Figure 1: Motivation for using a multimodal prior distribution from a topological point of view. If the prior distribution is mapped to a distribution with a different topology, the mapped distribution will inevitably have undesirable high likelihood areas. The black and red areas represent the typical sets of the prior and the data distribution, respectively. The gray and yellow areas represent high likelihood areas of the prior and the data distribution, respectively. While the distributions are shown in two-dimensions in this figure, this inconsistency between high likelihood areas and typical sets is a problem observed in high dimensional data. (Topology Mismatch)
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