Kernel Measures of Independence for non-iid Data

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Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “ork when the data are i.i.d. For non-i.i.d. data, assumptions on the form of dependency— oftens in term of graphical models or mixing conditions—are needed. For example, to cope with non-i.i.d. data, Zhang et al. (2008) proposes a Structured-HSIC where Psatisﬁes the conditional independence speciﬁed”
A Wild Bootstrap for Degenerate Kernel Tests (2014, background): “For a 1-approximating functional of an absolutely regular process [6], convergence in probability of the empirical HSIC to its population value was shown in [33].”
Generative and Latent Mean Map Kernels (2010, methodology): “Following the notation from [30], for a graphical model G with variable set Z and maximal cliques set C, let vc be universal kernels on the variable subset of Z induced by clique c ∈ C.”
Hilbert space embeddings of conditional distributions with applications to dynamical systems (2009, methodology): “In the same spirit as the decomposition of su.cient statistics in exponential families (Altun et al., 2004; Zhang et al., 2009), we use the concatenation of t the feature map .”
Gaussian Processes for Independence Tests with Non-iid Data in Causal Inference (2015, background): “Related Work We are only aware of one general test [Zhang et al. 2008] for unconditional independence with non-iid data.”