Monday, September 11, 2023

2023-09-14 / 11:00 ~ 12:00

by 이명수()

In this talk, we discuss the Neural Tangent Kernel. The NTK is closely related to the dynamics of the neural network during training via the Gradient Flow(or Gradient Descent). But, since the NTK is random at initialization and varies during training, it is quite delicate to understand the dynamics of the neural network. In relation to this issue, we introduce an interesting result: in the infinite-width limit, the NTK converge to a deterministic kernel at initialization and remains constant during training. We provide a brief proof of the result for the simplest case.

2023-09-15 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by 최우진(KAIST)

최근의 생성모델에 관하여 스탠포드대학의 Ermon교수팀에서 NeurIPS2019, ICLR2021에 발표한 아래의 2편의 논문을 집중 리뷰하면서 SDE를 이용한 Generative Modeling의 연구동향과 발전 방향을 심층토의 하게 됩니다.

2023-09-14 / 14:30 ~ 15:45

학과 세미나/콜로퀴엄 - 기타:

by ()

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

2023-09-11 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 최인혁(고등과학원)

In the past decades, there has been considerable progress in the theory of random walks on groups acting on hyperbolic spaces. Despite the abundance of such groups, this theory is inherently not preserved under quasi-isometry. In this talk, I will present our study of random walks on groups that satisfy a certain QI-invariant property that does not refer to an action on hyperbolic spaces. Joint work with Kunal Chawla, Kasra Rafi, and Vivian He.

2023-09-15 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학:

by ()

In many stochastic service systems, decision-makers find themselves making a sequence of decisions, with the number of decisions being unpredictable. To enhance these decisions, it is crucial to uncover the causal impact these decisions have through careful analysis of observational data from the system. However, these decisions are not made independently, as they are shaped by previous decisions and outcomes. This phenomenon is called sequential bias and violates a key assumption in causal inference that one person’s decision does not interfere with the potential outcomes of another. To address this issue, we establish a connection between sequential bias and the subfield of causal inference known as dynamic treatment regimes. We expand these frameworks to account for the random number of decisions by modeling the decision-making process as a marked point process. Consequently, we can define and identify causal effects to quantify sequential bias. Moreover, we propose estimators and explore their properties, including double robustness and semiparametric efficiency. In a case study of 27,831 encounters with a large academic emergency department, we use our approach to demonstrate that the decision to route a patient to an area for low acuity patients has a significant impact on the care of future patients.

2023-09-14 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

Questions of parameter estimation – that is, finding the parameter values that allow a model to best fit some data – and parameter identifiability – that is, the uniqueness of such parameter values – are often considered in settings where experiments can be repeated to gain more certainty about the data. In this talk, however, I will consider parameter estimation and parameter identifiability in situations where data can only be collected from a single experiment or trajectory. Our motivation comes from medical settings, where data comes from a patient; such limitations in data also arise in finance, ecology, and climate, for example. In this setting, we can try to find the best parameters to fit our limited data. In this talk, I will introduce a novel, alternative goal, which we refer to as a qualitative inverse problem. The aim here is to analyze what information we can gain about a system from the available data even if we cannot estimate its parameter values precisely. I will discuss results that allow us to determine whether a given model has the ability to fit the data, whether its parameters are identifiable, the signs of model parameters, and/or the local dynamics around system fixed points, as well as how much measurement error can be tolerated without changing the conclusions of our analysis. I will consider various classes of model systems and will illustrate our latest results with the classic Lotka-Volterra system.

2023-09-12 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: The square of every subcubic planar graph of girth at least 6 is 7-choosable

by 김석진(건국대)

The square of a graph $G$, denoted $G^2$, has the same vertex set as $G$ and has an edge between two vertices if the distance between them in $G$ is at most $2$. Wegner's conjecture (1977) states that for a planar graph $G$, the chromatic number $\chi(G^2)$ of $G^2$ is at most 7 if $\Delta(G) = 3$, at most $\Delta(G)+5$ if $4 \leq \Delta(G) \leq 7$, and at most $\lfloor \frac{3 \Delta(G)}{2} \rfloor$ if $\Delta(G) \geq 8$. Wegner's conjecture is still wide open. The only case for which we know tight bound is when $\Delta(G) = 3$. Thomassen (2018) showed that $\chi(G^2) \leq 7$ if $G$ is a planar graph with $\Delta(G) = 3$, which implies that Wegner's conjecture is true for $\Delta(G) = 3$. A natural question is whether $\chi_{\ell}(G^2) \leq 7$ or not if $G$ is a subcubic planar graph, where $\chi_{\ell}(G^2)$ is the list chromatic number of $G^2$. Cranston and Kim (2008) showed that $\chi_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph of girth at least 7. We prove that $\chi_{\ell}(G^2) \leq 7$ if $G$ is a subcubic planar graph of girth at least 6. This is joint work with Xiaopan Lian (Nankai University).

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