歷史演講 PAST TALKS

Abstract：

Testing independence has garnered increasing attention in the econometric and statistical literature. Many tests have been proposed, most of which are inconsistent against all departures from independence. Few of those tests, though consistent, suffer a significant loss of local power. This study proposes a mutual information test for testing independence. The proposed test is simple to implement and, with a slight loss of local power, is consistent against all departures from independence. The key driving factor is that we estimate the density ratio directly. This value is constant in a state of independence. This is in contrast with related studies that estimate the joint and marginal density functions to form the density ratio. A small-scale simulation study indicates that the proposed test outperforms the existing alternatives in various dependence structures.

20230112演講_張政教授(中國人民大學統計與大數據研究所)

Abstract：

Using the prefecture-level data of 284 cities in China during the period from 2004 through 2015, we investigate the environmental Kuznets curve (EKC) using spatial dynamic panel data models. Our model suggests an inverted U-shaped EKC, and the peak will come earlier considering the spillover effect. The shape of the EKC is supported by empirical evidence and is robust when we group cities by income level. Before introducing the paper, I will briefly introduce the fundamental idea of the spatial autoregressive (SAR) model with fixed effects.

20221222演講_張軒瑜研究員 (中華經濟研究院 綠色經濟研究中心 )

Abstract：

In this talk, we sketch the historical development of representation theory of reductive Lie groups, especially on the progress of solving the unitary dual problem. We will discuss this by first talking about finite groups, and then compact Lie groups and reductive Lie groups. Some major problems that have been solved for linear Lie groups are still mysterious for nonlinear Lie groups. We then discuss the growing importance of studying genuine representations of the nonlinear double cover of a real reductive Lie group. In particular, we are interested in the classification of genuine small representations and the algebraic properties that they carry. These small representations are part of the building blocks of the unitary dual of a nonlinear covering group, and have lots of applications in number theory.

20221216演講_蔡宛育教授 (中原大學應用數學系)

Abstract：

We consider the problem of lattice coding for the Gaussian wiretap channel. The main objective is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called secrecy function was proposed to characterize the eavesdropper’s probability of correctly decoding. The aim is to determine the global maximum value of the secrecy function, called (strong) secrecy gain.

In this talk, we will introduce the preliminary and basic principles of lattice coding and give an overview of the primary method used to design practical lattice codes to achieve high secrecy gains for the Gaussian wiretap channel. We will then summarize some recent results on lattice coding for the Gaussian wiretap channel and highlight some interesting problems in this research area.

20221215演講_林玄寅教授 (Simula UiB, Norway)

Abstract：

In this talk, we focus on the simplest kinetic equation, the so called linear Boltzmann equation, where the collision operator is hard potential with Grad cut-off assumption. We consider the solutions around two different global Maxwellians, and see the stability of the solution under the perturbation of the given background Maxwellians.

20221208演講_吳恭儉教授 (國立成功大學數學系)

[有學習時數]

演講者：

張副所長凱君 (台灣金融研訓院)

研究領域：

財務經濟、金融科技

學歷：

國立台灣大學

國際企業學系商學博士

張副所長凱君(台灣金融研訓院)本身具備良好的數理背景，此次演講，他將以數理的角度，深入淺出的介紹金融科技，並以他自身的經歷，告訴學生數學在金融業如何被廣泛地運用，以及學生在學時應該培養的能力與出社會應該具備的能力。

20221206演講_張副所長凱君 (台灣金融研訓院)

Abstract：

現今生成模型，除了圖片的生成外，在聲音、動畫、音樂、立體的內容，也都不斷進步。本次演講內容，我們會介紹我們最近在聲音轉換以及音樂生成方面的一些成果。在語音部份，我們改進及設計了一套語音轉換的系統，稱為 ASGAN-VC, 能以 zero-shot 的方式，將一個人的說話聲音轉成另外一個人的聲音。利用現代的架構和元件整合，轉換的品質在客觀及主觀的評量下，在聲音自然度以及對象相似度方面，較過去的轉換系統有更強的表現。而在音樂部份，我們設計的音樂生成系統，分析了過去一些系統的問題，加以改善，經由客觀及主觀評比，也在聲音品質及自然度方面，較過去系統有更好的表現。並且能指定情緒來生成音樂。

20221124演講_魏澤人教授 (國立陽明交通大學智慧科學暨綠能學院)

Abstract：

Bias and discrimination in Artificial Intelligence (AI) systems has been widely studied including tasks like AI-based facial recognition system. However, such bias has not been fully discussed in AI healthcare applications such as skin cancer detection, mortality prediction and healthcare utilization prediction algorithms. The state-of-the-art AI models have been shown to produce significant differences in underdiagnosis rates across racial and other demographic groups even when models only have access to the image itself. We introduced the bias problem in medical AI and then showed the experiments we conducted to comprehensively evaluate the ability of AI to recognize a patient's racial identity from medical images. Both private (Emory CXR, Emory Chest CT, Emory Cervical Spine, and Emory Mammogram) and public (MIMIC-CXR, CheXpert, National Lung Cancer Screening Trial, RSNA Pulmonary Embolism CT, and Digital Hand Atlas) datasets were used for the evaluation. Our results showed that medical AI systems can easily learn to recognize racial identity (AUC > 0.96) from medical images. However, the ability of AI deep learning models persisted over all anatomical regions and frequency spectrums of the images, suggesting the efforts to control this behavior are challenging. Finally, we proposed some possible solutions to eliminate the bias in the prediction of the AI imaging model. Our findings indicate that future AI medical imaging work should emphasize model performance audits on the basis of race, sex, and age.

20221117演講_郭柏志教授 (國立清華大學資工系)

NCTS/NCU Seminar on Computational Optimization with Applications

Abstract: 

We analyze measurement schemes under which 3D unwrapped phase retrieval can be reduced to projection tomography. Our motivation is to leverage highly successful projection-based techniques in cryo-EM to process diffraction data collected under measurement uncertainties such as sample heterogeneities, unknown orientations and positions. The resulting phase unwrapping problem for 3D projection tomography can be solved by various schemes including as special cases the conical tilting at a conical angle slightly greater than pi/4, the orthogonal dual-axis tilting and a combination of a conical tilting and an orthogonal single-axis tilting. Finally, we will discuss some results related to phase retrieval using 1-bit information.

20221116_Fannjiang

Abstract：

In this talk, I will discuss hitting probabilities of d-dimensional stochastic processes and random fields. I will start by reviewing some existing results on probability bounds for a process to hit a given set. Those results determine the critical dimension above which the set is polar (i.e., the set will not be hit almost surely), but in general do not determine whether the set is polar in the critical dimension. I will present a new sufficient condition for a compact set to be polar for a class of Gaussian random fields including fractional Brownian fields and systems of stochastic PDEs. Our result also solves an open problem on the collisions of eigenvalues of random matrices with Gaussian random field entries. This is joint work with Jian Song, Yimin Xiao and Wangjun Yuan.

20221103演講_李卓彥教授 (國立清華大學數學系)

Abstract：

The information bottleneck (IB) method is an information-theoretic approach to compress data while maximally preserving relevance about hidden features. The method has a broader application in machine learning and communication systems. This talk will review the basic idea of the IB method and some applications. A coding theorem will also be presented, showing how block coding can achieve the optimal trade-off between the compression rate and the relevance level.

20221020演講_翁健家教授 (國立臺灣海洋大學電機工程學系)

Abstract：

This is joint work with Chang-Yeol Jung, Bongsuk Kwon and Sunghwan Moon. In this talk, we prove the complete and partial phase synchronization for the Kuramoto oscillators with distributed time-delays and inertia effect. Our results assert that the Kuramoto models incorporated with a small variation of distributed time-delays and inertia effect still exhibit synchronization. This shows the robustness of the synchronization phenomena of the original Kuramoto model in the perturbation of time-delay and inertia effects.

20221013演講_夏俊雄教授 (國立台灣大學數學系)