In this paper we propose an L 1/2 regularizer which has a nonconvex penalty. The L 1/2 regularizer is shown to have many promising properties such as unbiasedness, sparsity and oracle properties. A reweighed iterative algorithm is proposed so that the solution of the L 1/2 regularizer can be solved through transforming it into the solution of a series of L 1 regularizers. The solution of the L 1/2 regularizer is more sparse than that of the L 1 regularizer, while solving the L 1/2 regularizer is much simpler than solving the L 0 regularizer. The experiments show that the L 1/2 regularizer is very useful and efficient, and can be taken as a representative of the Lp(0 < p < 1) regularizer.

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The result also applies to various sub-models of the stochastic blockmodel found in the literature.

In 2014, China introduced an ultra-low emissions (ULE) standards policy for renovating coal-fired power-generating units to limit SO2, NOX and PM emissions to 35, 50 and 10 mg m-3 , respectively. The ULE standard policy had ambitious levels (surpassing those of all other countries) and implementation timeline. We estimate emission reductions associated with the ULE policy by constructing a nationwide, unit-level, hourly-frequency emissions dataset using data from a continuous emission monitoring systems network covering 96-98% of Chinese thermal power capacity during 2014-2017. We find that between 2014 and 2017 China's annual power emissions of SO2, NOX and PM dropped by 65%, 60% and 72%, respectively. Our estimated emissions using actual monitoring data are 18-92% below other recent estimates. We detail the technologies used to meet the ULE standards and the determinants of compliance, underscoring the importance of ex-post evaluation and providing insights for other countries wishing to reduce their power emissions.

To meet the growing electricity demand, China’s power generation sector has become an increasingly large source of air pollutants. Specific control policymaking needs an inventory reflecting the overall, heterogeneous, time-varying features of power plant emissions. Due to the lack of comprehensive real measurements, existing inventories rely on average emission factors that suffer from many assumptions and high uncertainty. This study is the first to develop an inventory of particulate matter (PM), SO2 and NOX emissions from power plants using systematic actual measurements monitored by China’s continuous emission monitoring systems (CEMS) network over 96–98% of the total thermal power capacity. With nationwide, source-level, real-time CEMS-monitored data, this study directly estimates emission factors and absolute emissions, avoiding the use of indirect average emission factors, thereby reducing the level of uncertainty. This dataset provides plant-level information on absolute emissions, fuel uses, generating capacities, geographic locations, etc. The dataset facilitates power emission characterization and clean air policy-making, and the CEMS-based estimation method can be employed by other countries seeking to regulate their power emissions.

China has produced roughly half of the world's steel in recent years, but the country's iron and steel industry is a major source of air pollutants, especially particulate matter, SO2 and NOX emissions. To reduce such emissions, China imposed new emission standards in 2015 and promoted ultralow emission standards in 2019. Here, we use measurements from China's continuous emissions monitoring systems (covering 69-91% of national iron and steel production) to develop hourly, facility-level emissions estimates for China's iron and steel industry. In turn, we use this data to evaluate the emission reductions related to China's increasingly stringent policies. We find steady declines in emission concentrations at iron-and steelmaking plants since the 2015 standards were implemented. From 2014 to 2018, particulate matter and SO2 emissions fell by 47% and 42%, respectively, and NOX increased by 3%, even as the production increased by 14%. Moreover, we estimate that if all facilities achieve the ultralow emission standards, particulate matter, SO2 and NOX emissions will drop by a further 50%, 37% and 58%, respectively. Our results thus reveal the substantial benefits of the Chinese government's interventions to curb emissions from iron and steel production and emphasize the promise of ongoing ultralow emission renovations. [200 words]China's iron and steel industry dominates the global market, producing 45-53% of crude steel worldwide between 2010 and 2019 1-5 , and the country's crude steel production has grown faster than global production over the same period (at an average annual rate of 5% compared with 3% globally) 1 . As an energy-intensive industry, such production represents similarly large amounts of fossil fuel consumption; between 2010 and 2018, iron and steel production accounted for 7-9% of coal use in China 3,4,6,7 . In turn, the industry has greatly contributed to China's haze pollution [3][4][5][6][8][9][10] , accounting for 7-25%, 7-12% and 1-6% of the country's anthropogenic emissions of particulate matter (PM, including all PM size categories) 8,9 , sulfur dioxide (SO2) 8-10 and nitrogen oxide (NOX) 8-10 , respectively, between 2010 and 2015. In an effort to reduce emissions from iron-and steelmaking, China introduced emission standards for the major stationary sources (generating facilities, units, boilers and machines) in 2012 [11][12][13][14][15] , which are defined as the allowed upper limits of the emission concentrations in flue gas (in mg m -3 ; Supplementary Table 1) 2 . In 2015, China strengthened these standards by lowering the limits as much as 60%, 67% and 40% for PM, SO2 and NOX, respectively [11][12][13][14][15] . In addition, stricter local standards were designed for Shandong 16 and Hebei provinces 17 , reducing the limits in those provinces up to 50% and 40% lower than the national standards, respectively.In April 2019, China announced a set of even stricter ultralow emissions (ULE) standards 18 that reduce the 2015 standards by yet another 50-80%, 40-83% and 25-83% for PM, SO2 a...