Graduate Students Seminar

Speaker 1: Ahmet Aydin

Title

Introduction to Low-Rank Tensor Decompositions

Abstract

Many modern models and datasets are inherently high dimensional. As a result, arrays naturally extend to multi-dimensional arrays (tensors). This talk will provide brief overview of two widely used tensor decomposition methods and their low-rank approximations:

1. CANDECOMP/PARAFAC (CP) decomposition is a classical representation with well-established algorithms and software support. For approximation, we introduce the traditional alternating least squares (CP-ALS) algorithm.
2. Tensor-Train (TT) decomposition is a modern variant of CP that organizes components of the decomposition in a chain structure. For approximation, we introduce the TT-rounding algorithm that is based on singular value decomposition of substructures called cores.

Both CP and TT decompositions have robust implementations in MATLAB and Python, which will be briefly discussed. Finally, an incompressible fluid flow system with uncertainty will be presented as a numerical example consisting of space, time and stochastic dimensions.

Speaker 2: Vishal Subedi

Title

Cohort-level protection and individualized inference in AI based systems

Abstract

Artificial intelligence (AI)-based monitoring systems are increasingly employed in healthcare, finance, and ecological surveillance for early anomaly detection. However, such systems must balance cohort-level learning with individual-level decision-making to ensure personalized, adaptive, and trustworthy inference.

This work develops a unified Bayesian–Entropy–CUSUM framework for early change detection across large monitored cohorts. The framework is demonstrated on T₁-weighted MRI simulations generated with the Medigan GAN inpainting model, where tumor regions are synthetically inserted under varying signal-to-noise levels. Simulations show that entropy declines and CUSUM statistics rise sharply with tumor growth, producing early and accurate detections.