pot-pot plotcited by 2
  10. 2021A unified framework on defining depth for point process using function smoothingcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 0; 2023: 1; 2024: 0; 2025: 1; 2026: 2.

6 papers.

  1. 2021MMD Aggregated Two-Sample Testcited by 75
  2. 2021Composite Goodness-of-fit Tests with Kernelscited by 16
  3. 2026Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSDcited by 2
  4. 2023Bayes Hilbert Spaces for Posterior Approximationcited by 1
  5. 2025Model-Free Kernel Conformal Depth Measures Algorithm for Uncertainty Quantification in Regression Models in Separable Hilbert Spacescited by 0
  6. 2026Dimension-invariant uniform consistency of the empirical spatial distribution function and its associated spatial depth estimatorcited by 0