Wednesday, May 24, 2023

2023-05-25 / 11:00 ~ 12:00

by ()

We propose a kernel-based estimator to predict the mean response trajectory for sparse and irregularly measured longitudinal data. The kernel estimator is constructed by imposing weights based on the subject-wise similarity on L2 metric space between predictor trajectories, where we assume that an analogous fashion in predictor trajectories over time would result in a similar trend in the response trajectory among subjects. In order to deal with the curse of dimensionality caused by the multiple predictors, we propose an appealing multiplicative model with multivariate Gaussian kernels. This model is capable of achieving dimension reduction as well as selecting functional covariates with predictive significance. The asymptotic properties of the proposed nonparametric estimator are investigated under mild regularity conditions. We illustrate the robustness and flexibility of our proposed method via the simulation study and an application to Framingham Heart Study

2023-05-26 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by 길이만(성균관대)

This talk presents new methods of solving machine learning problems using probability models. For classification problems, the classifier referred to as the class probability output network (CPON) which can provide accurate posterior probabilities for the soft classification decision, is proposed. In this model, the uncertainty of decision is defined using the accuracy of estimation. The deep structure of CPON is also presented to obtain the best classification performance for the given data. Applications of CPON models are also addressed.

2023-05-30 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: How connectivity affects the extremal number of trees

by Suyun Jiang(Jianghan University)

The Erdős-Sós conjecture states that the maximum number of edges in an $n$-vertex graph without a given $k$-vertex tree is at most $\frac {n(k-2)}{2}$. Despite significant interest, the conjecture remains unsolved. Recently, Caro, Patkós, and Tuza considered this problem for host graphs that are connected. Settling a problem posed by them, for a $k$-vertex tree $T$, we construct $n$-vertex connected graphs that are $T$-free with at least $(1/4-o_k(1))nk$ edges, showing that the additional connectivity condition can reduce the maximum size by at most a factor of 2. Furthermore, we show that this is optimal: there is a family of $k$-vertex brooms $T$ such that the maximum size of an $n$-vertex connected $T$-free graph is at most $(1/4+o_k(1))nk$.

2023-05-26 / 16:00 ~ 17:30

SAARC 세미나 - SAARC 세미나:

by ()

In this talk, we are going to consider the Fermi-Pasta-Ulam (FPU) system with innitely many oscil- lators. We particularly see that Harmonic analysis approaches allow us to observe dispersive properties of solutions to a reformulated FPU system, and with this observation, solutions to the FPU system can be approximated by counter-propagating waves governed by the Korteweg de-Vries (KdV) equation as the lattice spacing approaches zero. Additionally, we see dierent phenomena detected in the periodic FPU system.

2023-05-26 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by 오민환(서울대학교)

Despite much recent progress in analyzing algorithms in the linear MDPs and their variants, the understanding of more general transition models is still very restrictive. We study provably efficient RL algorithms for the MDP whose state transition is given by a multinomial logistic model. We establish the regret guarantees for the algorithms based on multinomial logistic function approximation. We also comprehensively evaluate our proposed algorithm numerically and show that it consistently outperforms the existing methods, hence achieving both provable efficiency and practical superior performance.

2023-05-24 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Stochasticity in gene expression is an important source of cell-to-cell variability (or noise) in clonal cell populations. So far, this phenomenon has been studied using the Gillespie Algorithm, or the Chemical Master Equation, which implicitly assumes that cells are independent and do neither grow nor divide. This talk will discuss recent developments in modelling populations of growing and dividing cells through agent-based approaches. I will show how the lineage structure affects gene expression noise over time, which leads to a straightforward interpretation of cell-to-cell variability in population snapshots. I will also illustrate how cell cycle variability shapes extrinsic noise across lineage trees. Finally, I outline how to construct effective chemical master equation models based on dilution reactions and extrinsic variability that provide surprisingly accurate approximations of the noise statistics across growing populations. The results highlight that it is crucial to consider cell growth and division when quantifying cellular noise.

2023-05-25 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

While deep learning has many remarkable success stories, finding a satisfactory mathematical explanation on why it is so effective is still considered an open challenge. One recent promising direction for this challenge is to analyse the mathematical properties of neural networks in the limit where the widths of hidden layers of the networks go to infinity. Researchers were able to prove highly-nontrivial properties of such infinitely-wide neural networks, such as the gradient-based training achieving the zero training error (so that it finds a global optimum), and the typical random initialisation of those infinitely-wide networks making them so called Gaussian processes, which are well-studied random objects in machine learning, statistics, and probability theory. These theoretical findings also led to new algorithms based on so-called kernels, which sometimes outperform existing kernel-based algorithms. The purpose of this talk is to explain these recent theoretical results on infinitely wide neural networks. If time permits, I will briefly describe my work in this domain, which aims at developing a new neural-network architecture that has multiple nice theoretical properties in the infinite-width limit. This work is jointly pursued with Fadhel Ayed, Francois Caron, Paul Jung, Hoil Lee, and Juho Lee.

Events for the 취소된 행사 포함