Yan Luo

Yan Luo, Zhu Wang

In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could be subject to different diffusion coefficients, initial conditions, boundary conditions, and body forces. The proposed algorithm leads to a single discrete system for the group with multiple right-hand-side vectors by introducing an ensemble average of the diffusion coefficient functions and using a new semi-implicit time integration method. The system could be solved more efficiently than multiple linear systems with a single right-hand-side vector. We first apply the algorithm to deterministic parabolic PDEs and derive a rigorous error estimate that shows the scheme is first-order accurate in time and is optimally accurate in space. We then extend it to find stochastic solutions of parabolic PDEs with random coefficients and put forth an ensemble-based Monte Carlo method. The effectiveness of the new approach is demonstrated through theoretical analysis. Several numerical experiments are presented to illustrate our theoretical results.

Yan Luo, Zhu Wang

A first-order, Monte Carlo ensemble method has been recently introduced for solving parabolic equations with random coefficients in [26], which is a natural synthesis of the ensemble-based, Monte Carlo sampling algorithm and the ensemble-based, first-order time stepping scheme. With the introduction of an ensemble average of the diffusion function, this algorithm leads to a single discrete system with multiple right-hand sides for a group of realizations, which could be solved more efficiently than a sequence of linear systems. In this paper, we pursue in the same direction and develop a new multilevel Monte Carlo ensemble method for solving random parabolic partial differential equations. Comparing with the approach in [26], this method possesses a high-order accuracy in time and further reduces the computational cost by using the multilevel Monte Carlo method. Rigorous numerical analysis shows the method achieves the optimal rate of convergence. Several numerical experiments are presented to illustrate the theoretical results.

Yan Luo, Muhammad Osama Khan, Congcong Wen et al.

Recent progress in generative AI, especially diffusion models, has demonstrated significant utility in text-to-image synthesis. Particularly in healthcare, these models offer immense potential in generating synthetic datasets and training medical students. However, despite these strong performances, it remains uncertain if the image generation quality is consistent across different demographic subgroups. To address this critical concern, we present the first comprehensive study on the fairness of medical text-to-image diffusion models. Our extensive evaluations of the popular Stable Diffusion model reveal significant disparities across gender, race, and ethnicity. To mitigate these biases, we introduce FairDiffusion, an equity-aware latent diffusion model that enhances fairness in both image generation quality as well as the semantic correlation of clinical features. In addition, we also design and curate FairGenMed, the first dataset for studying the fairness of medical generative models. Complementing this effort, we further evaluate FairDiffusion on two widely-used external medical datasets: HAM10000 (dermatoscopic images) and CheXpert (chest X-rays) to demonstrate FairDiffusion's effectiveness in addressing fairness concerns across diverse medical imaging modalities. Together, FairDiffusion and FairGenMed significantly advance research in fair generative learning, promoting equitable benefits of generative AI in healthcare.

Leila Gheisi, Henry Chu, Raju Gottumukkala et al.

The use of artificial intelligence (AI) in automated disease classification significantly reduces healthcare costs and improves the accessibility of services. However, this transformation has given rise to concerns about the fairness of AI, which disproportionately affects certain groups, particularly patients from underprivileged populations. Recently, a number of methods and large-scale datasets have been proposed to address group performance disparities. Although these methods have shown effectiveness in disease classification tasks, they may fall short in ensuring fair prediction of disease progression, mainly because of limited longitudinal data with diverse demographics available for training a robust and equitable prediction model. In this paper, we introduce TransFair to enhance demographic fairness in progression prediction for ocular diseases. TransFair aims to transfer a fairness-enhanced disease classification model to the task of progression prediction with fairness preserved. Specifically, we train a fair EfficientNet, termed FairEN, equipped with a fairness-aware attention mechanism using extensive data for ocular disease classification. Subsequently, this fair classification model is adapted to a fair progression prediction model through knowledge distillation, which aims to minimize the latent feature distances between the classification and progression prediction models. We evaluate FairEN and TransFair for fairness-enhanced ocular disease classification and progression prediction using both two-dimensional (2D) and 3D retinal images. Extensive experiments and comparisons with models with and without considering fairness learning show that TransFair effectively enhances demographic equity in predicting ocular disease progression.

Yukang Jiang, Jianying Pan, Yanhe Shen et al.

Retina image processing is one of the crucial and popular topics of medical image processing. The macula fovea is responsible for sharp central vision, which is necessary for human behaviors where visual detail is of primary importance, such as reading, writing, driving, etc. This paper proposes a novel method to locate the macula through a series of morphological processing. On the premise of maintaining high accuracy, our approach is simpler and faster than others. Furthermore, for the hospital's real images, our method is also able to detect the macula robustly.