# Prediction and Management of Regional Economic Scale Based on Machine Learning Model

Authors: Zhiqiang Jiang
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

The country is developing rapidly and the economy is taking off. For the country, the economic development of each region is very important, and the economy is the key to measuring the development of a region. To this end, the machine learning model is combined with regional economic scale prediction and management, and the two are studied together to obtain the following: (1) The key to measuring the regional economy is the growth rate of GDP and GDP. For the economic comparison between region A and region B, the economic scale is predicted by machine learning model. The regional economic development is better, which has an important basis for the comparison of the following methods. (2) There are many ways to improve the regional economy. Among them, the development of the industrial economy has the highest degree of regional economic indicators GDP and GDP growth rate. (3) The machine learning model has many benefits in the development of regional economic forecasting. Among them, reducing errors has the greatest impact on the regional economy. By comparison, it can be known that the accuracy of the regional economic forecasting under the machine learning model and the required forecasting time have been greatly optimized.


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## Body

## 1. Introduction

We focus on two key issues: the problem of selecting relevant features and the problem of selecting relevant examples. Progress on these topics in empirical and theoretical work in machine learning is described, and a general framework for comparing different approaches is presented, and some challenges for future work in this field are concluded [1]. A different method of convergence analysis is used, which in our opinion is richer than the traditionally proposed method. He argues that the evolution of the global regional distribution is more important than the evolution of the average or representative economy implied in the concept of convergence or convergence. In addition, geo space plays an important role in analyzing inequality between regional economies. To do this, use spatial association tests recently developed in the spatial econometric literature and combine them with convergence analyses. In particular, this method is applied to the analysis of regional dynamics and convergence in the European Union (EU). In this context, progress in the integration process highlights the problem of economic disparities at regional level. The convergence process ended in the late 1970s at a time of great changes in economic activity [2]. Goldberg is one of the most prominent researchers in the field—he has published more than 100 research articles on genetic algorithms and was a student of John Holland, the father of genetic algorithms—and his deep understanding of the material shines through. Contains a complete list of Pascal Genetic Algorithms that C programmers can easily understand, covering key topics in the field, including intersections, mutations, and body proportions, providing young computer scientists with enough information to implement genetic algorithms and provide them with it. The peers explain genetic algorithms [3]. Rather than sorting documents by topic, it looks at the problem of sorting documents by general sentiment, e.g., deciding whether feedback is positive or negative, machine learning methods using movie reviews as informative criteria definitely outperform rudimentary humans methods; however, three machine learning methods are not as effective as scaling methods in classifying sentiment and classifying original topics, and we examine factors that make the problem of sentiment classification more difficult [4]. TensorFlow is suitable for large heterogeneous environments. It includes multi-core processors, general-purpose GPUs. and a custom device called a processor, which we publish as a widely used open source project in our learning research [5]. Supervised machine learning is an algorithm that searches externally provided instances to reason about to generate general hypotheses and then makes predictions about future instances. In other words, the goal of supervised learning is to create a compact class label distribution model from the predicted features, and the resulting classifier is used to assign class labels to test cases where the expected attribute values are known, but the class label values are unknown. Several classification techniques for controlled machine learning are described [6]. Machine learning algorithms often require careful tuning of model hyperparameters, regularization terms, and optimization parameters. This method can optimize the performance of a given learning algorithm for a given task, where the GP-induced tractable posterior distribution makes efficient use of information gleaned from previous experiments and allows parameters to be used as then to try to make the best choice [7]. Machine learning algorithms can use generalization from examples to determine how to perform key tasks. This is often feasible and inexpensive in situations where manual programming is not possible. Ambitious goals can be achieved when more information is available, and many textbooks are needed to successfully develop machine learning applications. Here are 12 core concepts from machine learning researchers and practitioners [8]. Textbooks for graduate studies introduce basic concepts and methods of machine learning. It describes some important modern algorithms, provides a theoretical basis for these algorithms, and illustrates key aspects of their application. The aim is to introduce new theoretical tools and concepts and to provide concise evidence even for relatively advanced topics. Fundamentals of machine learning fill the need for a general textbook that also provides theoretical detail and highlights evidence. Some topics that are often overlooked are covered in more detail here. For example, entire chapters are devoted to regression, multiclass classification, and classification. The appendix lays the theoretical foundation for what follows, providing a brief overview of probability, a brief introduction to convex optimization, tools for grouping bounds, and some fundamental properties of the matrices and norms used in this book [9]. In a project investigating the use of machine learning techniques to detect oil spills, we encountered several critical issues that we believe merit the attention of the research community. Based on our specific case studies, we illustrate topics such as question formulation, selection of assessment standards, and data processing. We relate these problems to the characteristics of oil pollution applications, for example, in region B, they have an unbalanced class distribution, which is common in many applications. Our solutions to these problems have been implemented in the Canadian Environmental Hazard Detection System (CEHDS), which is about to be field tested [10]. MXNet is a machine learning hub for many languages ​​that integrates into the host language and, when combined with the main language, combines the declared symbolic expressions with the necessary computational matrices to provide automatic discrimination for MXNet gradient generation, processing, and memory savings, and describes how to handle character expression insertion and related tensor operations, and our preliminary tests show good results when using large neural networks with multiple GPUs [11]. A large number of international studies have shown that the “resource curse effect” is also applicable to the long-term growth cycle of China’s regional economy, and it is believed that it is one of the key factors leading to regional development differences. By constructing a resource richness index representing energy and resources, it focuses on examining the relationship between natural endowments and economic growth in each province, and proposes some specific policies to accelerate the resource curse. Resource-rich regions also experienced economic growth [12]. In recent years, economic geographers have used the concept of “cultural embedding” extensively to study how spatially diverse sets of cultural practices, norms, values, and beliefs shape firm innovation performance in dynamic regional economies. However, our understanding of these causal relationships remains biased, reinforced by a “superlocalized” notion of cultural embedding that locates the role of institutional actors outside of “places” and across borders. Therefore, this article provides an empirical analysis of the theoretical and theoretical underpinnings of a high-tech regional economy in Salt Lake City, Utah, to examine the day-to-day causal mechanisms, practices, and processes—local or local—through which businesses go. The cultural integration of the region is represented, performed and (un)intentionally (re)produced [13]. Taking Philadelphia as an example, a form of community development that functions at the intersection of regional development and community revitalization is proposed. A focus of this type of community development is understanding the demands and possibilities of workers and the strategies needed to connect them to non-community economic opportunities [14]. Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallelism like MapReduce cannot be adequately expressed, while low-level tools like MPI and Pthreads let ML experts solve the same design challenges over and over again. For common patterns in ML, we developed GraphLab, which improves on MapReduce and others by concisely expressing asynchronous iterative algorithms with sparse computational dependencies. Parallel versions of Lasso and compressed sensing to demonstrate the expressive power of the GraphLab framework [15].


## 2. Machine Learning and Principles of Regional Economy

### 2.1. Basic Content of Regional Economy

The regional economy has the following themes: 1. the relationship between time and space, the distribution mechanism, and the economic development trajectory and economic development variables affecting international relations. 2. Interactions and patterns of global economic phenomena, geographic relationships, and geography. 3. The theoretical basis of geographical phenomena and their influence on geographical relations in international society, economy, and culture. Geographical factors are the main determinants of regional economies. Regional economics is a field of study that deals with the protection of national interests in international competition from a geographic perspective. It is always important to carry out cooperation in neighboring areas in the economic activities of a country. Natural conditions such as humidity, sunlight, and the earth affect its development and growth and sometimes play a very important role. Assuming that productivity develops to a certain level, the development of regional economy is affected by financial investment in science and technology and labor constraints. The positive effects mainly include the following: (1) improve the high allocation between regional flow and production, and support regional market expansion and economic growth. (2) The development of regional economic groups adds new content to the multi-polarization of the world economy and supports the development of economic globalization. Its main disadvantage is that all regional economic blocs are exclusive and often discriminatory measures are taken against countries and regions outside the bloc, which makes more battles between economic groups and organizations, which will raise the level of competition in regional economies to unprecedented level. This brings difficulties to economic globalization.


### 2.2. Economic Forecasting Steps

Economic forecasting shows the development law of economic phenomena and the relationship between different economic phenomena, predicting economic trends, future trends, and probabilities of economic phenomena; economic forecasting is first of all to predict the economic situation of a country, such as growth rate, economic structure, price development, population employment, tax revenue and expenditure development, supply, production, and sales different products. At the same time, the international economic situation should also be taken into account, for example, region B predicts international economic fluctuations and changes in international markets. Your forecast typically includes four items, which are recurring prognostic processes. This cycle typically occurs twice a year, and a forecast report is generated approximately every six months. It is shown in Figure1.Figure 1
Step diagram of economic forecasting.Figure1 shows the detailed steps of forecasting the economy. The first step is to determine the content of the forecast, which can be divided into five categories: forecasting and analysis of product market trends; forecasting and analysis of capital requirements; forecasting and analysis of costs; forecasting and analysis of sales; predictive analysis of profit, then collect information, select and identify the collected data, and then analyze and predict. Check and verify after the results are obtained.


### 2.3. Introduction to Machine Learning

Machine learning is an interdisciplinary course combining probability theory, estimation theory, and probability knowledge. And complex algorithms that use computers as tools, which are designed to mimic how humans learn in real time. And effectively transform existing content into knowledge structures for reinforcement learning. The contents of machine learning are as follows: (1) Machine learning is the realization of artificial intelligence, which improves the efficiency of empirical learning algorithms (2) Machine learning is the study of computer algorithms that can be automatically improved through experience. (3) In machine learning, it uses past data to improve the performance of computer programs. Machine learning can be divided into this, as shown in the following Figure2:Figure 2
Machine learning classification.For Figure2, this paper presents the classification of machine learning. Machine learning is the forecast method of this article in regional economies. There are four different classification schemes to classify: classification by learning objectives, classification by data shape, classification by learning method, and classification by learning method. Classification also differs according to different classification modes. Teaching methods are divided into inductive and deduction. Comparison, analysis, and classification of learning objectives are divided into concepts, rules, functions, and categories, Bayesian data shape classification is divided into structured and unstructured learning. Teaching methods are classified into controlled, uncontrolled, and reinforced.


## 2.1. Basic Content of Regional Economy

The regional economy has the following themes: 1. the relationship between time and space, the distribution mechanism, and the economic development trajectory and economic development variables affecting international relations. 2. Interactions and patterns of global economic phenomena, geographic relationships, and geography. 3. The theoretical basis of geographical phenomena and their influence on geographical relations in international society, economy, and culture. Geographical factors are the main determinants of regional economies. Regional economics is a field of study that deals with the protection of national interests in international competition from a geographic perspective. It is always important to carry out cooperation in neighboring areas in the economic activities of a country. Natural conditions such as humidity, sunlight, and the earth affect its development and growth and sometimes play a very important role. Assuming that productivity develops to a certain level, the development of regional economy is affected by financial investment in science and technology and labor constraints. The positive effects mainly include the following: (1) improve the high allocation between regional flow and production, and support regional market expansion and economic growth. (2) The development of regional economic groups adds new content to the multi-polarization of the world economy and supports the development of economic globalization. Its main disadvantage is that all regional economic blocs are exclusive and often discriminatory measures are taken against countries and regions outside the bloc, which makes more battles between economic groups and organizations, which will raise the level of competition in regional economies to unprecedented level. This brings difficulties to economic globalization.


## 2.2. Economic Forecasting Steps

Economic forecasting shows the development law of economic phenomena and the relationship between different economic phenomena, predicting economic trends, future trends, and probabilities of economic phenomena; economic forecasting is first of all to predict the economic situation of a country, such as growth rate, economic structure, price development, population employment, tax revenue and expenditure development, supply, production, and sales different products. At the same time, the international economic situation should also be taken into account, for example, region B predicts international economic fluctuations and changes in international markets. Your forecast typically includes four items, which are recurring prognostic processes. This cycle typically occurs twice a year, and a forecast report is generated approximately every six months. It is shown in Figure1.Figure 1
Step diagram of economic forecasting.Figure1 shows the detailed steps of forecasting the economy. The first step is to determine the content of the forecast, which can be divided into five categories: forecasting and analysis of product market trends; forecasting and analysis of capital requirements; forecasting and analysis of costs; forecasting and analysis of sales; predictive analysis of profit, then collect information, select and identify the collected data, and then analyze and predict. Check and verify after the results are obtained.


## 2.3. Introduction to Machine Learning

Machine learning is an interdisciplinary course combining probability theory, estimation theory, and probability knowledge. And complex algorithms that use computers as tools, which are designed to mimic how humans learn in real time. And effectively transform existing content into knowledge structures for reinforcement learning. The contents of machine learning are as follows: (1) Machine learning is the realization of artificial intelligence, which improves the efficiency of empirical learning algorithms (2) Machine learning is the study of computer algorithms that can be automatically improved through experience. (3) In machine learning, it uses past data to improve the performance of computer programs. Machine learning can be divided into this, as shown in the following Figure2:Figure 2
Machine learning classification.For Figure2, this paper presents the classification of machine learning. Machine learning is the forecast method of this article in regional economies. There are four different classification schemes to classify: classification by learning objectives, classification by data shape, classification by learning method, and classification by learning method. Classification also differs according to different classification modes. Teaching methods are divided into inductive and deduction. Comparison, analysis, and classification of learning objectives are divided into concepts, rules, functions, and categories, Bayesian data shape classification is divided into structured and unstructured learning. Teaching methods are classified into controlled, uncontrolled, and reinforced.


## 3. Regional Economic Algorithm

### 3.1. Measure the Absolute Difference Index of Regional Economy

This section uses different methods to calculate and analyze the extent of regional imbalance in my country. Statistical disequilibrium can be due to differences between individuals, discrete differences describe differences between individuals, and each measure is defined as follows: full distance, also known as range, describes the difference between the maximum and minimum values of a variable distance, setymax and ymin are the maximum and minimum value of the regional economic level, then the total distance R is:
(1)R=ymax−ymin.The mean differenceD is the mean of the absolute difference between the index value and the mean value:
(2)D=∑i=1nyi−y¯n.yi is the overall economic development status of the region i, y¯=1/n∑i=1nyi. Expressed as the average value of the economic development status of this region, n is the region quantity.The standard deviation, also known as the mean squared error, is a commonly used indicator to measure the variance of an indicator in statistics. The calculation formula is:(3)S=∑i=1nyi−y¯2n.


### 3.2. Relative Difference Measurement Indicators of Regional Economy

Relative differences measure the relative relationship between individuals. In the regional economy, three indicators are often used to measure the relative differences between individuals: relative magnitude, imbalance difference, and coefficient of variation.(1)
Relatively poorThe relative range is:(4)d=ymax−yminy¯.(2)
Poor imbalanceThe imbalance difference is:(5)B=1−yminymax.The imbalance gap refers to the ratio of the imbalance gap between the backward regions and the developed regions. The larger the difference, the more unbalanced the development between regions. Assumeymax and ymin, it is the maximum value and the minimum value between the economic development levels of each region at the same time. This formula is one of the relative relations of the relative difference measurement indicators of the regional economy.
(3)
Coefficient of variationThe coefficient of variation (CV) is calculated as:
(6)CV=Sy.This new algorithm can be used to express the differences between regions:(7)CVω=1y¯∑i=1nyi−y¯2×pi.Above, pi is the proportion of the population in the i region in the population of China, and the population-weighted coefficient of variation can compare the differences between regions. The obtained value is an important indicator to measure population differences. The higher the coefficient of variation of economic development between regions, the higher the weighted total coefficient of variation, that is, the more obvious the imbalance.


### 3.3. Exponential Measures

The value range of the Gini coefficient is [0, 1]. A Gini coefficient of 0 indicates that the income distribution among residents is absolutely even, that is to say, there is no difference in income between people. A Gini coefficient of 1 indicates that the income among residents is equal. The distribution is definitely not even. These two extreme cases only have theoretical significance, and generally do not appear in practical situations. Usually, the closer the value of the Gini coefficient is to 1, the stronger the imbalance of the structure and the larger the gap between regions.In addition to the basic statistical indicators to describe the regional economy, the Gini coefficient and Theil index are also commonly used indicators to describe the regional economy.The formula for solving the Gini coefficient can be converted into a mathematical formula as:(8)gini=12y¯∑i=1n∑j=1nyj−yinn−1.In order to determine the differences between regions more precisely, the weighted Gini coefficient is usually used, which takes into account the factors between the number of people:(9)gini=12y¯∑i=1n∑j=1nyj−yipipj.Inyi,y¯,pi, it has the same meaning as above, with an index used for the first time to study income differences between countries. Its calculation formula is:
(10)theil=1n∑i=1nyiy¯lnyiy¯.Further, this index can be decomposed, so that the source of the overall gap can be seen, and the respective changes of the gap between groups and within groups can be studied separately. Ifn regions are divided into K large region groups, each group is recorded as gk, k=1,2,⋯,K, group kgk. The number of regions included in the nk, ∑k=1Knk=n, and Tb and Tw are the difference between the groups and the difference within the group, respectively, then the formula for separating the Theil indices is:
(11)Theil=Tb+Tw=∑k=1Kyklnyknk/n+∑k=1Kyk∑i∈gkyiyklnyi/yk1/nk.Inyi, it represents the proportion of the index of region i to the total. In the above formula, the difference between groups and the difference within a group can also be expressed by the following formula:
(12)Tb∑k=1Kyklnyknk/n,(13)Tω=∑k=1Kyk∑i∈gkyiyklnyi/yk1/nk.Tb/Theil and Tw/Theil represent the contribution rate of between-group and within-group to the overall difference, respectively.


### 3.4. Convergence of Regional Economic Growth

To build with a new theory, if the amount specified at the beginning does not change, it takes the form of:(14)Y=KαL1−α,where Y is output, K is capital, L is labor, α and 1−α are the output elasticity of capital and the output elasticity of labor, respectively, 0<α<1. Divide both sides of the function by labor L, this formula is to describe the convergence assumption of regional economic growth.Processing yields a production function expressed in terms of output per capita and supply of capital per capita.(15)y=kα.Simplify formula (15) to get:
(16)ẏy=αk̇k.The above formula gives the growth rate of output per capita in the Solow growth model, for0<α<1. For example, the growth rate of per capita rate of return is positively correlated with the growth rate of per capita capital, that is, it increases and decreases at the same time, and the formula for increasing the amount is:
(17)K̇=I−δK=sFK,L,t−δK.K̇ is the differential of capital over time, I is the total investment, and 0≤s≤1, δ. For a fixed depreciation rate, the above formula states that the value added of the physical capital stock at the same time is equal to the total investment I minus depreciation. This formula is the capital accumulation equation for the neoclassical growth model at the same point in time.Divide both sides of the capital accumulation equation by labor incomeL(18)K̇/L=sḟk−δk,due to K̇=dK/L/dt=K̇/L−nk established, so that the K̇/L. Change it to a function of k, and because there are n=K̇/L, when n is established, so the above formula can be transformed into
(19)k̇=sfk−n+δk.n+δ is the depreciation rate of the labor rate of capital; if one of the conditions is satisfied, the equation becomes:
(20)k̇=−n+δk.This is the rate of decline in capital per capita.


### 3.5. Ensemble Model Algorithm

In machine learning, the data set created from the observation data is usually used as the training set of the training machine. Using the file algorithm can effectively improve the generalization ability of the system and provide the neural network file error probability formula. The probability of the integral error is:(21)perr=∑k>N/2NNKpk1−pN−k,p<1/2, integrated error probability perr. It decreases with the increase of N, and the output of the neural network ensemble is:
(22)V¯X=∑aωaVaX.The neural network generalization error and neural network files are in this order:(23)Ea=∫dxpxfx−Vax2,(24)E=∫dxpxfx−V¯x2.Weighted generalization error for each neural network:(25)E¯=∑ωaEa.The type of resources of each region often determines the characteristics of the industrial structure of that region. For example, the coastal area focuses on developing high-tech industries and finance, while the inland Northwest region focuses on agricultural production. However, most of the industrial structure of the region has advantages and disadvantages due to the development of the region. Although the advantages of the region are effectively exploited, the industrial structure of each region is very different. Therefore, in order to effectively improve the rational development of the industrial structure, we must switch to a diversified structure on the basis of resource development and continuously increase the proportion of tertiary industry.


## 3.1. Measure the Absolute Difference Index of Regional Economy

This section uses different methods to calculate and analyze the extent of regional imbalance in my country. Statistical disequilibrium can be due to differences between individuals, discrete differences describe differences between individuals, and each measure is defined as follows: full distance, also known as range, describes the difference between the maximum and minimum values of a variable distance, setymax and ymin are the maximum and minimum value of the regional economic level, then the total distance R is:
(1)R=ymax−ymin.The mean differenceD is the mean of the absolute difference between the index value and the mean value:
(2)D=∑i=1nyi−y¯n.yi is the overall economic development status of the region i, y¯=1/n∑i=1nyi. Expressed as the average value of the economic development status of this region, n is the region quantity.The standard deviation, also known as the mean squared error, is a commonly used indicator to measure the variance of an indicator in statistics. The calculation formula is:(3)S=∑i=1nyi−y¯2n.


## 3.2. Relative Difference Measurement Indicators of Regional Economy

Relative differences measure the relative relationship between individuals. In the regional economy, three indicators are often used to measure the relative differences between individuals: relative magnitude, imbalance difference, and coefficient of variation.(1)
Relatively poorThe relative range is:(4)d=ymax−yminy¯.(2)
Poor imbalanceThe imbalance difference is:(5)B=1−yminymax.The imbalance gap refers to the ratio of the imbalance gap between the backward regions and the developed regions. The larger the difference, the more unbalanced the development between regions. Assumeymax and ymin, it is the maximum value and the minimum value between the economic development levels of each region at the same time. This formula is one of the relative relations of the relative difference measurement indicators of the regional economy.
(3)
Coefficient of variationThe coefficient of variation (CV) is calculated as:
(6)CV=Sy.This new algorithm can be used to express the differences between regions:(7)CVω=1y¯∑i=1nyi−y¯2×pi.Above, pi is the proportion of the population in the i region in the population of China, and the population-weighted coefficient of variation can compare the differences between regions. The obtained value is an important indicator to measure population differences. The higher the coefficient of variation of economic development between regions, the higher the weighted total coefficient of variation, that is, the more obvious the imbalance.


## 3.3. Exponential Measures

The value range of the Gini coefficient is [0, 1]. A Gini coefficient of 0 indicates that the income distribution among residents is absolutely even, that is to say, there is no difference in income between people. A Gini coefficient of 1 indicates that the income among residents is equal. The distribution is definitely not even. These two extreme cases only have theoretical significance, and generally do not appear in practical situations. Usually, the closer the value of the Gini coefficient is to 1, the stronger the imbalance of the structure and the larger the gap between regions.In addition to the basic statistical indicators to describe the regional economy, the Gini coefficient and Theil index are also commonly used indicators to describe the regional economy.The formula for solving the Gini coefficient can be converted into a mathematical formula as:(8)gini=12y¯∑i=1n∑j=1nyj−yinn−1.In order to determine the differences between regions more precisely, the weighted Gini coefficient is usually used, which takes into account the factors between the number of people:(9)gini=12y¯∑i=1n∑j=1nyj−yipipj.Inyi,y¯,pi, it has the same meaning as above, with an index used for the first time to study income differences between countries. Its calculation formula is:
(10)theil=1n∑i=1nyiy¯lnyiy¯.Further, this index can be decomposed, so that the source of the overall gap can be seen, and the respective changes of the gap between groups and within groups can be studied separately. Ifn regions are divided into K large region groups, each group is recorded as gk, k=1,2,⋯,K, group kgk. The number of regions included in the nk, ∑k=1Knk=n, and Tb and Tw are the difference between the groups and the difference within the group, respectively, then the formula for separating the Theil indices is:
(11)Theil=Tb+Tw=∑k=1Kyklnyknk/n+∑k=1Kyk∑i∈gkyiyklnyi/yk1/nk.Inyi, it represents the proportion of the index of region i to the total. In the above formula, the difference between groups and the difference within a group can also be expressed by the following formula:
(12)Tb∑k=1Kyklnyknk/n,(13)Tω=∑k=1Kyk∑i∈gkyiyklnyi/yk1/nk.Tb/Theil and Tw/Theil represent the contribution rate of between-group and within-group to the overall difference, respectively.


## 3.4. Convergence of Regional Economic Growth

To build with a new theory, if the amount specified at the beginning does not change, it takes the form of:(14)Y=KαL1−α,where Y is output, K is capital, L is labor, α and 1−α are the output elasticity of capital and the output elasticity of labor, respectively, 0<α<1. Divide both sides of the function by labor L, this formula is to describe the convergence assumption of regional economic growth.Processing yields a production function expressed in terms of output per capita and supply of capital per capita.(15)y=kα.Simplify formula (15) to get:
(16)ẏy=αk̇k.The above formula gives the growth rate of output per capita in the Solow growth model, for0<α<1. For example, the growth rate of per capita rate of return is positively correlated with the growth rate of per capita capital, that is, it increases and decreases at the same time, and the formula for increasing the amount is:
(17)K̇=I−δK=sFK,L,t−δK.K̇ is the differential of capital over time, I is the total investment, and 0≤s≤1, δ. For a fixed depreciation rate, the above formula states that the value added of the physical capital stock at the same time is equal to the total investment I minus depreciation. This formula is the capital accumulation equation for the neoclassical growth model at the same point in time.Divide both sides of the capital accumulation equation by labor incomeL(18)K̇/L=sḟk−δk,due to K̇=dK/L/dt=K̇/L−nk established, so that the K̇/L. Change it to a function of k, and because there are n=K̇/L, when n is established, so the above formula can be transformed into
(19)k̇=sfk−n+δk.n+δ is the depreciation rate of the labor rate of capital; if one of the conditions is satisfied, the equation becomes:
(20)k̇=−n+δk.This is the rate of decline in capital per capita.


## 3.5. Ensemble Model Algorithm

In machine learning, the data set created from the observation data is usually used as the training set of the training machine. Using the file algorithm can effectively improve the generalization ability of the system and provide the neural network file error probability formula. The probability of the integral error is:(21)perr=∑k>N/2NNKpk1−pN−k,p<1/2, integrated error probability perr. It decreases with the increase of N, and the output of the neural network ensemble is:
(22)V¯X=∑aωaVaX.The neural network generalization error and neural network files are in this order:(23)Ea=∫dxpxfx−Vax2,(24)E=∫dxpxfx−V¯x2.Weighted generalization error for each neural network:(25)E¯=∑ωaEa.The type of resources of each region often determines the characteristics of the industrial structure of that region. For example, the coastal area focuses on developing high-tech industries and finance, while the inland Northwest region focuses on agricultural production. However, most of the industrial structure of the region has advantages and disadvantages due to the development of the region. Although the advantages of the region are effectively exploited, the industrial structure of each region is very different. Therefore, in order to effectively improve the rational development of the industrial structure, we must switch to a diversified structure on the basis of resource development and continuously increase the proportion of tertiary industry.


## 4. Research on Forecast Management of Regional Scale Economy

### 4.1. Comparison of Regional Economic Forecasting Methods

In economic development, there are four main methods for forecasting regional economy: (1) Trend forecasting method. Trend forecasting is mainly divided into two types: time series trend forecasting and spatial trend surface analysis. Surface analysis of spatial trends uses only mathematical methods and uses mathematical models to simulate the spatial distribution of geographic data and its regional trends. (2): Regression prediction method. Regression prediction involves determining the direction and rate of change of one or more variables based on changes in the independent variable (x), including unit regression (including non-variable and nonlinear regression multiple regression (including multiple linear regression and non-linear regression)). Regression economic value analysis not listed iscalled cost associated with raw materials, raw materials, fuel, energy and permanent depreciation of assets, work, etc. Consumption in production is called the direction of the product produced by the production method for industrial use and quantity. Storage and preservation of input-output forecast has the following characteristics: first, the method index is complex and the index is decomposed; second, the input-output table adopts a vertical and horizontal checkerboard type. Third, the quantitative relationship between various coefficients (material consumption coefficient, labor consumption coefficient, production inventory occupancy coefficient, production accumulation occupancy coefficient, etc.) And products. Fourth, the methods of input and output can be calculated using mathematics and electronic computers. The units of measurement are divided into physical and numerical types; different periods are divided into two types: static and dynamic, and are divided into national input-output, regional input-output, and sectoral and enterprise input-output according to different degrees. It is shown in Table 1.Table 1
Abbreviated form of input-output table.
Intermediate formFinal formMaterial consumptionFirst quadrantSecond quadrantNew value creationThird quadrantFourth quadrant(4) Combined forecasting methods, many advanced top-level testing methods are used in economic development, but in forecasting practice, when only one forecasting method is used, the forecasting results are often inaccurate or unreliable. When multiple state-of-the-art test methods are used for the same problem and combined appropriately, the advantages of different forecasting methods can be fully utilized, the shortcomings of a single method can be overcome, and the predictability of forecasting can be improved. The combination was first proposed in 1969. Since the prediction method, the method has developed rapidly and has the advantages of inspection method, recursive equilibrium joint inspection method, matrix method, and so on. These are some of the most commonly used methods at present, and a survey has been made on the frequency and accuracy of these methods in regional economic forecasting. The survey data is shown in the following figureThis article focuses on regional economic forecasting. There are various methods for regional economic forecasting. For different methods, the usual frequency of use and prediction accuracy are not the same. Compared with these methods, the utilization rate of trend forecasting method and I/O ratio forecasting method is above 20%, and only regression forecasting method is widely used, up to 36%, and the accuracy rate is over 80%. The accuracy of the method is over 90%, among which the complex analysis method has the highest accuracy.From Figure3, we can see that in terms of the four main methods of regional economic forecasting, the regression forecasting method is the most widely used, but in terms of accuracy, the combined forecasting method has higher accuracy, because it requires a combination of methods, so the degree of use is not high.Figure 3
Comparison of regional economic forecasting methods.


### 4.2. Regional Economic Comparison and Management

In the experimental survey, the regional economy is a key factor to measure the economic development status of a region. There are many indicators that affect the development of the regional economy. For example, the GDP growth rate in a region can measure the economic development trend of the region. The annual GDP growth value of the region is compared with the GDP growth rate to observe the regional economic situation of the two regions.Figure4 is a comparison of regional economic indicators between AB and AB. The main data for comparison are GDP, GDP growth rate, and the proportion in the whole country. These three data can reflect the local regional economic situation. GDP is the income from data collection, GDP growth rate is the increase in GDP compared to the GDP income in the previous period, and the national proportion is compared with the national GDP. It can be clearly seen that the three data at the A site in Figure 4 are higher than those at the B site. it can be seen that the regional economic situation of A site is the best.Figure 4
Comparison of regional economic indicators between A and B.Comparing the regional economic indicators of A and B, the GDP of A is 2,515.5 billion yuan, and B is lower than that of A. At the same time, the GDP growth rate and proportion are lower than those of A in the whole country. Through this data analysis of the A region, the economy is better than Region B. There are also many factors that affect the regional economy. We compare the reasons for the regional economic differences between A and B to analyze the impact of each factor on the regional economy.From Figure5, it can be seen that human resources, natural resources, and industrial structure are the three most influential factors for the regional economy. The regional economy of place A is better, and the score is better than that of place B in these three aspects. In terms of these three degrees of influence, the regional industrial structure has the greatest impact on the regional economy, while natural resources have the least impact on the regional economy. In order to keep up with the management of the regional economic scale, it is necessary to have a sufficient grasp of the methods for improving the regional economy. Through the survey, we found that there are three main methods for regional economic growth: (1) To speed up the development of the tertiary industry, we must first strengthen the tertiary industry. For the construction of key industrial fields, focus on key economic fields, introduce the policy of “retreat and three advances”, focus on the development of influential key enterprises to drive the growth of surrounding enterprises, form regional agglomeration development, and support the formation of business systems through large-scale comprehensive development to radiate drive business development in other fields such as financial insurance and information services. The development is to build a new retail chain to support the growth of retail consumption. Rationally plan the construction of modern logistics parks for recycling and reuse, and support the development of cluster formats and commercial logistics. Accelerate the renovation of the old city, increase the standardization of commercial streets, and support the development and improvement of the regional service industry. Utilize regional natural resources to create cultural tourism, attach importance to building a tourism service theme system, increase tourism market expansion efforts, build an integrated system of high-quality services, expand scale investment support, and create the Ministry of Eco-tourism. (2) To vigorously develop modern agriculture, we must first clarify the focus of work, grasp precise professional guidance, attach importance to farming, establish a modern, open, innovative, and market-oriented economic awareness, and improve service awareness and responsibility awareness. Plant to grow, to create. It is necessary to attach importance to supporting agriculture through science and technology, attach importance to the value of talents, and continuously improve the level of agriculture. Support marketing and organizational development. The second is to emphasize scientific planting and create economies of scale. Based on scientific planning, promote the vegetable basket plan, strengthen tent production, and create tourism projects with agricultural production experience to guide and promote development, support development, improve support measures, fully mobilize farmers’ enthusiasm for production, expand farmers’ knowledge reserves, and understand technological innovation and market changes. The third is to use the demonstration effect of typical cases to manage the overall development of farmers. Improve preferential policies, introduce measures to benefit the people, give full play to their role as representatives of breeding and display families, stimulate the enthusiasm for independent management, support the establishment of a support mechanism for large families, and encourage retail families to benefit from technical consultation, information acquisition services, and market diversification, to support the large-scale development of the aquaculture industry. (3) Give play to the leading role of key industries and promote the radiation effect of business services. Work with trade unions to support the reorganization of similar industries in the region. The second is to develop industrial parks, design cluster development, rationally plan regional commercial functions, and build characteristic industrial bases, tourism and cultural industries, and trade and logistics centers. Based on the advantages of regional resources, implement large projects and large groups, become bigger and stronger, and expand the development channels of enterprises through social infrastructure construction. Value-added, co-construction, and revitalization actions create a mutually beneficial situation for local enterprises. The fourth is to continuously optimize the internal and external business development environment, continuously improve existing policies, expand investment support, improve service quality, and provide appropriate channels for business development, thereby supporting regional economic development. We apply the above three methods to Region A at the same time to compare the GDP growth and total value of the region after applying different improvement methods.Figure 5
Comparison of differential influence and score.Figure6 shows the regional economic comparison of place A after three different methods have been applied. It can be seen that the regional economic data has been greatly improved after the three methods have been applied to some main data, but the best effect is to promote industrial. The development of the economy has increased the GDP output value by about 300 billion yuan, which has played a role in the rapid development of the regional economy.Figure 6
Data comparison after different methods in A.


### 4.3. The Impact of Machine Learning on Regional Economic Forecasting

When forecasting in this paper, we mainly use machine learning models to forecast the regional economy. Regional economic forecasting often needs to predict more variables and more time periods, so analysis and calculation are a relatively large and complex system technology. To reduce the burden of economic forecasting, the previous work in the field of economic forecasting was purely manual, with the most computation and time. For some forecasts (especially forecasting methods that use complex mathematical models), most analysts no longer need to just waste precious forecasting time, resulting in extremely valuable human resources not being used effectively, and weakening the timeliness of forecast results, Therefore, the forecast results cannot be adjusted. In view of the above deficiencies, great progress has been made in forecasting economic development. The use of computer networks can reduce the research time and cost of forecasting market research and forecasting expert advice. At the same time, in the rapidly changing information society, it is often difficult to obtain accurate and timely information only by using traditional manual methods. The impact of the above three advantages on the regional economy and the degree of public acceptance are shown in the figure.From Figure7, we can see that reducing the error is the highest among the three methods in terms of the impact of the machine learning model on the benefits of the regional economy and the degree of public acceptance. People rely most on this benefit.Figure 7
Comparison of machine learning model benefits.In this paper, we mainly use the linear model, decision tree model, ensemble model, and neural network model in the machine learning model to compare the accuracy of regional economic scale prediction and the time required for the prediction. The data is shown in the figure:Figure8 compares the regional economic comparison accuracy and prediction time under the four machine learning models. It can be seen from the figure that the integrated model has the highest accuracy, the lowest recall rate, and the highest F1 performance index. Therefore, regional economic forecasting method should choose an ensemble model to make predictions.Figure 8
Comparison of regional economic forecasts under machine learning models.Through the comparison of time, it can be seen that the decision tree model takes the longest to take 6.2 s, and the neural network model takes the shortest time, only 4.7 s. However, when making predictions, we prefer to choose higher accuracy and better performance indicators to make predictions. It is shown in Figure9.Figure 9
Comparison of prediction time under machine learning model.


## 4.1. Comparison of Regional Economic Forecasting Methods

In economic development, there are four main methods for forecasting regional economy: (1) Trend forecasting method. Trend forecasting is mainly divided into two types: time series trend forecasting and spatial trend surface analysis. Surface analysis of spatial trends uses only mathematical methods and uses mathematical models to simulate the spatial distribution of geographic data and its regional trends. (2): Regression prediction method. Regression prediction involves determining the direction and rate of change of one or more variables based on changes in the independent variable (x), including unit regression (including non-variable and nonlinear regression multiple regression (including multiple linear regression and non-linear regression)). Regression economic value analysis not listed iscalled cost associated with raw materials, raw materials, fuel, energy and permanent depreciation of assets, work, etc. Consumption in production is called the direction of the product produced by the production method for industrial use and quantity. Storage and preservation of input-output forecast has the following characteristics: first, the method index is complex and the index is decomposed; second, the input-output table adopts a vertical and horizontal checkerboard type. Third, the quantitative relationship between various coefficients (material consumption coefficient, labor consumption coefficient, production inventory occupancy coefficient, production accumulation occupancy coefficient, etc.) And products. Fourth, the methods of input and output can be calculated using mathematics and electronic computers. The units of measurement are divided into physical and numerical types; different periods are divided into two types: static and dynamic, and are divided into national input-output, regional input-output, and sectoral and enterprise input-output according to different degrees. It is shown in Table 1.Table 1
Abbreviated form of input-output table.
Intermediate formFinal formMaterial consumptionFirst quadrantSecond quadrantNew value creationThird quadrantFourth quadrant(4) Combined forecasting methods, many advanced top-level testing methods are used in economic development, but in forecasting practice, when only one forecasting method is used, the forecasting results are often inaccurate or unreliable. When multiple state-of-the-art test methods are used for the same problem and combined appropriately, the advantages of different forecasting methods can be fully utilized, the shortcomings of a single method can be overcome, and the predictability of forecasting can be improved. The combination was first proposed in 1969. Since the prediction method, the method has developed rapidly and has the advantages of inspection method, recursive equilibrium joint inspection method, matrix method, and so on. These are some of the most commonly used methods at present, and a survey has been made on the frequency and accuracy of these methods in regional economic forecasting. The survey data is shown in the following figureThis article focuses on regional economic forecasting. There are various methods for regional economic forecasting. For different methods, the usual frequency of use and prediction accuracy are not the same. Compared with these methods, the utilization rate of trend forecasting method and I/O ratio forecasting method is above 20%, and only regression forecasting method is widely used, up to 36%, and the accuracy rate is over 80%. The accuracy of the method is over 90%, among which the complex analysis method has the highest accuracy.From Figure3, we can see that in terms of the four main methods of regional economic forecasting, the regression forecasting method is the most widely used, but in terms of accuracy, the combined forecasting method has higher accuracy, because it requires a combination of methods, so the degree of use is not high.Figure 3
Comparison of regional economic forecasting methods.


## 4.2. Regional Economic Comparison and Management

In the experimental survey, the regional economy is a key factor to measure the economic development status of a region. There are many indicators that affect the development of the regional economy. For example, the GDP growth rate in a region can measure the economic development trend of the region. The annual GDP growth value of the region is compared with the GDP growth rate to observe the regional economic situation of the two regions.Figure4 is a comparison of regional economic indicators between AB and AB. The main data for comparison are GDP, GDP growth rate, and the proportion in the whole country. These three data can reflect the local regional economic situation. GDP is the income from data collection, GDP growth rate is the increase in GDP compared to the GDP income in the previous period, and the national proportion is compared with the national GDP. It can be clearly seen that the three data at the A site in Figure 4 are higher than those at the B site. it can be seen that the regional economic situation of A site is the best.Figure 4
Comparison of regional economic indicators between A and B.Comparing the regional economic indicators of A and B, the GDP of A is 2,515.5 billion yuan, and B is lower than that of A. At the same time, the GDP growth rate and proportion are lower than those of A in the whole country. Through this data analysis of the A region, the economy is better than Region B. There are also many factors that affect the regional economy. We compare the reasons for the regional economic differences between A and B to analyze the impact of each factor on the regional economy.From Figure5, it can be seen that human resources, natural resources, and industrial structure are the three most influential factors for the regional economy. The regional economy of place A is better, and the score is better than that of place B in these three aspects. In terms of these three degrees of influence, the regional industrial structure has the greatest impact on the regional economy, while natural resources have the least impact on the regional economy. In order to keep up with the management of the regional economic scale, it is necessary to have a sufficient grasp of the methods for improving the regional economy. Through the survey, we found that there are three main methods for regional economic growth: (1) To speed up the development of the tertiary industry, we must first strengthen the tertiary industry. For the construction of key industrial fields, focus on key economic fields, introduce the policy of “retreat and three advances”, focus on the development of influential key enterprises to drive the growth of surrounding enterprises, form regional agglomeration development, and support the formation of business systems through large-scale comprehensive development to radiate drive business development in other fields such as financial insurance and information services. The development is to build a new retail chain to support the growth of retail consumption. Rationally plan the construction of modern logistics parks for recycling and reuse, and support the development of cluster formats and commercial logistics. Accelerate the renovation of the old city, increase the standardization of commercial streets, and support the development and improvement of the regional service industry. Utilize regional natural resources to create cultural tourism, attach importance to building a tourism service theme system, increase tourism market expansion efforts, build an integrated system of high-quality services, expand scale investment support, and create the Ministry of Eco-tourism. (2) To vigorously develop modern agriculture, we must first clarify the focus of work, grasp precise professional guidance, attach importance to farming, establish a modern, open, innovative, and market-oriented economic awareness, and improve service awareness and responsibility awareness. Plant to grow, to create. It is necessary to attach importance to supporting agriculture through science and technology, attach importance to the value of talents, and continuously improve the level of agriculture. Support marketing and organizational development. The second is to emphasize scientific planting and create economies of scale. Based on scientific planning, promote the vegetable basket plan, strengthen tent production, and create tourism projects with agricultural production experience to guide and promote development, support development, improve support measures, fully mobilize farmers’ enthusiasm for production, expand farmers’ knowledge reserves, and understand technological innovation and market changes. The third is to use the demonstration effect of typical cases to manage the overall development of farmers. Improve preferential policies, introduce measures to benefit the people, give full play to their role as representatives of breeding and display families, stimulate the enthusiasm for independent management, support the establishment of a support mechanism for large families, and encourage retail families to benefit from technical consultation, information acquisition services, and market diversification, to support the large-scale development of the aquaculture industry. (3) Give play to the leading role of key industries and promote the radiation effect of business services. Work with trade unions to support the reorganization of similar industries in the region. The second is to develop industrial parks, design cluster development, rationally plan regional commercial functions, and build characteristic industrial bases, tourism and cultural industries, and trade and logistics centers. Based on the advantages of regional resources, implement large projects and large groups, become bigger and stronger, and expand the development channels of enterprises through social infrastructure construction. Value-added, co-construction, and revitalization actions create a mutually beneficial situation for local enterprises. The fourth is to continuously optimize the internal and external business development environment, continuously improve existing policies, expand investment support, improve service quality, and provide appropriate channels for business development, thereby supporting regional economic development. We apply the above three methods to Region A at the same time to compare the GDP growth and total value of the region after applying different improvement methods.Figure 5
Comparison of differential influence and score.Figure6 shows the regional economic comparison of place A after three different methods have been applied. It can be seen that the regional economic data has been greatly improved after the three methods have been applied to some main data, but the best effect is to promote industrial. The development of the economy has increased the GDP output value by about 300 billion yuan, which has played a role in the rapid development of the regional economy.Figure 6
Data comparison after different methods in A.


## 4.3. The Impact of Machine Learning on Regional Economic Forecasting

When forecasting in this paper, we mainly use machine learning models to forecast the regional economy. Regional economic forecasting often needs to predict more variables and more time periods, so analysis and calculation are a relatively large and complex system technology. To reduce the burden of economic forecasting, the previous work in the field of economic forecasting was purely manual, with the most computation and time. For some forecasts (especially forecasting methods that use complex mathematical models), most analysts no longer need to just waste precious forecasting time, resulting in extremely valuable human resources not being used effectively, and weakening the timeliness of forecast results, Therefore, the forecast results cannot be adjusted. In view of the above deficiencies, great progress has been made in forecasting economic development. The use of computer networks can reduce the research time and cost of forecasting market research and forecasting expert advice. At the same time, in the rapidly changing information society, it is often difficult to obtain accurate and timely information only by using traditional manual methods. The impact of the above three advantages on the regional economy and the degree of public acceptance are shown in the figure.From Figure7, we can see that reducing the error is the highest among the three methods in terms of the impact of the machine learning model on the benefits of the regional economy and the degree of public acceptance. People rely most on this benefit.Figure 7
Comparison of machine learning model benefits.In this paper, we mainly use the linear model, decision tree model, ensemble model, and neural network model in the machine learning model to compare the accuracy of regional economic scale prediction and the time required for the prediction. The data is shown in the figure:Figure8 compares the regional economic comparison accuracy and prediction time under the four machine learning models. It can be seen from the figure that the integrated model has the highest accuracy, the lowest recall rate, and the highest F1 performance index. Therefore, regional economic forecasting method should choose an ensemble model to make predictions.Figure 8
Comparison of regional economic forecasts under machine learning models.Through the comparison of time, it can be seen that the decision tree model takes the longest to take 6.2 s, and the neural network model takes the shortest time, only 4.7 s. However, when making predictions, we prefer to choose higher accuracy and better performance indicators to make predictions. It is shown in Figure9.Figure 9
Comparison of prediction time under machine learning model.


## 5. Conclusion

This paper studies the prediction and management of regional economic scale based on machine learning model. There are various methods for regional economic prediction, but the prediction accuracy and prediction time of regional economy have been greatly optimized after the machine learning model is used. The algorithm also helps to better predict the scale of the regional economy, and there are many ways to improve the scale of the regional economy. In the future, we should improve the regional economy and promote regional development based on the regional economic forecast based on the machine learning model, so that the country can be more prosperous.This paper analyzes regional economic forecasting and management based on machine learning models. For the regional economy, this is an extremely important indicator to measure the level of regional development. We performed analysis to predict this metric. The next step must be to improve the regional economy. Although this paper introduces the economic index method to improve the regional economy, it is still incomplete and does not consider the specific measures and their quality. Future research directions should be here.



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*Source: 2083099-2022-10-11.xml*