DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272021-02-26T10:23:43Z2021-02-26T10:23:43Zl-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficientsHamacher, PaulKim, Wansuhttp://hdl.handle.net/10203/2518972019-03-19T02:01:12ZTitle: l-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
Authors: Hamacher, Paul; Kim, WansuGraphs of bounded depth-2 rank-brittlenessKwon, O-joungOum, Sang-ilhttp://hdl.handle.net/10203/2799992021-01-28T05:50:48Z2021-03-01T00:00:00ZTitle: Graphs of bounded depth-2 rank-brittleness
Authors: Kwon, O-joung; Oum, Sang-il
Abstract: We characterize classes of graphs closed under taking vertex-minors and having noPnand no disjoint union ofncopies of the 1-subdivision ofK1,nfor somen. Our characterization is described in terms of a tree of radius 2 whose leaves are labeled by the vertices of a graphG, and the width is measured by the maximum possible cut-rank of a partition ofV(G)induced by splitting an internal node of the tree to make two components. The minimum width possible is called the depth-2 rank-brittleness ofG. We prove that for alln, every graph with sufficiently large depth-2 rank-brittleness containsPnor disjoint union ofncopies of the 1-subdivision ofK1,nas a vertex-minor.2021-03-01T00:00:00ZCounterfactual Fairness with Disentangled Causal Effect Variational AutoencoderKim, HyemiShin, SeungjaeJang, JoonHoSong, KyungwooJoo, WeonyoungKang, WanmoMoon, Il-Chulhttp://hdl.handle.net/10203/2809472021-02-22T06:30:15Z2021-02-09T00:00:00ZTitle: Counterfactual Fairness with Disentangled Causal Effect Variational Autoencoder
Authors: Kim, Hyemi; Shin, Seungjae; Jang, JoonHo; Song, Kyungwoo; Joo, Weonyoung; Kang, Wanmo; Moon, Il-Chul
Abstract: The problem of fair classification can be mollified if we develop a method to remove the embedded sensitive information from the classification features. This line of separating the sensitive information is developed through the causal inference, and the causal inference enables the counterfactual generations to contrast the what-if case of the opposite sensitive attribute. Along with this separation with the causality, a frequent assumption in the deep latent causal model defines a single latent variable to absorb the entire exogenous uncertainty of the causal graph. However, we claim that such structure cannot distinguish the 1) information caused by the intervention (i.e., sensitive variable) and 2) information correlated with the intervention from the data. Therefore, this paper proposes Disentangled Causal Effect Variational Autoencoder (DCEVAE) to resolve this limitation by disentangling the exogenous uncertainty into two latent variables: either 1) independent to interventions or 2) correlated to interventions without causality. Particularly, our disentangling approach preserves the latent variable correlated to interventions in generating counterfactual examples. We show
that our method estimates the total effect and the counterfactual effect without a complete causal graph. By adding a fairness regularization, DCEVAE generates a counterfactual fair dataset while losing less original information. Also, DCEVAE generates natural counterfactual images by only flipping sensitive information. Additionally, we theoretically show the differences in the covariance structures of DCEVAE and prior works from the perspective of the latent disentanglement.2021-02-09T00:00:00ZL-2-type contraction for shocks of scalar viscous conservation laws with strictly convex fluxKang, Moon-Jinhttp://hdl.handle.net/10203/2800152021-01-28T05:51:44Z2021-01-01T00:00:00ZTitle: L-2-type contraction for shocks of scalar viscous conservation laws with strictly convex flux
Authors: Kang, Moon-Jin
Abstract: We study the L-2-type contraction property of large perturbations around shock waves of scalar viscous conservation laws with strictly convex fluxes in one space dimension. The contraction holds up to a shift, and it is measured by a weighted relative entropy, for which we choose an appropriate entropy associated with the strictly convex flux. In particular, we handle shocks with small amplitude. This result improves the recent article [19] of the author and Vasseur on L-2-contraction property of shocks to scalar viscous conservation laws with a special flux, that is almost the Burgers flux.2021-01-01T00:00:00Z