Kernel Mean Embeddings

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Kernel mean embeddings represent distributions as averages of feature maps in a reproducing kernel Hilbert space, making complex distributions comparable without explicitly estimating their densities. Researchers use maximum mean discrepancy for two-sample testing, conditional embeddings and operator methods for dependence, and kernel-based estimators in tasks such as safety certification and coverage control. Current work also studies how to choose kernels and make embedding computations scalable, including through structured integration and feature approximations. A central tension is balancing expressive embeddings and reliable guarantees with the computational and statistical costs of high-dimensional or conditional problems.

Latest papers

11 papers2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

The Clustering Occupation Kernel (CLOCK) Method for Time Series Arising from Dynamical Systems
Oct 23, 2026Michael L. Wells, Kamel Lahouel, Victor Rielly +1Time Series Clustering Kernel Methods
Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 · Translational Genomics Research Institute, Phoenix, AZ 85004
Subgroup Rank-1 Lattice for Practical High-dimensional Black-box Integral Approximation
Sep 28, 2026Yueming LyuKernel Mean Embeddings Kernel Methods
Centre for Frontier AI Research (CFAR) Agency for Science, Technology and Research (A*STAR) 1 Fusionopolis Way #16-16 Connexis Singapore, 138632
Safety Certification is Classification
May 7, 2026Oliver Schön, Licio Romao, Sadegh SoudjaniKernel Mean Embeddings Dynamical Systems
ETH Zürich · Zürich, Switzerland · Technical University of Denmark +3
Gaussian mixture models in Hilbert spaces via kernel methods
May 7, 2026Daniel López-Montero, Antonio Álvarez-López, Marcos MatabuenaKernel Mean Embeddings Functional Data Analysis
Friedrich-Alexander-Universität Erlangen-Nürnberg · Universidad Autónoma de Madrid · Mohamed bin Zayed University of Artificial Intelligence
Measuring Differences between Conditional Distributions using Kernel Embeddings
May 4, 2026Peter Moskvichev, Siu Lun Chau, Dino SejdinovicKernel Mean Embeddings Maximum Mean Discrepancy
School of Mathematical Sciences, Adelaide University · College of Computing and Data Science, Nanyang Technological University
Generalising maximum mean discrepancy: kernelised functional Bregman divergences
Apr 27, 2026Russell Tsuchida, Frank NielsenKernel Mean Embeddings Functional Bregman Divergences
Department of Data Science and AI, Monash University, Australia. · Sony Computer Science Laboratories, Inc. Tokyo, Japan.
Infinite-Horizon Ergodic Control via Kernel Mean Embeddings
Apr 1, 2026Christian Hughes, Ian AbrahamErgodic Control Optimal Control
KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learning
Dec 22, 2025Eric Zimmermann, Harley Wiltzer, Justin Szeto +2Joint-Embedding Predictive Architecture Self-Supervised Visual Representation Learning
Microsoft Research, Cambridge, MA United States · Mila–Québec AI Institute, Montreal, Canada · McGill University, Montreal, Canada
Theoretical Refinement of CLIP by Utilizing Linear Structure of Optimal Similarity
Oct 17, 2025Naoki Yoshida, Satoshi Hayakawa, Yuhta Takida +3Cross-Modal Learning Kernel Mean Embeddings
The University of Tokyo · Sony Group Corporation · Sony AI
Verify when Uncertain: Beyond Self-Consistency in Black Box Hallucination Detection
Feb 20, 2025Yihao Xue, Kristjan Greenewald, Youssef Mroueh +1Kernel Mean Embeddings Selective Prediction
Department of Computer Science University of California, Los Angeles · MIT-IBM Watson AI Lab · IBM Research
Estimation of multiple mean vectors in high dimension
Mar 22, 2024Gilles Blanchard, Jean-Baptiste Fermanian, Hannah MarienwaldKernel Mean Embeddings Statistical Learning Theory
LMO, DATASHAPE · Université Paris Saclay, Institut Mathématique d’Orsay, France. · LMO +2

Oct 23, 2026J/K move · Enter open · S save

The Clustering Occupation Kernel (CLOCK) Method for Time Series Arising from Dynamical Systems

Michael L. Wells, Kamel Lahouel, Victor Rielly, Bruno Jedynak

Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 · Translational Genomics Research Institute, Phoenix, AZ 85004

Time Series Clustering Kernel Methods Kernel Mean Embeddings

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We introduce the Clustering Occupation Kernel (CLOCK) method, a novel representation-based framework for clustering time series arising from dynamical systems. CLOCK embeds observed sequences into a reproducing kernel Hilbert space (RKHS) via a time-averaged occupation kernel, enabling trajectory comparison through their RKHS norm. For systems governed by differential equations, this formulation rigorously approximates the kernel mean embedding of the invariant Sinai-Ruelle-Bowen (SRB) measure, meaning our dissimilarity metric approximates the maximum mean discrepancy (MMD) between attractors. To accommodate general time series, we introduce time lags via Takens' Embedding Theorem to reconstruct the phase space. Crucially, CLOCK natively handles trajectories of unequal lengths and irregularly-spaced observations. We validate the proposed metric using spectral clustering, demonstrating superior performance against benchmark methods on both synthetic datasets and a real-world intracranial large-scale electroencephalogram (EEG) dataset. Finally, ablation studies on the Lorenz-96 system are consistent with the theoretical convergence rates of the occupation kernels and highlight the method's strong robustness to zero-mean Gaussian noise.