Coresets for Dependency Networks
This addresses the scalability issue for probabilistic graphical models in large-scale data analysis, though it is incremental with limitations for certain exponential family distributions.
The paper tackles the problem of training Gaussian dependency networks on massive datasets by constructing coresets with provably bounded worst-case error, achieving coreset sizes independent of the original data size, but shows that this does not extend to Poisson DNs in general.
Many applications infer the structure of a probabilistic graphical model from data to elucidate the relationships between variables. But how can we train graphical models on a massive data set? In this paper, we show how to construct coresets -compressed data sets which can be used as proxy for the original data and have provably bounded worst case error- for Gaussian dependency networks (DNs), i.e., cyclic directed graphical models over Gaussians, where the parents of each variable are its Markov blanket. Specifically, we prove that Gaussian DNs admit coresets of size independent of the size of the data set. Unfortunately, this does not extend to DNs over members of the exponential family in general. As we will prove, Poisson DNs do not admit small coresets. Despite this worst-case result, we will provide an argument why our coreset construction for DNs can still work well in practice on count data. To corroborate our theoretical results, we empirically evaluated the resulting Core DNs on real data sets. The results