Random Function Priors for Correlation Modeling
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The likelihood model of many high dimensional data X_n can be expressed as p(X_n|Z_n,θ), where θ:=(θ_k)_k∈[K] is a collection of hidden features shared across objects (indexed by n). And Z_n is a non-negative factor loading vector with K entries where Z_nk indicates the strength of θ_k used to express X_n. In this paper, we introduce random function priors for Z_n that capture rich correlations among its entries Z_n1 through Z_nK. In particular, our model can be treated as a generalized paintbox model Broderick13 using random functions, which can be learned efficiently via amortized variational inference. We derive our model by applying a representation theorem on separately exchangeable discrete random measures.
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