Random Function Priors for Correlation Modeling
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:74247433, 2019.
Abstract
The likelihood model of high dimensional data $X_n$ can often be expressed as $p(X_nZ_n,\theta)$, where $\theta\mathrel{\mathop:}=(\theta_k)_{k\in[K]}$ is a collection of hidden features shared across objects, indexed by $n$, and $Z_n$ is a nonnegative factor loading vector with $K$ entries where $Z_{nk}$ indicates the strength of $\theta_k$ used to express $X_n$. In this paper, we introduce random function priors for $Z_n$ for modeling correlations among its $K$ dimensions $Z_{n1}$ through $Z_{nK}$, which we call population random measure embedding (PRME). Our model can be viewed as a generalized paintbox model \cite{Broderick13} using random functions, and can be learned efficiently with neural networks via amortized variational inference. We derive our Bayesian nonparametric method by applying a representation theorem on separately exchangeable discrete random measures.
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