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Admissible kernels for RKHS embedding of probability distributions

Author

Listed:
  • Liangzhi Chen

    (Sun Yet-sen University)

  • Thomas Hotz

    (Institute of Mathematics)

  • Haizhang Zhang

    (Sun Yat-sen University)

Abstract

Similarity measurement of two probability distributions is important in many applications of statistics. Embedding such distributions into a reproducing kernel Hilbert space (RKHS) has many favorable properties. The choice of the reproducing kernel is crucial in the approach. We study this question by considering the similarity of two distributions of the same class. In particular, we investigate when the RKHS embedding is “admissible” in the sense that the distance between the embeddings should become smaller when the expectations are getting closer or when the variance is increasing to infinity. We give conditions on the widely-used translation-invariant reproducing kernels to be admissible. We also extend the study to multivariate non-symmetric Gaussian distributions.

Suggested Citation

  • Liangzhi Chen & Thomas Hotz & Haizhang Zhang, 2021. "Admissible kernels for RKHS embedding of probability distributions," Statistical Papers, Springer, vol. 62(3), pages 1499-1518, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01144-5
    DOI: 10.1007/s00362-019-01144-5
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