Generative and Latent Mean Map Kernels
By Nishant A. Mehta, Alexander G. Gray. 2010
6 citations recorded by the source corpus.
We introduce two kernels that extend the mean map, which embeds probability measures in Hilbert spaces. The generative mean map kernel (GMMK) is a smooth similarity measure between probabilistic models. The latent mean map kernel (LMMK) generalizes the non-iid formulation of Hilbert space embeddings of empirical distributions in order to incorporate latent variable models. When comparing certain classes of distributions, the GMMK exhibits beneficial regularization and generalization properties not shown for previous generative kernels. We present experiments comparing support vector machine performance using the GMMK and LMMK between hidden Markov models to the performance of other methods on discrete and continuous observation sequence data. The results suggest that, in many cases, the GMMK has generalization error competitive with or better than other methods.
Subfields: Probabilistic & Bayesian Methods
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In Probabilistic & Bayesian Methods
- Krikamol Muandet
- Bharath K. Sriperumbudur
- Kenji Fukumizu
- Bernhard Schölkopf
- Arthur Gretton
- Dino Sejdinovic
- Yu Nishiyama
- Le Song
Citations in the corpus
- Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “It has been shown that the PPK is a special case of GMMK when ρ = 1 (Mehta and Gray 2010).”