Copula Entropy Research Articles

Prediction model of permeability index for blast furnace based on WD-NL-transformer

The permeability index is an important variable to reflect the operating state of a blast furnace quickly, intuitively and comprehensively. Given the multi-scale, nonlinear and massive characteristics of the blast furnace smelting process data, a prediction model of permeability index based on the WD-NL-transformer (wavelet de-noising-nonlinear-transformer) method was proposed. The key variables affecting permeability index were selected from multiple perspectives by Pearson correlation coefficient and copula entropy. The extreme outliers were optimised using box plots and Lagrange linear interpolation. A data set was constructed after wavelet de-noising to build the prediction model with nonlinear processing capability, time-series prediction capability, and early stopping method. The results show that the MSE of WD-NL-transformer is 0.0093, with the RMSE of 0.0086. Meanwhile, the R2 is 0.9859, and the running time is 19.59 s, which means the model has great prediction accuracy and inference speed. The proposed model could provide theoretical support for advanced control of permeability index, which is of practical significance to ensure the stability of blast furnace smelting and accelerate the metallurgical process of intelligent automation.

Which droughts are becoming more frequent? A copula entropy analysis on the return period of droughts in Europe

AbstractClimate change and global warming have increased the frequency of extreme events, particularly over the past decades. Changes in drought frequency are not yet understood, especially regarding which drought features are becoming more frequent (e.g., are longer or high-magnitude droughts becoming more frequent, or both?). In this study, we present a novel methodology to accurately and consistently estimate changes in return periods of different types of droughts. For this purpose, we implemented copula-entropy theory to assess drought frequencies and their changes. As an example of the application of the proposed method, we used data from the European Climate Assessment and Dataset (ECA&D), from which we selected 26 stations in Central Europe with over 100 years of data and low incidence of missing days ($$\le$$ ≤ 0.3%). The results of the new analysis indicate that there was a high variability in the frequency change patterns across Central Europe over the last century; however, most regions have experienced an increase in the frequency of medium-to-high intensity droughts. The use of the copula-entropy theory to assess drought frequency is a reliable method that allows systematic monitoring and easy updating of current knowledge, and is computationally efficient and statistically robust.

Explainable ResNet50 learning model based on copula entropy for cotton plant disease prediction

This paper presents a novel Deep Learning (DL) framework for cotton plant disease prediction based on Explainable Artificial Intelligence (XAI) and Copula entropy based-Grey Wolf Optimization (GWO) algorithm. The suggested framework uses a cotton plant image as input and pre-processes it to produce an image with enhanced contrast. Features are extracted from the leaf images with the ResNet50 CNN model. A crucial pre-processing model known as feature selection helps to improve the effectiveness of image classification by deleting extraneous or irrelevant features. Therefore, the Gray Wolf optimization (GWO) algorithm which is a global search method with potential use in feature selection is employed in this paper. The proposed framework introduces Copula entropy (CE) as an indicator of association to create the GWO’s initial population and enhance the GWO feature engineering process. For the GWO initialization procedure, CE has been used to choose the most significant features which substantially improved the quality of the GWO starting population and as a result improved the performance of the proposed CE-based GWO algorithm by 78.57 % faster than the traditional GWO as stated by the time complexity analysis. In addition, Feature importance explanation is determined using XAI layer. The final classification is achieved using Random Forests (RF) classifier which is an ensemble learning approach. According to the experimental results, the suggested model has a classification accuracy of 99 % and a mean squared error of 0.0383. Furthermore, the proposed model has been compared to state-of-the-art algorithms and the results showed that the proposed model has the superiority performance. The proposed model can therefore be used to track a variety of cotton areas to enable faster analysis and response, resulting in higher productivity.

Cooperative voltage control in distribution networks considering multiple uncertainties in communication

Delays, jitter, and packet loss in communication networks can impact the performance of cooperative voltage control systems in distribution networks. In distribution systems with a high penetration of renewable energy sources that do not respond promptly, these issues can even lead to system destabilization when voltage surges occur. Considering the interdependence of delay, jitter, and packet loss, the current direct approach of accumulating information entropy may result in the deterioration of dynamic control performance. Based on Copula entropy theory, a new multivariate communication uncertainty metric model is proposed. Using the multivariate Epanechnikov kernel function model, a method has been developed to estimate the multivariate non-independent uncertainty of a communication system. Accurate state estimation is integrated into event-triggered sliding mode control (ETSMC) of the distribution network to facilitate coordinated voltage control and enhance resilience against communication uncertainty. Design criteria for the controller and observer parameters are provided based on Lyapunov stability theory. Simulation results confirm that the proposed ETSMC offers significant improvements in control performance and system resilience to external power disturbances and multivariate communication uncertainty events.

Mutual information between Polish subindexes – the use of copula entropy around the time of the COVID-19 pandemic

In this paper, the copula theory is used to describe the dependence structure between variables, while the information theory provides the tools necessary to measure the uncertainty associated with these variables. What both theories have in common is copula entropy, which is strictly related to mutual information. The findings of this study, focusing on the dependence of the (sub)indexes of the Polish stock market during the pandemic period, may prove useful not only to investors from Poland, but also from other countries, especially Central European, in making investment decisions. The results of calculating the interdependencies between WIG, sectoral indexes and among sectoral indexes of the Polish economy using copula entropy and Pearson’s correlation are quite different. The source of the basic difference between copula entropy and Pearson’s correlation is that the former enables the measurement of nonlinear interdependencies, while the latter not. The interrelations on the stock markets are nonlinear and returns are not normally distributed in general. The use of copulas is also superior in terms of ranking correlation, as it is more general and allows the examination of the structure of dependencies between extreme values.

Dynamic Modeling Framework Based on Automatic Identification of Operating Conditions for Sintering Carbon Consumption Prediction

In iron and steel industry, sintering process requires huge carbon consumption. Achieving accurate and dynamic prediction of carbon consumption in this process is of evident significance to protect the environment and raise the economic efficiency of iron and steel industry. This paper develops an original dynamic modeling framework including automatic identification of operating conditions, modeling in different conditions, and dynamic prediction model of sintering carbon consumption. Firstly, an automatic kernel-based fuzzy C-means algorithm is presented for automatic identification of operating conditions. Dynamic relationships between the inputs and output of the model are analyzed by Copula Entropy, and then the relevant production data in each operating condition are determined by just-in-time learning method. Next, broad learning models are established under different operating conditions. Further, dynamic prediction model of sintering carbon consumption is designed, and the prediction error is adopted to quantify performance of the model and as one criteria to determine the update of production database. Finally, results of experiments using actual production data demonstrate the advantage and validity of the developed model compared with some advanced modeling methods. The developed model considers complex characteristics of the sintering process and presents a better dynamic performance and information mining performance.

Information Content of Inflation Expectations: A Copula-Based Model

Abstract This paper introduces a holistic framework that integrates copula modeling and information-theoretic measures to examine the information content of inflation expectations. Copulas are used to capture the dynamic dependence between inflation and expectations, accounting for extreme events and tail dependence. Information-theoretic measures are employed to quantify the information that expectations provide about inflation. Theoretical results establish a link between copula entropy and mutual information, propose a lower bound for copula entropy, and provide a practical tool for central banks to anchor expectations to achieve inflation targets. Empirical findings reveal higher uncertainty in the tails of the joint distribution and underscore the meaningful information carried by expected inflation for forecasting inflation, particularly with shorter-term expectations.

Vulnerability Analysis Method Based on Network and Copula Entropy.

With the deepening of the diversification and openness of financial systems, financial vulnerability, as an endogenous attribute of financial systems, becomes an important measurement of financial security. Based on a network analysis, we introduce a network curvature indicator improved by Copula entropy as an innovative metric of financial vulnerability. Compared with the previous network curvature analysis method, the CE-based curvature proposed in this paper can measure market vulnerability and systematic risk with significant advantages.

Mutual information between the main foreign subindices: The application of copula entropy around WHO’s declaration date at the time of the COVID-19 pandemic

Mutual information between the main foreign subindices: The application of copula entropy around WHO’s declaration date at the time of the COVID-19 pandemic

Searching for cognitive specializations of neurons using mutual information framework

Of particular interest for researching the cognitive specializations of neurons is their correlation with environmental variables and animal behavior. Mutual information (MI) is a preferable method for measuring such correlations, as it allows for the assessment of non-linear relationships between variables, detects synchronization, and provides both significance and strength quantification. However, calculating MI for real data is significantly challenging. In this study, we used updated MI calculation techniques to analyze the connection between calcium fluorescence signaling and behavioral variables. Our approach encompasses novel strategies which we compiled into a software program known as INTENS (Information-Theoretic Evaluation of Neuronal Specializations), and it enabled to identify specialized neurons in mice hippocampal calcium activity data while they explored the arena with varying levels of novelty. Numerous methods exist for analyzing the relationship between neuron spikes and behavioral variables, including information-theoretical approaches [1]. Extracting information about the relationship between calcium fluorescent signals and behavior is of particular interest due to the signal’s ability to provide crucial information about subthreshold activations of the neuron. In this study, we use the GCMI Gaussian copula entropy method to calculate mutual information [2]. This method relies on the fact that mutual information between two random variables is independent of their marginal distributions and only depends on the type of copula used (a multidimensional distribution where each marginal distribution is uniform). The actual MI was compared to its corresponding values computed on the time-shifted signals for assessing the statistical significance of the computed information association between the calcium signal and the behavioral variable. Additionally, we devised a technique for gauging the strength of the coupling effect. This involved normalizing the mutual information between the fluorescence signal and the behavior with the entropy value of both variables, previously calculated as random variables. Importantly, the approach outlined earlier is effective for analyzing continuous variables such as calcium signal and animal speed, as well as pairs of continuous and discrete variables such as calcium signal and the presence or absence of grooming. The analysis of calcium signals recorded from the CA1 region of the hippocampus revealed neuronal specializations related to the animal’s external environment, such as place cells, and specializations related to its behavioral activities, including neurons activated during running, rearing, and freezing. Some neurons selectively activated in response to discrete parameters included the animal’s location within the arena (center, walls, and corners) and its speed (rest, slow, and fast). A total of 781 specializations were detected across 472 neurons throughout all four sessions of the experiment. Notably, a single neuron could have several specializations. However, more than half (55%) of the neurons were found to have only one specialization.

Neurophysiology of creativity and machine learning applications for creative process’ stages differentiation through assessment of EEG/VP signals

Of particular interest for researching the cognitive specializations of neurons is their correlation with environmental variables and animal behavior. Mutual information (MI) is a preferable method for measuring such correlations, as it allows for the assessment of non-linear relationships between variables, detects synchronization, and provides both significance and strength quantification. However, calculating MI for real data is significantly challenging. In this study, we used updated MI calculation techniques to analyze the connection between calcium fluorescence signaling and behavioral variables. Our approach encompasses novel strategies which we compiled into a software program known as INTENS (Information-Theoretic Evaluation of Neuronal Specializations), and it enabled to identify specialized neurons in mice hippocampal calcium activity data while they explored the arena with varying levels of novelty. Numerous methods exist for analyzing the relationship between neuron spikes and behavioral variables, including information-theoretical approaches [1]. Extracting information about the relationship between calcium fluorescent signals and behavior is of particular interest due to the signal’s ability to provide crucial information about subthreshold activations of the neuron. In this study, we use the GCMI Gaussian copula entropy method to calculate mutual information [2]. This method relies on the fact that mutual information between two random variables is independent of their marginal distributions and only depends on the type of copula used (a multidimensional distribution where each marginal distribution is uniform). The actual MI was compared to its corresponding values computed on the time-shifted signals for assessing the statistical significance of the computed information association between the calcium signal and the behavioral variable. Additionally, we devised a technique for gauging the strength of the coupling effect. This involved normalizing the mutual information between the fluorescence signal and the behavior with the entropy value of both variables, previously calculated as random variables. Importantly, the approach outlined earlier is effective for analyzing continuous variables such as calcium signal and animal speed, as well as pairs of continuous and discrete variables such as calcium signal and the presence or absence of grooming. The analysis of calcium signals recorded from the CA1 region of the hippocampus revealed neuronal specializations related to the animal’s external environment, such as place cells, and specializations related to its behavioral activities, including neurons activated during running, rearing, and freezing. Some neurons selectively activated in response to discrete parameters included the animal’s location within the arena (center, walls, and corners) and its speed (rest, slow, and fast). A total of 781 specializations were detected across 472 neurons throughout all four sessions of the experiment. Notably, a single neuron could have several specializations. However, more than half (55%) of the neurons were found to have only one specialization.

Poverty improvement policies and household income: Evidence from China

The purposes of this research is to analyzed the impact of various policies on household incomes and to obtain the influential factors according to their importance. Utilizing a survey data of poor households supported by poverty improvement policies, for individual income, this research implements the traditional random forest method. To analyze the influence of strategies on the overall household earnings, we propose a novel splitting method centered on copula entropy and construct a novel choice tree. Finally, we conclude that the policies are generally effective but that levels of effectiveness are varied for people with different levels of income. We also identified the policy arrangement that has the greatest impact on household income.

Copula entropy-based golden jackal optimization algorithm for high-dimensional feature selection problems

Feature selection (FS) is a crucial process that aims to remove unnecessary features from datasets. It plays a role in data mining and machine learning (ML) by reducing the risk associated with high-dimensional datasets. FS is considered a challenging problem that is difficult to solve efficiently due to its combinatorial nature. As the size of the problem increases, the computation time also grows. Recently, researchers have focused on metaheuristic FS algorithms specifically designed for high-dimensional datasets. Therefore, this article proposes a powerful metaheuristic algorithm called Binary Enhanced Golden Jackal Optimization (BEGJO), which is an improved version of the recently published Golden Jackal Optimization (GJO) algorithm. The original GJO algorithm faces challenges when dealing with high-dimensional FS problems, as it tends to get trapped in local optima. To address this issue, various enhancement strategies are employed to improve the efficiency of GJO. The proposed BEGJO algorithm utilizes Copula Entropy (CE) to reduce the dimensionality of high-dimensional FS problems while maintaining high classification accuracy using the K-Nearest Neighbour (K-NN) classifier. Additionally, four enhancement strategies are incorporated to enhance the exploration and exploitation capabilities of the fundamental GJO algorithm. The BEGJO algorithm is transformed into its binary form using the sigmoid transfer function, aligning it with the nature of the FS problem. It is then tested on various high-dimensional benchmark datasets. The effectiveness of BEGJO is evaluated by comparing it with well-known algorithms in terms of classification accuracy, feature dimension, and processing time. BEGJO outperforms other algorithms in terms of classification accuracy and feature dimension and ranks up to fourth in terms of processing time. Furthermore, the advantageous use of CE is demonstrated by comparing the performance of the proposed algorithm with traditional FS algorithms. Statistical evaluations are conducted to further validate the effectiveness and superiority of the proposed algorithm. The results confirm that BEGJO is an effective solution for high-dimensional FS problems.

Research on Establishing Corneal Edema after Phacoemulsification Prediction Model Based on Variable Selection with Copula Entropy

Corneal edema (CE) affects the outcome of phacoemulsification. Effective ways to predict the CE after phacoemulsification are needed. On the basis of data from patients conforming to the protocol of the AGSPC trial, 17 variables were selected to predict CE after phacoemulsification by constructing a CE nomogram through multivariate logistic regression, which was improved via variable selection with copula entropy. The prediction models were evaluated using predictive accuracy, the area under the receiver operating characteristic curve (AUC), and decision curve analysis (DCA). Data from 178 patients were used to construct prediction models. After copula entropy variable selection, which shifted the variables used for prediction in the CE nomogram from diabetes, best corrected visual acuity (BCVA), lens thickness and cumulative dissipated energy (CDE) to CDE and BCVA in the Copula nomogram, there was no significant change in predictive accuracy (0.9039 vs. 0.9098). There was also no significant difference in AUCs between the CE nomogram and the Copula nomogram (0.9637, 95% CI 0.9329-0.9946 vs. 0.9512, 95% CI 0.9075-0.9949; p = 0.2221). DCA suggested that the Copula nomogram has clinical application. This study obtained a nomogram with good performance to predict CE after phacoemulsification, and showed the improvement of copula entropy for nomogram models.

A CNN approach based on correlation metrics to chemical process fault classifications with limited labelled data

AbstractThis paper proposes a novel correlation metrics‐based convolutional neural network (CNN) classification model for chemical process fault diagnoses, creating a heuristic representation concerning process variable locations in grey correlation space (GCS) in terms of the copula entropy to guide the learning of classifiers. The proposed method based on correlation metrics can help solve the problem of insufficient information caused by a lack of labelled data. Specifically, variable correlations are fused into a heuristic matrix to provide prior knowledge for network learning in compensating data information before the CNN is employed to build the classifier for mining features in GCS. Driven by this mechanism, fault classifications in the case of small numbers of fault samples are successfully implemented. With successful simulation experiments carried out on the Tennessee Eastman (TE) process platform, we found that in GCS, different fault samples can represent hugely different features, while data resulting from the same fault rarely contribute to different ones. This observation lays a solid foundation for constructing superior fault classifiers. In addition, compared with conventional approaches, the proposed method has demonstrated better fault classification performances in the case of limited labelled fault samples.

Statistical Analysis on Economic Development in China

With the rapid growth of China's economy, all walks of life have developed healthily and stably. The relationship between education, finance and economy is becoming closer and closer. It is urgent to investigate the relationship between the three to achieve the right remedy. It is urgent to investigate the relationship between the three to achieve right remedy. The study of the relationship between education, finance and economy has certain representativeness and practical significance. Firstly, using Pearson correlation coefficient analysis method and copula entropy, this paper selects the index data of the three subsystems of education. Firstly, using Pearson correlation coefficient analysis method and copula entropy, this paper selects the index data of the three subsystems of education, finance and economy in Hubei Province from 2005 to 2020, and discusses the correlation degree between education, finance and economy in detail. Secondly, it constructs the coupling coordination degree model of the three subsystems of education, finance and economy, obtains the coordination degree and Secondly , it constructs the coupling coordination degree model of the three subsystems of education, finance and economy, obtains the coordination degree and coordinated development level of the three subsystems, and constructs the GM (1,1) grey-prediction model to predict the coupling coordination degree in The results show that there is a strong correlation between education and finance, education and economy, finance and economy. It is predicted that it will continue It is predicted that it will continue the previous slow upward trend from 2021 to 2024, and initially reach the stage of good coordinated development in 2024. In order to further promote the coordinated development of regional education, finance and economy in China and provide reference for the construction of domestic education finance In order to further promote the coordinated development of regional education, finance and economy in China and provide reference for the construction of domestic education finance economy system, this paper puts forward reasonable suggestions: starting from the internal governance of the two systems, promote the benign This paper puts forward reasonable suggestions: starting from the internal governance of the two systems, promote the benign development of the three systems; Increase investment in education and pay attention to the quality of education and teaching; Accelerate the paper puts forward reasonable suggestions: starting from the internal governance of the two systems, promote the benign development of the three systems; Increase investment in education and pay attention to the quality of education and teaching; accelerate the optimization and upgrading of education structure and economic structure; Strengthen financial supervision and improve the participation of The Government of the Republic of Korea will continue to promote the development of the three systems; Increase investment in education and pay attention to the quality of education and teaching; Accelerate the optimization and upgrading of education structure and economic structure; Strengthen financial supervision and improve the participation of investors in the financial market.

Impact of climate change and planting date shifts on growth and yields of double cropping rice in southeastern China in future

CONTEXTIt is predicted that climate change characterized by global warming will adversely affect the rice. To study the impacts of future climate change on rice growth and yields are of significance to ensure world food supply. OBJECTIVEThis study aims to explore the growth and yield changes of double cropping rice in Southeast China, determine the key meteorological factors affecting the yield of double cropping rice and analyze the impact of planting date shifts on the phenology and yield of double cropping rice. METHODSThe phenology and yield of double cropping rice in the future was simulated based on Decision Support System for Agrotechnology Transfer (DSSAT) v4.7.5. The relationship between double cropping rice yield and meteorological factors is explored by using feature importance (IF) based on Random Forests model and copula entropy (CE). The impact of planting date shifts on phenology and yield of double cropping rice was determined by changing the planting date. RESULTS AND CONCLUSIONSThe result suggested that the yield of double cropping rice increased by 2.6%, 1.8%, −2.0% and 0.1% respectively under the scenarios for SSP1–2.6, SSP2–4.5, SSP3–7.0 and SSP5–8.5 when considered the effects of CO2. With the increase of radiative forcing, the precipitation (Pre) and solar radiation (SRAD) on yield of double cropping rice would become less and less important, and the importance of temperature on yield of double cropping rice would be greater and greater. Early planting of early rice and late planting of late rice will increase the length of phenology and yield of double cropping rice. However, the increased phenological length for early rice is mainly due to the increase for length of planting to anthesis (P-A), and late rice is due to the increase for length of anthesis to maturation (A-M). When the optimal planting date is adopted, the rice yield will increase by 4.6%, 5.4%, 3.4% and 10.2%, respectively. SIGNIFICANCEThis study provides adaptive measures and suggestions for local decision makers on how to deal with the impact of future climate change.

Mixed vine copula flows for flexible modeling of neural dependencies.

Recordings of complex neural population responses provide a unique opportunity for advancing our understanding of neural information processing at multiple scales and improving performance of brain computer interfaces. However, most existing analytical techniques fall short of capturing the complexity of interactions within the concerted population activity. Vine copula-based approaches have shown to be successful at addressing complex high-order dependencies within the population, disentangled from the single-neuron statistics. However, most applications have focused on parametric copulas which bear the risk of misspecifying dependence structures. In order to avoid this risk, we adopted a fully non-parametric approach for the single-neuron margins and copulas by using Neural Spline Flows (NSF). We validated the NSF framework on simulated data of continuous and discrete types with various forms of dependency structures and with different dimensionality. Overall, NSFs performed similarly to existing non-parametric estimators, while allowing for considerably faster and more flexible sampling which also enables faster Monte Carlo estimation of copula entropy. Moreover, our framework was able to capture low and higher order heavy tail dependencies in neuronal responses recorded in the mouse primary visual cortex during a visual learning task while the animal was navigating a virtual reality environment. These findings highlight an often ignored aspect of complexity in coordinated neuronal activity which can be important for understanding and deciphering collective neural dynamics for neurotechnological applications.

Predicting Monthly Runoff of the Upper Yangtze River Based on Multiple Machine Learning Models

Accurate monthly runoff prediction is significant to extreme flood control and water resources management. However, traditional statistical models without multi-variable input may fail to capture runoff changes effectively due to the dual effect of climate change and human activities. Here, we used five multi-input machine learning (ML) models to predict monthly runoff, where multiple global circulation indexes and surface meteorological indexes were selected as explanatory variables by the stepwise regression or copula entropy methods. Moreover, four univariate models were adopted as benchmarks. The multi-input ML models were tested at two typical hydrological stations (i.e., Gaochang and Cuntan) in the Upper Yangtze River. The results indicate that the LSTM_Copula (long short-term memory model combined with copula entropy method) model outperformed other models in both hydrological stations, while the GRU_Step (gate recurrent unit model combined with stepwise regression method) model and the RF_Copula (random forest model combined with copula entropy method) model also showed satisfactory performances. In addition, the ML models with multi-variable input provided better predictability compared with four univariate statistical models, and the MAPE (mean absolute percentage error), RMSE (root mean square error), NSE (Nash–Sutcliffe efficiency coefficient), and R (Pearson’s correlation coefficient) values were improved by 5.10, 4.16, 5.34, and 0.43% for the Gaochang Station, and 10.84, 17.28, 13.68, and 3.55% for the Cuntan Station, suggesting the proposed ML approaches are practically applicable to monthly runoff forecasting in large rivers.

Frequency Stability Prediction of Power Systems Using Vision Transformer and Copula Entropy.

This paper addresses the problem of frequency stability prediction (FSP) following active power disturbances in power systems by proposing a vision transformer (ViT) method that predicts frequency stability in real time. The core idea of the FSP approach employing the ViT is to use the time-series data of power system operations as ViT inputs to perform FSP accurately and quickly so that operators can decide frequency control actions, minimizing the losses caused by incidents. Additionally, due to the high-dimensional and redundant input data of the power system and the O(N2) computational complexity of the transformer, feature selection based on copula entropy (CE) is used to construct image-like data with fixed dimensions from power system operation data and remove redundant information. Moreover, no previous FSP study has taken safety margins into consideration, which may threaten the secure operation of power systems. Therefore, a frequency security index (FSI) is used to form the sample labels, which are categorized as “insecurity”, “relative security”, and “absolute security”. Finally, various case studies are carried out on a modified New England 39-bus system and a modified ACTIVSg500 system for projected 0% to 40% nonsynchronous system penetration levels. The simulation results demonstrate that the proposed method achieves state-of-the-art (SOTA) performance on normal, noisy, and incomplete datasets in comparison with eight machine-learning methods.