It then serves as probabilistic prior to regularize the inverse problem(1).

Toachievethis, webuildonInfluenceFunction(IF)andproposesource-awareIF 2,whichleverages the generation process of the probabilistic labels to decompose the end model's training objective and then calculate the influence associated with each (data, source, class)tuple.

Although tremendous success has been achieved in spatial and network representation separately in recent years, there exist very little works on the representation of spatial networks. Extracting powerful representations from spatial networks requires the development of appropriate tools to uncover the pairing of both spatial and network information in the appearance of node permutation invariant, and rotation and translation invariant. Hence it can not be modeled merely with either spatial or network models individually. To address these challenges, this paper proposes a generic framework for spatial network representation learning. Specifically, a provably information-lossless and rotation-translation invariant representation of spatial information on networks is presented. Then a higher-order spatial network convolution operation that adapts to our proposed representation is introduced. To ensure efficiency, we also propose a new approach that relied on sampling random spanning trees to reduce the time and space complexity fromO(N3) to O(N).

In this work, we propose a new approach to R-D estimation from the perspective of optimal transport.

Structured representations of images that model visual relationships are beneficialformanyvision andvision-language applications.

We consider learning the structures of Gaussian latent tree models with vector observations when a subset of them are arbitrarily corrupted. First, we present the sample complexities of Recursive Grouping (RG)and Chow-Liu Recursive Grouping (CLRG)without theassumption thattheeffectivedepth isbounded in the number of observed nodes, significantly generalizing the results in Choi et al. (2011). We show that Chow-Liu initialization inCLRG greatly reduces the sample complexity ofRG from being exponential in the diameter of the tree to onlylogarithmic inthediameter forthehidden Markovmodel (HMM).