Monday, March 14, 2022

2022-03-17 / 12:00 ~ 13:00

by ()

This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between dimensionality-reduced conditional distributions of different protected classes. The incorporation of MMD naturally leads to an exact and tractable mathematical formulation of fairness with good statistical properties. We formulate the problem of fair PCA subject to MMD constraints as a non-convex optimization over the Stiefel manifold and solve it using the Riemannian Exact Penalty Method with Smoothing (REPMS; Liu and Boumal, 2019). Importantly, we provide local optimality guarantees and explicitly show the theoretical effect of each hyperparameter in practical settings, extending previous results. Experimental comparisons based on synthetic and UCI datasets show that our approach outperforms prior work in explained variance, fairness, and runtime. This paper is accepted to the 36th AAAI Conference on Artificial Intelligence (AAAI 2022).

2022-03-17 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

The Gordon-Bender-Knuth identities are determinant formulas for the sum of Schur functions of partitions with bounded length. There are interesting combinatorial consequences of the Gordon-Bender-Knuth identities, for instance, connections between standard Young tableaux of bounded height, lattice walks in a Weyl chamber, and noncrossing matchings. In this talk we prove an affine analog of the Gordon-Bender-Knuth identities and study their combinatorial properties. As a consequence we obtain an unexpected connection between cylindric standard Young tableaux and r-noncrossing and s-nonnesting matchings. This is joint work with JiSun Huh, Christian Krattenthaler, and Soichi Okada.

2022-03-21 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Ramsey numbers of cycles versus general graphs

by 김재훈(KAIST)

The Ramsey number $R(F,H)$ is the minimum number $N$ such that any $N$-vertex graph either contains a copy of $F$ or its complement contains $H$. Burr in 1981 proved a pleasingly general result that for any graph $H$, provided $n$ is sufficiently large, a natural lower bound construction gives the correct Ramsey number involving cycles: $R(C_n,H)=(n-1)(\chi(H)-1)+\sigma(H)$, where $\sigma(H)$ is the minimum possible size of a colour class in a $\chi(H)$-colouring of $H$. Allen, Brightwell and Skokan conjectured that the same should be true already when $n\geq |H|\chi(H)$. We improve this 40-year-old result of Burr by giving quantitative bounds of the form $n\geq C|H|\log^4\chi(H)$, which is optimal up to the logarithmic factor. In particular, this proves a strengthening of the Allen-Brightwell-Skokan conjecture for all graphs $H$ with large chromatic number. This is joint work with John Haslegrave, Joseph Hyde and Hong Liu

2022-03-17 / 12:00 ~ 12:50

대학원생 세미나 - 대학원생 세미나: Fast and efficient MMD-based fair PCA via optimization over Stiefel manifold

by 이정현(KAIST)

2022-03-18 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

We prove global Holder gradient estimates for bounded positive weak solutions of fast diffusion equations in smooth bounded domains with homogeneous Dirichlet boundary condition, which then leads us to establish their optimal global regularity. It solves a problem raised by Berryman and Holland in 1980. This is joint work with Jingang Xiong.

2022-03-14 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Rank- and tree-width of supercritical random graphs

by Tuan Anh Do(Graz공대 / IBS 이산수학그룹)

It is known that the rank- and tree-width of the random graph G(n,p) undergo a phase transition at p=1/n; whilst for subcritical p, the rank- and tree-width are bounded above by a constant, for supercritical p, both parameters are linear in n. The known proofs of these results use as a black box an important theorem of Benjamini, Kozma, and Wormald on the expansion of supercritical random graphs. We give a new, short, and direct proof of these results, leading to more explicit bounds on these parameters, and also consider the rank- and tree-width of supercritical random graphs closer to the critical point, showing that this phase transition is smooth. This is joint work with Joshua Erde and Mihyun Kang.

2022-03-18 / 10:30 ~ 11:45

학과 세미나/콜로퀴엄 - 대수기하학: An introductory guide to mixed Hodge modules #6

by 정승조(전북대학교)

Morihiko Saito's theory of mixed Hodge modules is a far generalisation of classical Hodge theory, which is based on the theory of perverse sheaves, D-modules, variations of Hodge structures. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. Naturally they are accompanied by perverse sheaves via the Riemann–Hilbert correspondence. This guide consists of about 8 talks, which may cover: review of classical Hodge theory, D-modules and filtered D-modules, nearby and vanishing cycles, etc. The main goal is to understand the notion of mixed Hodge modules and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry.

Events for the 취소된 행사 포함