A method for stochastic simulation of time series data based on a greedy learning Gaussian mixture model

Abstract

This invention belongs to the technical field of data modeling and stochastic simulation, and discloses a method for stochastic simulation of time-series data based on a greedy learning Gaussian mixture model. The method includes the following steps: S1 Constructing a model containing... K S2: A Gaussian mixture model with Gaussian components is established and the parameter set of the Gaussian components is initialized; S3: The two-dimensional vector is divided into two parts corresponding one-to-one with the Gaussian components. K A set of disjoint first-generation subsets; for any first-generation subset, randomly select two data points in the subset, and use these two data points to divide the subset into two disjoint second-generation subsets, calculate the parameter set of each second-generation subset, and use the second-generation subsets as candidate components; perform local and global optimization on the candidate components; S3 K=K+ 1. Return to step S2 until the termination condition is met. The Gaussian mixture model obtained in this way is the optimal Gaussian mixture model. This invention solves the problem of low simulation accuracy in existing stochastic simulation methods.

Description

Technical Field

[0001] This invention belongs to the technical field of data modeling and stochastic simulation, and more specifically, relates to a method for stochastic simulation of time series data based on a greedy learning Gaussian mixture model. Background Technology

[0002] Stochastic simulation is a crucial technique for power system planning and operation, widely applied to stochastic modeling of time-series data such as runoff, wind speed, power output, and load. However, limitations imposed by observation techniques and uneven spatial distribution of monitoring stations make it difficult to capture the long-term variability of real-world conditions using historical observation data, thus hindering its effectiveness in meeting the practical needs of power system management and optimization. Therefore, generating a large number of simulation sequences through efficient stochastic simulation methods for time-series data is of great significance for addressing uncertainties that may arise in the future but were not observed historically, and for enhancing the scientific rigor of power system management.

[0003] Currently, existing stochastic simulation methods mainly include statistical-driven methods, Copula function methods, and generative adversarial networks (GANs). Statistical-driven methods are simple in structure and clear in concept, but suffer from drawbacks such as high dependence on linear and Gaussian distribution assumptions or inability to extrapolate extreme scenarios. While Copula functions and GANs have made progress in nonlinear representation, the former still requires pre-setting the marginal distribution form and faces difficulties in high-dimensional modeling, while the latter's black-box nature makes it difficult to explicitly analyze the generated distribution. Against this backdrop, Gaussian Mixture Models (GMMs) have become a new breakthrough in stochastic simulation methods due to their multimodal fitting ability and explicit probabilistic structure. However, their parameter estimation relies on the traditional Expectation-Maximization (EM) algorithm, which suffers from initial value sensitivity, the need to pre-set the number of components, and susceptibility to local optima, limiting their applicability to complex time-series data. For GMM parameter optimization, existing technologies mainly focus on the latent variable handling mechanism of the EM algorithm, proposing variant algorithms such as categorical EM, stochastic EM, and Monte Carlo EM, achieving improvements in computational efficiency, convergence speed, or model complexity. However, these variant algorithms each have their own focus and still face common problems such as sensitivity to initial values, local optima, and accuracy-efficiency tradeoffs, lacking systematic solutions. Therefore, it is necessary to propose a more accurate, reliable, and efficient GMM parameter optimization method to reasonably capture the characteristics of time-series data and further improve the accuracy of GMM in stochastic simulation of time-series data. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a time-series data stochastic simulation method based on a greedy learning Gaussian mixture model, solving the problem of low simulation accuracy in existing stochastic simulation methods.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for constructing a Gaussian mixture model based on greedy learning is provided, the method comprising the following steps:

[0006] S1 constructs a two-dimensional vector corresponding to each time step of the data to be processed using the data to be processed, and constructs a corresponding two-dimensional vector containing... K A Gaussian mixture model with Gaussian components is generated, and the parameter set of the Gaussian mixture model is initialized.

[0007] S2 divides the two-dimensional vector into components that correspond one-to-one with the Gaussian components. K A set of disjoint subsets of generation; for any subset of generation A k Two data points are randomly selected from this subset, and the subset is then used to... A k The system is divided into two disjoint second-generation subsets, and the parameter set of each second-generation subset is calculated. The second-generation subsets are used as candidate components.

[0008] The candidate components are filtered to obtain the filtered candidate components;

[0009] Calculate the candidate components after arbitrary filtering and the... K The Gaussian components form a collection K+ The log-likelihood function of a Gaussian mixture model with one Gaussian component, and the maximum value of the log-likelihood function. K+ One Gaussian mixture model is used as the new Gaussian mixture model, and the parameter set of the new Gaussian mixture model is updated;

[0010] S3 K = K + 1. Return to step S2 until the termination condition is met. The Gaussian mixture model obtained in this way is the optimal Gaussian mixture model.

[0011] More preferably, the Gaussian mixture model is as follows:

[0012] ;

[0013] in, For multidimensional vectors x The probability density function; It is a multidimensional Gaussian probability density function; It is the set of parameters to be optimized in GMM, where It is GMM's first k The mixing weights of Gaussian components, It is the first k The mean vector of each component It is the first k The covariance matrix of each component; K This represents the total number of Gaussian components in the current model. D For multidimensional vectors x Dimensions.

[0014] More preferably, the second-generation subset is as follows:

[0015] ;

[0016] in, , These are two disjoint second-generation subsets; a , b These are two randomly selected data point vectors; x Describing a subset of generation A k Data points in the data.

[0017] More preferably, the parameter set includes a mean vector, a covariance matrix, and a mixture weight; the mean and covariance of the second-generation subset are calculated using the elements in the second-generation subset, and the mixture weight of the second-generation subset is 50% of the mixture weight of the first-generation subset.

[0018] More preferably, the step of screening the candidate components is as follows:

[0019] (1) Perform preliminary screening of candidate components; the condition for preliminary screening is that the number of elements in the candidate components or the mixed weight of the candidate components is greater than or equal to a preset threshold.

[0020] (2) Update the parameter set of the candidate components obtained from the initial screening until the preset conditions are met;

[0021] (3) Further filter the updated candidate components and retain the candidate components that meet the filtering conditions; the further filtering condition is that the weight of the updated candidate component is greater than or equal to the preset component weight threshold.

[0022] More preferably, the formula for updating the parameter set of the candidate components obtained from the initial screening is as follows:

[0023] ;

[0024] in, It is GMM's first K+ Mixing weights for a single Gaussian component; Represents the mixed weights of the candidate components; It is the first K+ The mean vector of one component. It is the first K+ The covariance matrix with one component; K+ 1 represents the total number of Gaussian components in the model after adding the new candidate components; For sample data points x i For the K+A latent variable with one component represents x i Does it belong to the first K+ One component; Let be the posterior probability of the latent variable, representing the th... K+ 1 component pair x i Response rate; for a subset of generations A k The number of data points in the middle; For the original K The probability density function of a component Gaussian mixture model.

[0025] More preferably, in step (2), the preset conditions are as follows:

[0026] ;

[0027] in, For the original K Component Gaussian mixture model with the addition of a component Gaussian mixture model A k The first obtained by splitting S After 1 candidate component, during the parameter optimization iteration K+ Log-likelihood function of a 1-component Gaussian mixture model; Update the convergence conditions for the preset parameters; Represents the mixed weights of the candidate components; The parameter set for the candidate components; For the original K The probability density function of a component Gaussian mixture model; This is the probability density function of the Gaussian mixture model after adding candidate components.

[0028] More preferably, in step S2, the formula for updating the parameter set of the new Gaussian mixture model is as follows:

[0029] ;

[0030] in, It is GMM's first k The mixing weights of Gaussian components; It is the first k The mean vector of each component; It is the first k The covariance matrix of each component; For sample data points x i For the k The latent variables of each component represent x i Does it belong to the first k One component; Let be the posterior probability of the latent variable, representing the th... k Each component pair x i Response rate; M This represents the total number of sample data points.

[0031] According to another aspect of the present invention, a method for stochastic simulation of time-series data based on a greedy learning Gaussian mixture model is provided, the method comprising the following steps:

[0032] The probability density function and conditional cumulative distribution function of the two-dimensional vector of data to be simulated are established using the Gaussian mixture model described above.

[0033] The simulated values ​​for each time point in each year are calculated using the conditional cumulative distribution function, thereby obtaining the random simulated data for the target year.

[0034] More preferably, the probability density function and the conditional cumulative distribution function are as follows:

[0035] ;

[0036] The first i Year t Simulated values ​​at time as follows:

[0037] ;

[0038] in, x 1, x 2 refers to two-dimensional vectors respectively. x t The first and second column elements; p ( x 2 | x 1 )and F ( x 2 | x 1 ( ) are known x 1 hour x 2 The conditional probability density function and conditional cumulative distribution function of the Gaussian mixture model; It is GMM's first k The mixing weights of Gaussian components; They are known respectively x 1 The mean vector and covariance matrix; They are known respectively x 1 hour x2 The conditional mean vector and conditional covariance matrix; These are uniformly random numbers.

[0039] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0040] 1. This invention introduces a greedy learning strategy into the parameter optimization process of a Gaussian mixture model by progressively adding Gaussian components. This innovative design incorporates three aspects: a split-candidate component generation mechanism, two-stage optimization, and dual threshold constraints. While ensuring model simplicity, it also optimizes the number of optimal components. K (Lower) improves the ability to fit data, achieves synergistic optimization of computational efficiency and model robustness, and improves the simulation accuracy of stochastic simulation.

[0041] 2. The greedy learning Gaussian mixture model used in this invention, while ensuring ease of model construction and optimization, possesses the ability to accurately describe the intra-annual and inter-annual autocorrelation characteristics of time series. Its simulation data maintains higher simulation accuracy than comparative methods in terms of preserving the statistical characteristics of the observed time series (mean, standard deviation, skewness coefficient, etc.). Furthermore, the simulation data of this invention comprehensively considers coverage and interval width, achieving accurate coverage of the core data distribution at different confidence levels. It has the smallest interval width compared to comparative methods, thus avoiding the risk of overgeneralization and ensuring excellent uncertainty quantification capabilities.

[0042] 3. This invention does not require a pre-defined data distribution or reliance on linear assumptions. Its explicit probability structure enhances the interpretability of the model and improves the accuracy and reliability of the invention's stochastic simulation of time-series data. Attached Figure Description

[0043] Figure 1 This is a flowchart of a time-series data stochastic simulation method based on a greedy learning Gaussian mixture model, constructed according to a preferred embodiment of the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0045] like Figure 1 As shown, this invention proposes a method for stochastic simulation of time-series data based on a greedy learning Gaussian mixture model (GL-GMM), with the following specific steps:

[0046] S1: Obtain the time series dataset of historical observations and input the preset parameters of the greedy learning algorithm.

[0047] Obtain time series datasets of historical observations ,in M For the dataset size, N For the duration of time. Constructed by... t- Time 1 data Q t-1 and the t Time data Q t Two-dimensional vector x t .variable X The expression form is:

[0048]

[0049] In the formula: Q t Represents the historical observation time series data sequence number. t A vector of time points; if the length of a time point is 1 day, then... N= 365; If the duration is 10 days, then N= 36; If the time period is one month, then N= 12; A two-dimensional vector represents the dimension of the sample data. D= 2.

[0050] Input the preset parameters of the greedy learning algorithm and set the maximum number of components. The number of candidate components to be split for each existing component S Sample size threshold Weight threshold Stop iteration threshold Regularization coefficient .

[0051] A Gaussian mixture model with one component is constructed based on the observation data, and the model parameters are initialized.

[0052] GMM is a composite probabilistic model, through K It is composed of a linear superposition of individual Gaussian distributions, and its mathematical description is as follows:

[0053]

[0054] in, For multidimensional vectors x The probability density function; It is a multidimensional Gaussian probability density function; It is the set of parameters to be optimized in GMM, where It is GMM's first k The mixing weights of Gaussian components, It is the first k The mean vector of each component It is the first k The covariance matrix of each component; K This represents the total number of Gaussian components in the current model. D For multidimensional vectors x Dimensions.

[0055] Based on the variables described in S1 X For every moment t Two-dimensional vector x t Construct a Gaussian mixture model with one component, i.e. K = 1;

[0056] The initial mixing weights of its components are as follows: = 1; Mean vector of the components Two-dimensional vector x t The mean of the components and the covariance of the components are... Two-dimensional vector x t The covariance plus the regularization term; the above constitutes the initial parameter set of the model. θ .

[0057] According to the initial parameter set θ Calculate the log-likelihood function of the initial model. L 1；

[0058]

[0059] S3: Perform a global parameter space search on each component of the existing Gaussian mixture model and use a split candidate component generation mechanism to obtain the expected number of candidate components.

[0060] S31: Soft partitioning based on posterior probability has transformed the two-dimensional vector... x t Divided into K Disjoint subsets each subset A k This corresponds to a Gaussian component in the existing mixture model. ;

[0061] In the formula: This represents the current number of Gaussian components. For the first i Sample data points xi For the k The hidden variables of each component represent the selection status of each sub-component; is the posterior probability of the latent variable.

[0062] S32: The split-type candidate component generation mechanism is as follows: A k Two data points are randomly selected uniformly across the global scope. a and b Based on Euclidean distance metric A k Divide into two disjoint subsets and ;

[0063] S33: Subset and The subsets will be used as two new candidate components. The mean vector and covariance matrix of the elements in the subset will be calculated as parameters of the candidate components, and 50% of the mixed weight of the parent component will be inherited as the initial weight.

[0064] S34: Repeat S32 and S33 to obtain the next two candidate components, until each subset is obtained. A k Generate the expected S Group candidate components; a total of K × S One candidate component.

[0065] S4: Apply dual threshold constraints and local optimization to the candidate components of S3, and optimize and update the parameters of the candidate components.

[0066] right K × S The candidate components are initially screened, and constraints are imposed by a component sample size threshold and a weight threshold. When the number of samples to which a candidate component belongs or the weight of the candidate component is lower than the dual threshold constraints, the component is removed.

[0067] For each candidate component selected in the initial screening, EM local optimization is performed. The initial parameters for EM local optimization are the mean vector and covariance matrix of each candidate component. The parameters of each component in the existing Gaussian mixture model are fixed, and only the mixing weights of the candidate components are optimized. and parameter set This simplifies the multi-component parameter optimization problem into a two-component parameter optimization problem. ;

[0068] Where: the parameter set of the optimized candidate components , For the first k The first set splits into its first... S A candidate subset, for A k The number of data points in the middle.

[0069] The iteration stopping condition is set to ;

[0070]

[0071] In the formula: For the existing K The probability density function of the component mixture model. Let be the probability density function of the newly added component. This is the probability density function of the mixture model after adding the new component. This is the probability density function of the mixture model after adding the new component. (Using...) To indicate the first In the next iteration, the first... k The set splits out the first S The log-likelihood function of the mixture model after candidate components.

[0072] The candidate components after parameter optimization are further screened by using a component weight threshold as a constraint. If the weight of a candidate component is lower than this threshold, it is eliminated.

[0073] S5: Optimize the candidate components after parameter optimization as described in S4, add the selected components to the existing Gaussian mixture model described in S2, and perform global optimization to update the parameters of the Gaussian mixture model.

[0074] Based on the maximum likelihood principle, the candidate component that maximizes the log-likelihood function of the mixture model is selected from the candidate components optimized and screened in step S4 and added as a new component, in conjunction with the existing components. K Component mixing models together form a new K+ One-component mixed model.

[0075] Using the weights and parameter set of the hybrid model after adding the new components as initial values, a global EM optimization is performed to complete the parameter update.

[0076]

[0077] S6: Repeat S3-S5 until the termination condition of the greedy learning algorithm is met, and obtain the final optimized Gaussian mixture model.

[0078] Specifically, repeat steps S3-S5 until the number of components reaches the preset maximum number of components. K max Or the log-likelihood function satisfies L K >L K+1 The termination condition is that the number of model components is equal to the number of ideal components. K * The corresponding log-likelihood function is the global maximum.

[0079] Output model ideal component count K * Mix the weight sets and parameter sets of each component of the model to obtain the final optimized Gaussian mixture model.

[0080] S7: Based on the optimized Gaussian mixture model described in S6, perform random simulation of time series data to obtain the simulation sequence.

[0081] S71: Based on the final optimized Gaussian mixture model described in S6, construct a two-dimensional vector. x t = [ x 1 , x 2 The conditional probability relationship of ]:

[0082]

[0083] In the formula: x 1 , x 2 Each refers to a two-dimensional vector x t The first and second column elements; p ( x 1 , x 2 ) represents a vector x 1 with vector x 2 The probability density function; F ( x t ) represents a vector x 1 with vector x 2 Two-dimensional joint distribution; This represents the bivariate Gaussian probability density function.

[0084] S72: Based on the law of total probability and the law of conditional probability, deduce the known... x 1 hour x2 The conditional probability density function of a Gaussian mixture distribution p ( x 2 | x 1 ) and conditional cumulative distribution function F ( x 2 | x 1 ):

[0085]

[0086] In the formula: p ( x 1 )for x 1 The marginal probability density function, They represent x 1 The mean vector and covariance matrix; They are known respectively x 1 hour x 2 The conditional mean vector and conditional covariance matrix are calculated using the following formulas:

[0087]

[0088] S73: When conducting the first year's stochastic simulation, first let the simulated runoff... (in M For the number of years in the sample data, For the first i Year N (Observed runoff at each time point) generate a uniform random number. And assign it to the condition CDF, i.e. Thus further obtaining the first year's first t Simulated values ​​at time , t = t + 1. Repeat the above process until... t = N Then the first year of stochastic simulation is completed.

[0089] S74: In the process of the i In the annual random simulation, a uniform random number is first generated and assigned to the conditional CDF, i.e. to further obtain the first i Year t Simulated values ​​at time, t = t +1. It should be noted that... Repeat the above process until... t = N Then the first step is completed. iA stochastic simulation of the year.

[0090] S75: Order i = i + 1. Repeat step S74 until... Then it's complete. The stochastic simulation of the year (of which) (The target number of years to be generated).

[0091] The present invention will be further described below with reference to specific embodiments.

[0092] Historical runoff time-series data at monthly, decadal, and daily scales from 1940 to 2022 at the Pingshan Hydrological Station in the lower reaches of the Jinsha River were selected as the implementation object to test the simulation effect of the stochastic simulation method based on the greedy learning Gaussian mixture model.

[0093] The methods of this invention, the GMM method optimized from the traditional EM algorithm, the Copula method, the seasonal autoregressive method (SAR), and the conditional generative adversarial network method (CGAN) were used to randomly generate monthly, decadal, and daily runoff sequences with a length of 1000 years, and then compared and analyzed. The randomly generated runoff sequences were required to have high efficiency in terms of statistical characteristic preservation, autocorrelation structure representation, and uncertainty quantification. The examples used metrics such as mean, variance, skewness coefficient, root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), autocorrelation coefficient (ACF), coverage rate (CR), and interval width (IW) to measure the quality of the generated sequences.

[0094] ;

[0095] ;

[0096] .

[0097] Tables 1, 2, and 3 present the quantitative evaluation results of the statistical characteristics of the randomly simulated sequences generated by each method at monthly, decadal, and daily scales, respectively. The results show that the GL-GMM method exhibits a significant advantage in preserving the statistical characteristics of runoff sequences at different time scales. At the monthly and decadal scales, GL-GMM achieves the best levels in RMSE, MAE, and MAPE for the mean, variance, and skewness coefficient, with a particularly significant reduction in the error of the skewness coefficient. However, in terms of preserving the runoff mean at the daily scale, although the MAPE of GL-GMM (0.87%) is slightly lower than that of the Copula method (0.54%), this difference remains within the high-precision range and does not affect its overall advantage in the other three indicators. The bolded numbers in Tables 1, 2, and 3 indicate that this method has the smallest error.

[0098] .

[0099] Table 4 shows the average autocorrelation coefficients (ACFs) and their normalized values ​​for runoff sequences generated by different methods. The data shows that as the time scale is refined from monthly to daily, the normalized values ​​of the ACFs of the runoff sequences generated by each method exhibit a significant increasing trend, indicating that short-term runoff processes have stronger temporal correlation characteristics. Among them, the GL-GMM method achieves the highest ACF values ​​at all three scales (0.6330 for monthly, 0.8868 for decadal, and 0.9898 for daily), verifying its superior performance in preserving the time-dependent structure. The bolded numbers in Table 4 indicate that this method has the largest ACF value.

[0100] .

[0101] Table 5 presents the accuracy descriptions of runoff sequences generated by different methods, specifically the evaluation of coverage rate (CR) and interval width (IW). The results show that, with increasing confidence levels, the CR and IW of the randomly simulated sequences generated by the GL-GMM method exhibit a synchronous and uniform growth trend. This indicates that the generated sequences can stably converge to a reasonable probability distribution at the corresponding confidence level as the probability constraints strengthen, avoiding the abnormal phenomena observed in other methods (such as Copula and SAR) such as stagnant CR growth or sudden increases in IW at specific confidence levels. While achieving more accurate coverage, the GL-GMM method uses a more stringent interval to characterize the true distribution of runoff sequences, avoiding accuracy loss due to excessive interval expansion. Compared to traditional methods, it demonstrates superior uncertainty modeling advantages.

[0102] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a Gaussian mixture model based on greedy learning, characterized in that, The method includes the following steps: S1 constructs a two-dimensional vector corresponding to each time step of the data to be processed using the data to be processed, and constructs a corresponding two-dimensional vector containing... K A Gaussian mixture model with Gaussian components is established, and the parameter set of the Gaussian mixture model is initialized; the data to be processed is the historical runoff time series data of hydrological stations at the monthly, ten-day, and daily scales. S2 divides the two-dimensional vector into components that correspond one-to-one with the Gaussian components. K A set of disjoint subsets of generation; for any subset of generation A k Two data points are randomly selected from this subset, and the subset is then used to... A k The system is divided into two disjoint second-generation subsets, and the parameter set of each second-generation subset is calculated. The second-generation subsets are used as candidate components. The candidate components are filtered to obtain the filtered candidate components; Calculate the candidate components after arbitrary filtering and the... K The Gaussian components form a collection K+ The log-likelihood function of a Gaussian mixture model with one Gaussian component, and the maximum value of the log-likelihood function. K+ One Gaussian mixture model is used as the new Gaussian mixture model, and the parameter set of the new Gaussian mixture model is updated; S3 K=K+ 1. Return to step S2 until the termination condition is met. The Gaussian mixture model obtained in this way is the optimal Gaussian mixture model. The steps for filtering the candidate components are as follows: (1) Perform preliminary screening of candidate components; the condition for preliminary screening is that the number of elements in the candidate components or the mixed weight of the candidate components is greater than or equal to a preset threshold. (2) Update the parameter set of the candidate components obtained from the initial screening until the preset conditions are met; (3) Further filter the updated candidate components and retain the candidate components that meet the filtering conditions; the further filtering condition is that the weight of the updated candidate component is greater than or equal to the preset component weight threshold. The formula for updating the parameter set of the candidate components obtained from the initial screening is as follows: in, It is GMM's first K+ Mixing weights for a single Gaussian component; Represents the mixed weights of the candidate components; It is K+ The mean vector of one component. It is K+ The covariance matrix with one component; K+ 1 represents the total number of Gaussian components in the model after adding the new candidate components; For sample data points x i For the K+ A latent variable with one component represents x i Does it belong to the first K+ One component; Let be the posterior probability of the latent variable, representing the th... K+ 1 component pair x i Response rate; For a generation of subsets A k The number of data points in the middle; For the original K The probability density function of a component Gaussian mixture model.

2. The method for constructing a Gaussian mixture model based on greedy learning as described in claim 1, characterized in that, The Gaussian mixture model is as follows: in, For multidimensional vectors x The probability density function; It is a multidimensional Gaussian probability density function; It is the set of parameters to be optimized in GMM, where It is GMM's first k The mixing weights of Gaussian components, It is k The mean vector of each component It is k The covariance matrix of each component; K This represents the total number of Gaussian components in the current model. D For multidimensional vectors x Dimensions.

3. The method for constructing a Gaussian mixture model based on greedy learning as described in claim 1 or 2, characterized in that, The second-generation subset is as follows: in, , These are two disjoint second-generation subsets; a , b These are two randomly selected data point vectors; x Describing a subset of generation A k Data points in the data.

4. The method for constructing a Gaussian mixture model based on greedy learning as described in claim 3, characterized in that, The parameter set includes a mean vector, a covariance matrix, and a mixture weight; the mean and covariance of the second-generation subset are calculated using the elements in the second-generation subset, and the mixture weight of the second-generation subset is 50% of the mixture weight of the first-generation subset.

5. The method for constructing a Gaussian mixture model based on greedy learning as described in claim 1, characterized in that, In step (2), the preset conditions are as follows: in, For the original K Component Gaussian mixture model with the addition of a component Gaussian mixture model A k The first obtained by splitting S After the candidate component, the first During secondary parameter optimization iteration K+ The log-likelihood function of a one-component Gaussian mixture model; Update the convergence criteria for the preset parameters; Represents the mixed weights of the candidate components; The parameter set for the candidate components; For the original K The probability density function of a component Gaussian mixture model; This is the probability density function of the Gaussian mixture model after adding candidate components.

6. The method for constructing a Gaussian mixture model based on greedy learning as described in claim 1, characterized in that, In step S2, the formula for updating the parameter set of the new Gaussian mixture model is as follows: in, It is GMM's first k The mixing weights of Gaussian components; It is k The mean vector of each component; It is k The covariance matrix of each component; For sample data points x i For the k The latent variables of each component represent x i Does it belong to the first k One component; Let be the posterior probability of the latent variable, representing the th... k Each component pair x i Response rate; M This represents the total number of sample data points.

7. A method for stochastic simulation of time-series data based on a greedy learning Gaussian mixture model, characterized in that, The method includes the following steps: The probability density function and conditional cumulative distribution function of the two-dimensional vector of data to be simulated are established using the Gaussian mixture model according to any one of claims 1-6; The simulated values ​​for each time point in each year are calculated using the conditional cumulative distribution function, thereby obtaining the random simulated data for the target year.

8. The method for stochastic simulation of time-series data based on a greedy learning Gaussian mixture model as described in claim 7, characterized in that, The probability density function and conditional cumulative distribution function are as follows: No. i Year t Simulated values ​​at time as follows: in, x 1, x 2 refers to two-dimensional vectors respectively. x t The first and second column elements; p ( x 2 | x 1 )and F ( x 2 | x 1 ( ) are known x 1 hour x 2 The conditional probability density function and conditional cumulative distribution function of the Gaussian mixture model; It is GMM's first k The mixing weights of Gaussian components; They are known respectively x 1 The mean vector and covariance matrix; They are known respectively x 1 hour x 2 The conditional mean vector and conditional covariance matrix; These are uniformly random numbers.

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