On Investigating the Conservative Property of Score-Based Generative Models

Existing Score-based Generative Models (SGMs) can be categorized into constrained SGMs (CSGMs) or unconstrained SGMs (USGMs) according to their parameterization approaches. CSGMs model probability density functions as Boltzmann distributions, and assign their predictions as the negative gradients of some scalar-valued energy functions. On the other hand, USGMs employ flexible architectures capable of directly estimating scores without the need to explicitly model energy functions. In this paper, we demonstrate that the architectural constraints of CSGMs may limit their modeling ability. In addition, we show that USGMs' inability to preserve the property of conservativeness may lead to degraded sampling performance in practice. To address the above issues, we propose Quasi-Conservative Score-based Generative Models (QCSGMs) for keeping the advantages of both CSGMs and USGMs. Our theoretical derivations demonstrate that the training objective of QCSGMs can be efficiently integrated into the training processes by leveraging the Hutchinson trace estimator. In addition, our experimental results on the CIFAR-10, CIFAR-100, ImageNet, and SVHN datasets validate the effectiveness of QCSGMs. Finally, we justify the advantage of QCSGMs using an example of a one-layered autoencoder

Long-Term Exposure to Ambient Fine Particulate Matter and Chronic Kidney Disease: A Cohort Study

BACKGROUND: Chronic kidney disease (CKD) is a serious global public health challenge, but there is limited information on the connection between air pollution and risk of CKD. OBJECTIVE: The aim of this study was to investigate the association between long-term exposure to particulate matter (PM) with an aerodynamic diameter of less than [Formula: see text] ([Formula: see text]) and the development of CKD in a large cohort. METHODS: A total of 100,629 nonCKD Taiwanese residents age 20 y or above were included in this study between 2001 and 2014. Ambient [Formula: see text] concentration was estimated at each participant's address using a satellite-based spatiotemporal model. Incident CKD cases were identified by an estimated glomerular filtration rate (eGFR) of less than [Formula: see text]. We collected information on a wide range of potential confounders/modifiers during the medical examinations. Cox proportional hazard regression was applied to calculate hazard ratios (HRs). RESULTS: During the follow-up, 4,046 incident CKD cases were identified, and the incidence rate was 6.24 per 1,000 person-years. In contrast with participants with the first quintile exposure of [Formula: see text], participants with the fourth and fifth quintiles exposure of [Formula: see text] had increased risk of CKD development, adjusting for age, sex, educational level, smoking, drinking, body mass index, systolic blood pressure, fasting glucose, total cholesterol, and self-reported heart disease or stroke, with an HR [95% confidence interval (CI)] of 1.11 (1.02, 1.22) and 1.15 (1.05, 1.26), respectively. A significant concentration-response trend was observed ([Formula: see text]). Every [Formula: see text] increment in the [Formula: see text] concentration was associated with a 6% higher risk of developing CKD (HR: 1.06, 95% CI: 1.02, 1.10). Sensitivity and stratified analyses yielded similar results. CONCLUSIONS: Long-term exposure to ambient [Formula: see text] was associated with an increased risk of CKD development. Our findings reinforce the urgency to develop global strategies of air pollution reduction to prevent CKD. https://doi.org/10.1289/EHP3304

Long-Term Exposure to Ambient Fine Particulate Matter and Chronic Kidney Disease: A Cohort Study

BACKGROUND: Chronic kidney disease (CKD) is a serious global public health challenge, but there is limited information on the connection between air pollution and risk of CKD. OBJECTIVE: The aim of this study was to investigate the association between long-term exposure to particulate matter (PM) with an aerodynamic diameter of less than [Formula: see text] ([Formula: see text]) and the development of CKD in a large cohort. METHODS: A total of 100,629 nonCKD Taiwanese residents age 20 y or above were included in this study between 2001 and 2014. Ambient [Formula: see text] concentration was estimated at each participant's address using a satellite-based spatiotemporal model. Incident CKD cases were identified by an estimated glomerular filtration rate (eGFR) of less than [Formula: see text]. We collected information on a wide range of potential confounders/modifiers during the medical examinations. Cox proportional hazard regression was applied to calculate hazard ratios (HRs). RESULTS: During the follow-up, 4,046 incident CKD cases were identified, and the incidence rate was 6.24 per 1,000 person-years. In contrast with participants with the first quintile exposure of [Formula: see text], participants with the fourth and fifth quintiles exposure of [Formula: see text] had increased risk of CKD development, adjusting for age, sex, educational level, smoking, drinking, body mass index, systolic blood pressure, fasting glucose, total cholesterol, and self-reported heart disease or stroke, with an HR [95% confidence interval (CI)] of 1.11 (1.02, 1.22) and 1.15 (1.05, 1.26), respectively. A significant concentration-response trend was observed ([Formula: see text]). Every [Formula: see text] increment in the [Formula: see text] concentration was associated with a 6% higher risk of developing CKD (HR: 1.06, 95% CI: 1.02, 1.10). Sensitivity and stratified analyses yielded similar results. CONCLUSIONS: Long-term exposure to ambient [Formula: see text] was associated with an increased risk of CKD development. Our findings reinforce the urgency to develop global strategies of air pollution reduction to prevent CKD. https://doi.org/10.1289/EHP3304