Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming

Due to the unobservability of confoundings, there has been widespread concern about how to compute causality quantitatively. To address this challenge, proxy-based negative control approaches have been commonly adopted, where auxiliary outcome variables $\bm{W}$ are introduced as the proxy of confoundings $\bm{U}$. However, these approaches rely on strong assumptions such as reversibility, completeness, or bridge functions. These assumptions lack intuitive empirical interpretation and solid verification techniques, hence their applications in the real world are limited. For instance, these approaches are inapplicable when the transition matrix $P(\bm{W} \mid \bm{U})$ is irreversible. In this paper, we focus on a weaker assumption called the partial observability of $P(\bm{W} \mid \bm{U})$. We develop a more general single-proxy negative control method called Partial Identification via Sum-of-ratios Fractional Programming (PI-SFP). It is a global optimization algorithm based on the branch-and-bound strategy, aiming to provide the valid bound of the causal effect. In the simulation, PI-SFP provides promising numerical results and fills in the blank spots that can not be handled in the previous literature, such as we have partial information of $P(\bm{W} \mid \bm{U})$

Experimental implementation of generalized Grover's algorithm of multiple marked states and its application

Generalized Grover's searching algorithm for the case in which there are multiple marked states is demonstrated on a nuclear magnetic resonance (NMR) quantum computer. The entangled basis states (EPR states) are synthesized using the algorithm.Comment: 20 pages,3 figure

Convolutional Neural Networks for Early Diagnosing of Breast Cancer

Title from PDF of title page, viewed December 22, 2022Dissertation advisors: An-Lin Cheng and Jenifer AllsworthVitaIncludes bibliographical references (pages 72-84)Dissertation (Ph.D.)--Department of Mathematics, Department of Biomedical and Health Informatics, University of Missouri--Kansas City, 2022Due to the high demand for mammograms, radiologists are swamped with many patients' mammograms. Radiologists' workload has increased dramatically over the last 15 years during on-call hours. This rise is due to an increase in the number of computed tomography (CT). Previous research published in the early 2000s found a 22% increase in radiology examinations during on-call hours in the United States over four years. The shortage of radiologists has recently worsened due to the COVID-19 pandemic. Based on their training and experience, radiologists classify mammography images as benign or malignant. Automating this diagnostic process with a machine learning algorithm may improve diagnosis speed and accuracy. This research aims to propose an effective automated algorithm system that lessens the workload of radiologists while improving speed and accuracy. This study uses Convolution Neural Networks (CNN) to assist radiologists in classifying lesions by incorporating repeated imaging. In addition, longitudinal electronic health record (EHR) data prior to diagnosis will augment the ML algorithm to improve its accuracy. This study takes a novel approach to the fusion model because only a few models have been developed to integrate both clinical and imaging data for diagnostic purposes, and few of them have included both EHR and longitudinal imaging data. Therefore, this study compared various multi-modal fusion and single models that can use pixel-based data (image) and EHR data from a large urban medical center.Introduction -- Foundation -- Research method (CNN) -- Result43 -- Combination of imaging data and EHR in CNN -- Conclusion and future wor