Ozone is one of the most important air pollutants, with significant impacts on human health, regional air quality and ecosystems. In this study, we use geographic information and environmental information of the monitoring site of 5577 regions in the world from 2010 to 2014 as feature input to predict the long-term average ozone concentration of the site. A Bayesian optimization-based XGBoost-RFE feature selection model BO-XGBoost-RFE is proposed, and a variety of machine learning algorithms are used to predict ozone concentration based on the optimal feature subset. Since the selection of the underlying model hyperparameters is involved in the recursive feature selection process, different hyperparameter combinations will lead to differences in the feature subsets selected by the model, so that the feature subsets obtained by the model may not be optimal solutions. We combine the Bayesian optimization algorithm to adjust the parameters of recursive feature elimination based on XGBoost to obtain the optimal parameter combination and the optimal feature subset under the parameter combination. Experiments on long-term ozone concentration prediction on a global scale show that the prediction accuracy of the model after Bayesian optimized XGBoost-RFE feature selection is higher than that based on all features and on feature selection with Pearson correlation. Among the four prediction models, random forest obtained the highest prediction accuracy. The XGBoost prediction model achieved the greatest improvement in accuracy.

The digital economy has become an important driving force for the steady development of China's economy, and enterprise innovation is a key element for an enterprise's survival and development. This paper constructs a mathematical model to measure the scale of digital economic development and the efficiency of enterprise innovation. It builds a fixed effects model and mediated effects model to study the effect of the development of the digital economy on enterprise innovation based on data from 30 provinces from 2012 to 2020. The results show that (1) there is a significant positive effect of the digital economy on enterprise innovation with an impact coefficient of 0.028, and the economic meaning of the coefficient is that for every 1-point increase in the digital economy index, the ratio of R&D capital expenditures to the enterprise's operating income increases by 0.028% points. This finding remains significant in the robustness test. (2) A further test of the mediating effect finds that the digital economy can drive enterprise innovation by reducing financing constraints. (3) In the regional heterogeneity analysis, it is found that the effect of the digital economy in promoting enterprise innovation is more prominent in the central region, and the impact coefficients are 0.04, 0.06, 0.025, and 0.024 for the eastern, central, western, and northeastern regions, respectively. Taking the central region as an example, the economic meaning of the coefficient is that for every 1-point increase in the digital economy index, the ratio of R&D capital expenditures to the enterprise's operating income increases by 0.06% points. The findings of this paper are of practical significance to enterprises in enhancing their innovation capabilities and promoting the high-quality development of China's economy.

A model with high accuracy and strong generalization performance is conducive to preventing serious pollution incidents and improving the decision-making ability of urban planning. This paper proposes a new neural network structure based on seasonal–trend decomposition using locally weighted scatterplot smoothing (Loess) (STL) and a dependency matrix attention mechanism (DMAttention) based on cosine similarity to predict the concentration of air pollutants. This method uses STL for series decomposition, temporal convolution, a bidirectional long short-term memory network (TCN-BiLSTM) for feature learning of the decomposed series, and DMAttention for interdependent moment feature emphasizing. In this paper, the long short-term memory network (LSTM) and the gated recurrent unit network (GRU) are set as the baseline models to design experiments. At the same time, to test the generalization performance of the model, short-term forecasts in hours were performed using PM_2.5, PM₁₀, SO₂, NO₂, CO, and O₃ data. The experimental results show that the model proposed in this paper is superior to the comparison model in terms of root mean square error (RMSE) and mean absolute percentage error (MAPE). The MAPE values of the 6 kinds of pollutants are 6.800%, 10.492%, 9.900%, 6.299%, 4.178%, and 7.304%, respectively. Compared with the baseline LSTM and GRU models, the average reduction is 49.111% and 43.212%, respectively.

Time series analysis predicts the future based on existing historical data and has a wide range of applications in finance, economics, meteorology, biology, engineering, and other fields. Although the combination of decomposition techniques and machine learning algorithms can effectively solve the problem of predicting nonstationary sequences, this kind of decomposition-integration-prediction strategy of the prediction method has serious defects. After the decomposition of the division of the training set and the test set, the information of the test set in the process of decomposition of the information leakage ultimately shows a high accuracy of the prediction of the illusionary. This paper proposes three improvement strategies for this type of “information leakage” problem: sliding window decomposition (SW-EMD), single training and multiple decomposition (STMP-EMD), and multiple training and multiple decomposition (MTMP-EMD). They are combined with a bidirectional multiscale temporal convolutional network (MSBTCN), bidirectional long- and short-term memory network (BiLSTM), and attention mechanism (DMAttention), which introduces a dependency matrix based on cosine similarity to be applied to water quality prediction. The experimental results show that the model achieves good performance in the prediction of three water quality indicators (pH, DO and KMnO₄), and the accuracies of the three models proposed in this paper are improved by 1.958% and 0.853% in terms of the RMSE and MAPE, respectively, compared with those of the mainstream LSTM models. The key contributions of this study include the following: (1) three methods are proposed to improve the class EMD decomposition, which can effectively solve the problem of “information leakage” that exists in the current models via class EMD decomposition; (2) the CEEMDAN-MSBTCN-BiLSTM-DMAttention model structure is innovated by combining improved class EMD decomposition methods; and (3) the three improved decomposition methods proposed in this paper can effectively solve the problem of “information leakage” and optimize the prediction model at the same time. This study provides an effective experimental method for water quality prediction and can effectively address the problem of “overfitting” models via class EMD decompositions during model training and testing.