Semigroup Kernels on Measures

By Marco Cuturi, Kenji Fukumizu, Jean-Philippe Vert. 2005

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Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “In Cuturi et al. (2005), the semi-group kernels were designed for objects with additive semi-group structure such 10Intuitively, the gradient of log-likelihood ui specifies how the parameter θ contributes to the process of generating the example xi (Jaakkola and Haussler 1998).”
Learning Theory for Distribution Regression (2014, background): “This category includes work on semigroup kernels (Cuturi et al., 2005), non-extensive information theoretical kernel constructions (Martins et al.”
Learning from Distributions via Support Measure Machines (2012, methodology): “Unlike previous works (Jebara et al. 2004, Cuturi et al. 2005, Martins et al. 2009), we adopt a Hilbert space embedding to represent the distribution as a point in an RKHS (Berlinet & Agnan 2004, Smola et al. 2007).”
Positive definite matrices and the S-divergence (2011, background): “βformed from symmetric real positive deﬁnite matrices, and characterizesthe values of βnecessary and suﬃcient for Hβ to be positive deﬁnite. We note here that the case β= 1 was essentially treated in [27], in the context of semigroup kernels on measures. Theorem 3.10. Let X1,...,Xm be real symmetric”
Integrating structured biological data by Kernel Maximum Mean Discrepancy (2006, background): “For detailed discussions of the problem of defining kernels between distributions and sets, see (Cuturi et al., 2005; Hein and Bousquet, 2005).”
From Dependence to Causation (2016, background): “In a separate strand of research, there has been multiple proposals to learn from probability distributions (Jebara et al., 2004; Hein and Bousquet, 2005; Cuturi et al., 2005; Martins et al., 2009; Muandet et al., 2012; Póczos et al., 2013).”
Towards a Learning Theory of Cause-Effect Inference (2015, unknown): “In a separate strand of research, there has been several attempts to learn from probability distributions in a principled manner (Jebara et al., 2004; Hein & Bousquet, 2004; Cuturi et al., 2005; Martins et al., 2009; Muandet et al., 2012).”