Applied Math Days
Foundations, Frontiers and Applications of Data Science

DATE：2025/12/22 MON.

LOCATION：Room 202, Astromath. Building, NTU

ORGANIZERS

• Chun-Yen Shen, Mathematics, NTU
• Mao-Pei Tsui, Mathematics, NTU
• Hau-Tieng Wu, Mathematics, NYU/AS
• Shih-Hsien Yu, Mathematics, AS

AGENDA

SPEAKERS

(1) Yen-Chang Huang (Department of Applied Mathematics, National Yang Ming Chiao Tung University)

Title: Detection and localization of defects on natural leather surfaces
Abstract: Manual visual inspection of leather defects is a crucial but labor-intensive and error-prone step in quality assurance. We propose an automated system for leather defect detection and localization using deep learning and image processing. The system first performs defect detection (classification) using an AlexNet feature extractor and an SVM classifier for high accuracy. The critical second stage is defect localization (instance segmentation) to map the defect boundary. We combine a variational method and a discrete method to achieve precise boundary segmentation. Comparing object detection architectures, Faster R-CNN significantly outperformed YOLOv2, achieving a superior Intersection over Union (IoU) of 73%. This work validates a robust, quantifiable methodology that replaces subjective human inspection with spatial analysis driven by deep learning, enhancing industrial quality assurance.

(2) Colin McSwiggen (Institute of Mathematics, Academia Sinica)

Title: Calibration and continuity
Abstract: A statistical model is said to be calibrated if it has the appropriate level of confidence in its own predictions: that is, the confidence that it assigns to a predicted outcome should accurately reflect that outcome's likelihood.  For example, if a weather model is calibrated, then out of all of the days when the model predicts a 30% chance of rain, we should expect that it actually will rain on 30% of them.  Calibration is crucial for managing the risks associated with incorrect predictions, but modern deep learning models are systematically miscalibrated: they are overconfident when they are incorrect.  To make matters worse, theorists can't agree about how miscalibration should be quantified!  The prevailing miscalibration metric in engineering applications is the expected calibration error (ECE), which has been widely criticized because it is discontinuous: a tiny change in the model can lead to a large change in the error.  In this talk, I'll try to convince you that this problem isn't really a problem, that ECE was fine all along, and that engineers should feel free to keep using it the way they always have (at least for binary classification tasks).  The argument will require us to answer a strange but fundamental question about conditional expectations in basic probability.

(3) Tzu-Chi Liu (Department of Mathematics, National Taiwan University)

Title: Mathematically Principled Artifact Removal for Real-Time Deep Brain Stimulation
Abstract: Adaptive deep brain stimulation (aDBS) modulates neural activity based on symptom-related biomarkers, promising improved efficacy and energy efficiency over conventional DBS. A persistent challenge, however, is stimulation-induced artifacts that corrupt neural recordings and compromise real-time biomarker extraction.
We present SMARTA+, a computationally efficient algorithm for removing both periodic stimulation and transient DC artifacts. SMARTA+ leverages modern random matrix theory to model local field potentials as noise with a separable covariance structure, and employs an approximate nearest neighbor scheme to achieve real-time performance. Using semi-real aDBS and Parkinson’s patient data, SMARTA+ outperforms existing methods in artifact suppression, preserves spectral–temporal features from beta to high-frequency oscillations, and improves beta-burst detection. These results highlight SMARTA+ as a mathematically principled and practical tool for advancing closed-loop neuromodulation.

(4) Junho Yang (Institute of Statistical Science, Academia Sinica)

Title: A new central limit theorem for spatial point processes, with an application to inference in the frequency domain
Abstract: In this presentation, we show a strong-mixing central limit theorem (CLT) for statistics formulated as the integrated periodogram of an observed point pattern. Since the statistic involves a quadratic term of the discrete Fourier transform, classical techniques, such as Bolthausen’s method, cannot be directly applied. Instead, we use a series of approximations to linearize the periodogram and then prove the CLT using a telescopic sum method. As an application, we prove the asymptotic normality of the model parameter estimator for spatial point processes via the Whittle likelihood. This work is based on collaborative research with Yongtao Guan at CHUK-Shenzhen.

(5) Chun-Hao Yang (Institute of Statistics and Data Sciences, National Taiwan University)

Title: Uncertainty of Network Topology with Applications to Out-of-Distribution Detection 
Abstract: Persistent homology (PH) is a crucial concept in computational topology, providing a multiscale topological description of a space. It is particularly significant in topological data analysis, which aims to make statistical inference from a topological perspective. In this work, we introduce a new topological summary for Bayesian neural networks, termed the predictive topological uncertainty (pTU). The proposed pTU measures the uncertainty in the interaction between the model and the inputs. It provides insights from the model perspective: if two samples interact with a model in a similar way, then they are considered identically distributed. We also show that the pTU is insensitive to the model architecture. As an application, pTU is used to solve the out-of-distribution (OOD) detection problem, which is critical to ensure model reliability. Failure to detect OOD input can lead to incorrect and unreliable predictions. To address this issue, we propose a significance test for OOD based on the pTU, providing a statistical framework for this issue. The eNectiveness of the framework is validated through various experiments, in terms of its statistical power, sensitivity, and robustness.

(6) Yuki Chino (Department of Applied Mathematics, National Yang Ming Chiao Tung University)

Title: Statistical mechanics from the mathematical point of view
Abstract: The talk will explain statistical mechanics from the viewpoint of mathematics. In statistical mechanics we treat several models to describe some macroscopic phenomenon analyzing microscopic interactions. In general the analysis is based on probability theory. We will consider some basic models as examples and if time permits, also my current research.

(7) Shu-Chin Lin (Institute of Statistics and Data Sciences, National Taiwan University)

Title: Domain Selection for Functional Linear Models
Abstract: In this talk, I will discuss scalar-on-function linear regression, focusing on the domain selection problem. While the functional predictor X(t) is observed over a compact domain, the scalar response Y may be associated with X(t) only on a specific subdomain. Hall and Hooker (2016) proposed two methods for estimating this domain of association but highlighted the challenge of accurately identifying the domain boundary when the coefficient function transitions smoothly to zero. To address this issue, we adopt a reproducing kernel Hilbert space (RKHS) framework, introducing a domain estimator and establishing its asymptotic properties under mild smoothness conditions.

(8) Jun Kitagawa (Department of Mathematics, Michigan State University)

Title: Transporting measures: a brief overview
Abstract: I will discuss a number of variational problems involving transporting one probability measure onto another, and very brief touch upon some of my recent work on the metric structures induced by such problems. These include the classical Monge-Kantorovich problem, sliced and disintegrated Monge-Kantorovich distances, and branched transport. 

Registration：[LINK]