Wednesday, September 13, 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

2023-09-19 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Orthogonal matroids over tracts

by 김동규(KAIST & IBS 이산수학그룹)

Even delta-matroids generalize matroids, as they are defined by a certain basis exchange axiom weaker than that of matroids. One natural example of even delta-matroids comes from a skew-symmetric matrix over a given field $K$, and we say such an even delta-matroid is representable over the field $K$. Interestingly, a matroid is representable over $K$ in the usual manner if and only if it is representable over $K$ in the sense of even delta-matroids. The representability of matroids got much interest and was extensively studied such as excluded minors and representability over more than one field. Recently, Baker and Bowler (2019) integrated the notions of $K$-representable matroids, oriented matroids, and valuated matroids using tracts that are commutative ring-like structures in which the sum of two elements may output no element or two or more elements. We generalize Baker-Bowler's theory of matroids with coefficients in tracts to orthogonal matroids that are equivalent to even delta-matroids. We define orthogonal matroids with coefficients in tracts in terms of Wick functions, orthogonal signatures, circuit sets, and orthogonal vector sets, and establish basic properties on functoriality, duality, and minors. Our cryptomorphic definitions of orthogonal matroids over tracts provide proofs of several representation theorems for orthogonal matroids. In particular, we give a new proof that an orthogonal matroid is regular (i.e., representable over all fields) if and only if it is representable over $\mathbb{F}_2$ and $\mathbb{F}_3$, which was originally shown by Geelen (1996), and we prove that an orthogonal matroid is representable over the sixth-root-of-unity partial field if and only if it is representable over $\mathbb{F}_3$ and $\mathbb{F}_4$. This is joint work with Tong Jin.

2023-09-20 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Typically, the mathematical description of reaction networks involves a system of parameter-dependent ordinary differential equations. Generally, one is interested in the qualitative and quantitative behavior of solutions in various parameter regions. In applications, identifying the reaction parameters is a fundamental task. Reduction of dimension is desirable from a practical perspective, and even necessary when different timescales are present. For biochemical reaction networks, a classical reduction technique assumes quasi-steady state (QSS) of certain species. From a general mathematical perspective, singular perturbation theory – involving a small parameter – is often invoked. The talk is mathematically oriented. The following points will be discussed: Singular perturbation reduction in general coordinates. (“How does one compute reductions?”) Critical parameters for singular perturbations. (“How does one find small parameters?”) Quasi-steady state and singular perturbations. (“What is applicable, what is correct?”)

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.

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