Keywords:amortized variational inference, set, image completion, 3D scene reconstruction
Amortized variational inference is a powerful tool to approximate intractable posterior distributions over local latent variables using parametric functions (e.g., neural networks). In this paper, we study amortized variational inference for permutation-invariant sets rather than fixed dimensional vectors, which has a wide range of applications, such as uncertainty-aware regression and image completion. One of the difficulties in constructing functions on sets is that there are many possible sizes for sets. Hence, it is inefficient, in terms of computational costs, to optimize them for sets of all possible sizes. In this paper, we show that, in the context of amortized variational inference, it is possible to guarantee that functions optimized for sets of bounded sizes generalize to sets of arbitrary sizes by choosing an appropriate functional form. In the experiments, we first confirm that this form of the function is able to approximate posteriors from sets of any sizes better than other possible functional forms using a toy dataset, and then we report their performance in practical applications, such as 1D regression, image completion.
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