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The likelihood model of high dimensional data $X_n$ can often be expressed as$p(X_n|Z_n,\theta)$, where $\theta\mathrel{\mathop:}=(\theta_k)_{k\in[K]}$ is acollection 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 $\theta_k$ used to express $X_n$. In this paper, weintroduce random function priors for $Z_n$ for modeling correlations among its$K$ dimensions $Z_{n1}$ through $Z_{nK}$, which we call \textit{populationrandom measure embedding} (PRME). Our model can be viewed as a generalizedpaintbox model~\cite{Broderick13} using random functions, and can be learnedefficiently with neural networks via amortized variational inference. We deriveour Bayesian nonparametric method by applying a representation theorem onseparately exchangeable discrete random measures.

Random Function Priors for Correlation Modeling