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Abstract:
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We develop a graphical model approach, sparse additive graphical models, to estimate a compatible dependence structure. The approach is motivated by the robust estimation of conditional non-linear dependence, namely kernel partial correlation (KPC). As a generalization of partial correlation, KPC uses kernel based approaches for both conditioning and measuring remaining associations. Although effective, the dependence structure from KPC is not compatible to a probability density function. In order to estimate a compatible dependence structure, we propose a graphical model approach based on an additive function space. Our approach starts from the assumption that a mean vector of multiple random variables is related to an additive space. The conditional independence is inferred by explicitly estimating components of the additive function, called sparse additive graphical models. The complexity of our approach is small compared to others and the estimate from the approach is compatible to a multivariate distribution. These are very useful features because it can facilitate efficient missing value imputation of multivariate datasets.
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