Month: September 2022

The 11th KMGS will be held on September 29th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite a speaker Junyoung Park (박준영) from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.

Slot (AM 11:50~PM 12:30)
[Speaker] Junyoung Park (박준영) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Cheolwoo Park (박철우 교수님), Prof. Jeongyoun Ahn (안정연 교수님)
[Title] Kernel methods for radial transformed compositional data with many zeros
[Discipline] Statistics
[Abstract]
Compositional data analysis with a high proportion of zeros has gained increasing popularity, especially in chemometrics and human gut microbiomes research. Statistical analyses of this type of data are typically carried out via a log-ratio transformation after replacing zeros with small positive values. We should note, however, that this procedure is geometrically improper, as it causes anomalous distortions through the transformation. We propose a radial transformation that does not require zero substitutions and more importantly results in essential equivalence between domains before and after the transformation. We show that a rich class of kernels on hyperspheres can successfully define a kernel embedding for compositional data based on this equivalence. The applicability of the proposed approach is demonstrated with kernel principal component analysis.
[Language] Korean (English if it is requested)

The 10th KMGS will be held on September 15th, Thursday, at Natural Science Building (E6-1) Room 1501.
We invite two speakers Sungho Han (한성호) and Hoil Lee (이호일) from the Dept. of Mathematical Sciences, KAIST.
The abstracts of the talks are as follows.

1st slot (AM 11:50~PM 12:10)
[Speaker] Sungho Han (한성호) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Moon-Jin Kang (강문진 교수님)
[Title] Large time behavior of one-dimensional barotropic compressible Navier-Stokes equations
[Discipline] Analysis (PDE)
[Abstract]
We will discuss on large time behavior of the one dimensional barotropic compressible Navier-Stokes equations with initial data connecting two different constant states. When the two constant states are prescribed by the Riemann data of the associated Euler equations, the Navier-Stokes flow would converge to a viscous counterpart of Riemann solution. This talk will present the latest result on the cases where the Riemann solution consist of two shocks, and introduce the main idea for using to prove.
[Language] Korean

2nd slot (PM 12:15~12:35)
[Speaker] Hoil Lee (이호일) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. Ji Oon Lee (이지운 교수님)
[Title] On infinitely wide deep neural networks
[Discipline] Probability theory, Deep learning
[Abstract]
Deep neural networks have proven to work very well on many complicated tasks. However, theoretical explanations on why deep networks are very good at such tasks are yet to come. To give a satisfactory mathematical explanation, one recently developed theory considers an idealized network where it has infinitely many nodes on each layer and an infinitesimal learning rate. This simplifies the stochastic behavior of the whole network at initialization and during the training. This way, it is possible to answer, at least partly, why the initialization and training of such a network is good at particular tasks, in terms of other statistical tools that have been previously developed. In this talk, we consider the limiting behavior of a deep feed-forward network and its training dynamics, under the setting where the width tends to infinity. Then we see that the limiting behaviors can be related to Bayesian posterior inference and kernel methods. If time allows, we will also introduce a particular way to encode heavy-tailed behaviors into the network, as there are some empirical evidences that some neural networks exhibit heavy-tailed distributions.
[Language] Korean (English if it is requested)

We are informing you of the schedule of the KAIST Math Graduate student Seminar(KMGS) 2022 Fall. We look forward to your attention and participation!

In this seminar, 6 talks will be held on Thursday from 11:50 to 12:40 in Room 1501 on the first floor of the Natural Science Building(E6-1).

Lunch will be provided after each talk.