Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully applied to various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.

Changes in land use patterns, types, and intensities significantly impact ecosystem services. This study follows the time series logic from history to the expected future to investigate the spatial and temporal characteristics of land use changes in Ezhou and their potential impacts on the ecosystem services value (ESV). The results show that the Markov–FLUS model has strong applicability in predicting the spatial pattern of land use, with a Kappa coefficient of 0.9433 and a FoM value of 0.1080. Between 2000 and 2020, construction land expanded continuously, while water area remained relatively stable, and other land types experienced varying degrees of contraction. Notably, the area of construction land expanded significantly compared to 2000, and it expanded by 70.99% in 2020. Moreover, the watershed area expanded by 9.30% from 2000 to 2010, but there was very little change in the following 10 years. Under the three scenarios, significant differences in land use changes were observed in Ezhou City, driven by human activities, particularly the strong expansion of construction land. In the inertial development scenario, construction land expanded to 313.39 km² by 2030, representing a 38.30% increase from 2020. Conversely, under the farmland protection scenario, construction land increased to 237.66 km², a 4.89% rise from 2020. However, in the ecological priority development scenario, the construction land area expanded to 253.59 km², a 10.13% increase from 2020. Compared to 2020, the ESV losses in the inertia development and farmland protection scenarios were USD 4497.71 and USD 1072.23, respectively, by 2030. Conversely, the ESV under the ecological protection scenario increased by USD 2749.09, emphasizing the importance of prioritizing ecological protection in Ezhou City’s development. This study may provide new clues for the formulation of regional strategies for sustainable land use and ecosystem restoration.

The changes of land use/land cover (LULC) are important factor affecting the intensity of the urban heat island (UHI) effect. Based on Landsat image data of Wuhan, this paper uses cellular automata (CA) and artificial neural network (ANN) to predict future changes in LULC and LST. The results show that the built-up area of Wuhan has expanded, reaching 511.51 and 545.28 km², while the area of vegetation, water bodies and bare land will decrease to varying degrees in 2030 and 2040. If the built-up area continues to expand rapidly, the proportion of 30~35 °C will rise to 52.925% and 55.219%, and the affected area with the temperature >35 °C will expand to 15.264 and 33.612 km², respectively. The direction of the expansion range of the LST temperature range is obviously similar to the expansion of the built-up area. In order to control and alleviate UHI, the rapid expansion of impervious layers (built-up areas) should be avoided to the greatest extent, and the city’s “green development” strategy should be implemented.