Abrar Zahin

Abrar Zahin, Rajasekhar Anguluri, Lalitha Sankar et al.

In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line of work addressing this "robust model selection" problem narrows its focus to tree-structured graphical models. Even within this specific class of models, exact structure recovery is shown to be impossible. However, several algorithms have been developed that are known to provably recover the underlying tree-structure up to an (unavoidable) equivalence class. In this paper, we extend these results beyond tree-structured graphs. We first characterize the equivalence class up to which general graphs can be recovered in the presence of noise. Despite the inherent ambiguity (which we prove is unavoidable), the structure that can be recovered reveals local clustering information and global connectivity patterns in the underlying model. Such information is useful in a range of real-world problems, including power grids, social networks, protein-protein interactions, and neural structures. We then propose an algorithm which provably recovers the underlying graph up to the identified ambiguity. We further provide finite sample guarantees in the high-dimensional regime for our algorithm and validate our results through numerical simulations.

Abrar Zahin, Le Thanh Tan, Rose Qingyang Hu

In this paper, we propose a novel framework for the smart healthcare system, where we employ the compressed sensing (CS) and the combination of the state-of-the-art machine learning based denoiser as well as the alternating direction of method of multipliers (ADMM) structure. This integration significantly simplifies the software implementation for the lowcomplexity encoder, thanks to the modular structure of ADMM. Furthermore, we focus on detecting fall down actions from image streams. Thus, teh primary purpose of thus study is to reconstruct the image as visibly clear as possible and hence it helps the detection step at the trained classifier. For this efficient smart health monitoring framework, we employ the trained binary convolutional neural network (CNN) classifier for the fall-action classifier, because this scheme is a part of surveillance scenario. In this scenario, we deal with the fallimages, thus, we compress, transmit and reconstruct the fallimages. Experimental results demonstrate the impacts of network parameters and the significant performance gain of the proposal compared to traditional methods.