A component selection method for t-mixture linear mixed effect model

Abstract

This application discloses a component selection method for a t-mix linear mixed-effects model. The method includes: acquiring observational data and initializing a t-mix linear mixed-effects model with excessively redundant components; iteratively executing the following steps: calculating the posterior statistic of the observational data; updating the model parameters based on the posterior statistic by maximizing an objective function containing a specific penalty term, configured to impose a stronger penalty on mixing proportion parameters with smaller values, thereby driving the mixing proportions of redundant components to approach zero; removing components with zero mixing proportions and reorganizing the model. After iteration until convergence, the final number of effective components and parameter estimates for each component are output. This method solves the problems of high computational cost and low efficiency in determining the number of components in complex models using related techniques, achieving simultaneous parameter estimation and automatic component selection within a single framework, thus improving the computational efficiency of the model.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method for selecting components in a t-mixed linear mixed-effects model. Background Technology

[0002] In modern data analysis, mixture-effects models are widely used to process longitudinal or clustered data. To identify potentially heterogeneous subgroups, technicians employ mixed linear mixture-effects models. When the data contains outliers or exhibits a heavy-tailed distribution, a t-distribution is further introduced to construct a t-mixed linear mixture-effects model to improve model stability. This approach has been widely used in fields such as biomedicine and social sciences.

[0003] The typical approach to determining the number of components in a t-mixed linear mixed-effects model is to first define several possible component numbers, then fit the complete model using the EM algorithm for each candidate number, and finally select the optimal result by comparing indicators such as the Bayesian information criterion. In this process, the degrees of freedom parameters of the t-distribution usually require additional processing.

[0004] However, this approach has several obvious drawbacks: it requires repeated model fitting, resulting in high computational costs; model parameter estimation and component selection are two separate steps and cannot be performed simultaneously; the algorithm results are easily affected by initial values ​​and may not yield the optimal solution; and it cannot automatically identify and remove unnecessary components during the calculation process, leading to the final model potentially containing redundant parts. These shortcomings result in inefficiency and model redundancy, making it difficult to meet the demands of practical applications for efficient and robust models. Summary of the Invention

[0005] This application provides a component selection method for a t-mixed linear mixed-effects model, which solves the problems of high computational load and low efficiency in determining the number of components in complex models in related technologies. It realizes the simultaneous completion of parameter estimation and automatic component selection within a single framework, thereby improving the computational efficiency of the model.

[0006] This application provides a method for selecting components in a t-mixture linear mixed-effects model, the method comprising: Step S1: Obtain observation data; Step S2: Initialize the t-mix linear mixture effect model, wherein the initial number of components of the t-mix linear mixture effect model is an integer greater than 1; Step S3: Calculate the posterior statistic of the observed data based on the current parameters of the t-mixed linear mixed effects model; Step S4: Based on the posterior statistic, update the parameters of the t-mixed linear mixed effects model by maximizing a preset objective function. The preset objective function includes a penalty term acting on the mixing ratio parameter of the t-mixed linear mixed effects model. The strength of the penalty term increases as the value of the mixing ratio parameter decreases. Step S5: Remove components whose mixing ratio parameter is zero after the update, reorganize the parameter structure of the current parameter of the t-mixing linear mixture effect model, and update the number of effective components in the t-mixing linear mixture effect model; Step S6: Iteratively execute steps S3 to S5 until the preset convergence condition is met; Step S7: Output the number of effective components and parameter estimates of each component in the converged t-mixed linear mixed effect model.

[0007] Optionally, step S5 includes: Monitor the changing trends of the penalty intensity of each component in the t-mixed linear mixed effect model; If the mixing ratio parameter of a certain component is detected to decrease continuously in multiple iterations, and the value of the mixing ratio parameter becomes zero after the current iteration, then the component is removed. Based on the removal results, the parameter structure of the current parameters of the t-mixed linear mixed-effects model is restructured, and the number of effective components is updated so that subsequent iterations can continue to be performed based on the updated model.

[0008] Optionally, step S3 includes: Based on the current parameters, calculate the probability density of each observation data under each component in the t-mixed linear mixed effect model; Based on the probability density and the mixing ratio parameters of the current t-mixed linear mixed effect model, calculate the posterior probability of each observed data belonging to each component; Based on the posterior probability and the t-distribution degrees of freedom parameters of each component in the current t-mixed linear mixed effects model, calculate the conditional expectation of the scaling variable; Based on the posterior probability and the mixed-effects structure parameters of the current t-mixed linear mixed-effects model, the conditional expectation of the random effects is calculated.

[0009] Optionally, step S4 includes: Based on the posterior statistic, calculate the conditional expectation of the log-likelihood of the complete data; Based on the conditional expectation, a penalty term is added to the mixing ratio parameter of the t-mixed linear mixed effect model to form a preset objective function; By maximizing the preset objective function, the updated parameters of the t-mixed linear mixed effect model are obtained; Wherein, the penalty term applies a greater penalty intensity to the component with a smaller value in the mixing ratio parameter than it applies to the component with a larger value.

[0010] Optionally, the step of adding a penalty term to the mixing ratio parameter of the t-mixed linear mixed-effects model based on the conditional expectation to form a preset objective function includes: Obtain the penalty intensity adjustment parameters; Based on the penalty intensity adjustment parameter, a penalty term function is constructed, wherein the output value of the penalty term function increases as the input mixing ratio parameter value decreases; The penalty function is added to the conditional expectation to form the preset objective function.

[0011] Optionally, the steps for obtaining the penalty intensity adjustment parameters include: Obtain a set of candidate values ​​for the penalty intensity adjustment parameters; Based on each candidate value, construct the penalty term function and execute steps S2 to S6 to obtain the corresponding evaluation model; Calculate the Bayesian information criterion value for each of the evaluation models based on the Bayesian information criterion. The candidate values ​​that generate the optimal Bayesian information criterion value will be used as the obtained penalty intensity adjustment parameters.

[0012] Optionally, the step of initializing the t-mixed linear mixed-effects model in step S2 includes: Multiple initial component allocation strategies are employed to generate multiple sets of initial cluster labels for the observed data; For each set of initial cluster labels, a set of parameters of the mixed-effects model are independently initialized to form multiple initial parameter sets; For each of the multiple initial parameter sets, the iterative optimization process from step S3 to step S6 is executed independently to obtain multiple candidate models; Based on the preset model selection criteria, an optimal model is selected from the multiple candidate models as the initialized t-mixed linear mixed effect model.

[0013] Optionally, the penalty term function is constructed as follows: , in, The number of observed objects, The penalty intensity adjustment parameter, Let be the number of free parameters for each component in the t-mixed linear mixed-effects model. For a preset minimum positive number, The number of effective components in the current iteration. For the first The mixing ratio parameters of each component.

[0014] Optionally, in the step of obtaining the updated t-mixed linear mixed-effects model parameters, the first... Mixing ratio parameters of each component Update value Determine by the following formula: , in, The first one calculated in step S3 The observed object belongs to the first The posterior probability of each component. This represents the number of effective components at the start of this iteration.

[0015] Optionally, the t-distribution degree of freedom parameter of the t-distribution t-distribution degrees of freedom parameters of each component Update by solving the following equation: , in, For the Digamma function, The conditional expectation of the scaling variable calculated in step S3. The value of the previous iteration. For the first The number of repeated observations of each observation object.

[0016] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: 1. By introducing a penalty term whose intensity increases as the mixing ratio decreases, and setting a mechanism for removing low-proportion components and corresponding parameter update rules in the iteration, the process of selecting the number of model components is directly embedded into the iterative framework of model parameter estimation. During the iteration process, the mixing ratio of redundant components is automatically compressed and redundant components are removed, thereby completing parameter estimation and model structure determination simultaneously within a single computational flow. This avoids the cumbersome process of repeated modeling and post-comparison for different preset component numbers required by related technologies, significantly improving computational efficiency.

[0017] 2. By introducing and adaptively updating the degrees of freedom parameters specific to the t-distribution, the model can flexibly match the tail thickness characteristics of the data. Compared with the traditional Gaussian mixture model, this model assigns a more reasonable probability distribution to observations that are far from the center, making the parameter estimation process less susceptible to interference from a few extreme values. Thus, when outliers exist or the data itself exhibits a thick-tailed distribution, it can obtain more stable estimation results and more accurate component quantity judgments.

[0018] 3. By employing multiple initial allocation strategies for optimal initialization, the reliance on a single starting point is effectively reduced, alleviating the problems of the Expectation-Maximization algorithm being sensitive to initial values ​​and prone to getting trapped in local optima. Simultaneously, through an adaptive penalty intensity selection process based on the Bayesian information criterion, the determination of the penalty intensity parameter is transformed from a step relying on external manual comparison into an internally integrated and automated optimization process, improving the automation level and repeatability of the results. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the component selection method for the t-mixed linear mixed effect model of this application; Figure 2 This is a flowchart illustrating the component selection method for the t-mixed linear mixed-effects model of this application; Figure 3 This is a schematic diagram illustrating the process of maximizing the objective function to update the model parameters in the component selection method of the t-mixed linear mixed effects model of this application; Figure 4 A schematic diagram illustrating the process of removing redundant components in the component selection method of the t-mixed linear mixed effect model of this application; Figure 5 This is a histogram comparing the component quantity selection results of the method of this invention and the comparative method on contaminated Gaussian data in a simulation experiment. Figure 6 This is a schematic diagram of the terminal structure of the hardware operating environment involved in one embodiment of this application. Detailed Implementation

[0020] To address the problems of low computational efficiency, lack of automation, and sensitivity to outliers or extreme values ​​in the data when determining the number of components in a t-mixed linear mixed-effects model, this application proposes a component selection method for such models. An optimization objective function with a specific penalty term is constructed, and within an improved expectation-maximization algorithm framework, parameter estimation and an automatic component elimination mechanism based on this penalty term are integrated into the same iterative process. Furthermore, the algorithm's stability is improved by integrating multi-starting-point initialization and an information-criterion-based adaptive penalty intensity selection strategy. This achieves simultaneous parameter estimation and component selection within a single framework, significantly improving computational efficiency. The introduction of the t-distribution enhances the robustness of the estimation process, and the integrated optimization process improves the algorithm's automation level and the reproducibility of the results.

[0021] To better understand the above technical solutions, exemplary embodiments of this application will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of this application are shown in the drawings, it should be understood that this application can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art.

[0022] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0023] Example 1 In this embodiment, a method for selecting components in a t-mixed linear mixed-effects model is provided.

[0024] Reference Figure 1 and Figure 2 The component selection method of the t-mixed linear mixed effect model in this embodiment includes the following steps: Step S1: Obtain observation data; In this embodiment, observation data refers to a collected dataset with a repeating measurement structure. Typically, it is... ,in The number of objects observed. For the first A fixed-effects design matrix for samples, with dimensions of . It contains p fixed-effect covariates, such as time, treatment group, etc. For the first The response vector of each observed object is an observation vector with dimension . ; For the first The random effects design matrix for each observation object has dimensions of . It typically includes covariates corresponding to random intercepts and random slopes.

[0025] Optionally, a structured observation dataset that meets the model requirements is obtained. This dataset contains longitudinal or repeated measurement records of multiple samples, each record having a response variable y, a fixed-effects covariate X, and a random-effects covariate. This observation dataset forms the basis for all subsequent model initialization, estimation, and selection.

[0026] Step S2: Initialize the t-mix linear mixture effect model, wherein the initial number of components of the t-mix linear mixture effect model is an integer greater than 1; In this embodiment, the initial number of components is set to an integer greater than the actual number of components, so that the algorithm has enough space for filtering.

[0027] Optionally, a sufficiently large initial number of components can be preset. Perform multi-starting-point optimal initialization. Specifically, this includes the following steps: Step S210: Using various initial component allocation strategies, generate multiple sets of initial cluster labels for the observation data; In this embodiment, at least three strategies can be employed to... The observed objects were initially classified into Within each cluster, multiple sets of initial component member labels are formed.

[0028] Alternatively, various initial component assignment strategies may be employed, including distance-based clustering assignment, constraint-adjusted clustering assignment, and random assignment.

[0029] Step S220: For each group of initial clustering labels, independently initialize a set of parameters for the mixed-effects model to form multiple candidate initial parameter sets; In this embodiment, for each initial label, the initial model parameters of the data within that cluster are calculated, such as based on least squares estimation. Based on residual estimation , , set initial Thus, multiple different sets of initial parameters can be obtained. .

[0030] Step S230: For the multiple candidate initial parameter sets, execute the iterative optimization process from steps S3 to S6 independently to obtain multiple candidate models; In this embodiment, for each initial parameter set Run a simplified iterative optimization cycle independently, for example, execute steps S3 to S6 several times until the log-likelihood change is less than a preset change threshold or the maximum number of iterations is reached, to obtain multiple candidate models and their parameters. .

[0031] Step S240: Based on the preset model selection criteria, select an optimal model from the multiple candidate models as the initialized t-mixed linear mixed effect model.

[0032] In this embodiment, the Bayesian information criterion value of each candidate model is calculated, and the candidate model with the smallest Bayesian information criterion value is selected, and its parameters are used as the initialized t-mixed linear mixed effects model.

[0033] In this embodiment, multiple initial assignment strategies are employed to generate multiple sets of initial clustering labels, and multiple rounds of optimization are performed in parallel. Finally, the optimal candidate model is selected as the initialization result based on the BIC criterion. This strategy effectively alleviates the sensitivity of the EM algorithm to initial values ​​and reduces the risk of getting trapped in local optima. By exploring from multiple starting points, the probability of finding the global optimum is increased, significantly improving the robustness of the algorithm and the stability of parameter estimation.

[0034] Step S3: Calculate the posterior statistic of the observed data based on the current parameters of the t-mixed linear mixed effects model; In this embodiment, based on the current parameters of the model The conditional expectation of all missing information is calculated. Posterior statistics are the expectation or probability of latent variables given the current model parameters and observed data; these statistics are the core output of the E-step of the EM algorithm. In the first iteration, the current parameters refer to the initialized model parameters; in subsequent iterations, the current parameters refer to the updated model parameters after the previous iteration.

[0035] Optionally, the posterior statistic includes the posterior probability, the conditional expectation of the scaling variable, and the conditional expectation of the random effect.

[0036] Among them, the posterior probability Given the current model parameters and the Observation data of one observation object Under the conditions, this sample belongs to the first... The probability of each component. When calculating the posterior probability, firstly, based on the current model parameters, calculate the probability density of each observed data point under each component in the t-mixed linear mixed-effects model; based on the probability density and the mixing ratio parameters of the current t-mixed linear mixed-effects model, calculate the posterior probability of each observed data point belonging to each component; calculate using the following formula: ; in, For the first Current estimate of the vector of fixed effects coefficients for each component. For the first Current estimate of the covariance matrix of the random effects of each component. For the first Current estimates of the degrees of freedom parameters of the component t-distribution. , and That is, the current model parameters . This represents the number of valid components in the current iteration. For probability density, This is the mixing ratio parameter.

[0037] Conditional expectation of scaling variables It is a latent variable introduced into the scaled mixture representation of the t-distribution. Following a gamma distribution, its conditional expectation can be considered an observed quantity within the EM framework, transforming the difficult-to-solve t-distribution problem into a normal distribution problem. When calculating the conditional expectation of the scaling variable, based on the aforementioned posterior probability and the degrees of freedom parameters of the t-distribution for each component in the current t-mixed linear mixed effects model, the conditional expectation of the scaling variable is calculated using the following formula: ; in, For the first The number of repeated observations of an object, i.e., the dimension of the response vector; For the first Current estimates of the variance of the component error; For the first The squared Mahalanobis distance of each sample under the j-th component. This calculation is an important part of the E-step, although the posterior probability is not explicitly included in the formula. ,but Calculation and The calculations are all based on the same set of current parameters, and will with Together, they serve as sufficient statistics for subsequent M-step parameter updates.

[0038] Conditional expectation of random effects and its covariance Given component attribution and observational data, the random effects of latent variables are considered. The optimal estimate and its uncertainty measure. When calculating the conditional expectation of the random effect, the conditional expectation of the random effect is calculated based on the posterior probability and the mixed-effects structure parameters of the current t-mixed linear mixed-effects model. Conditional expectation of random effect. and its covariance Calculated using the following formula: ; ; Among them, the conditional expectation of random effects In the calculation formula, the posterior probability is based on the fact that the calculation is performed for each component. And estimate based on the current parameters of the component. , and These conditions are performed independently, and their expected values ​​are... In subsequent M-step updates, it will be compared with the posterior probability. Weighted combinations are used to update the overall parameters of each component. That is, the calculated... , It will serve as a sufficient statistic for updating all parameters in the M-step of the EM algorithm.

[0039] In this embodiment, the t-distribution is used as the joint distribution of the error and random effects of the mixture components, and latent variables and conditional expectations are introduced through a scale mixture representation. The calculation transforms the t-distribution into a normal distribution, facilitating the analytical expression for parameter estimation. This improves the model's robustness, making it less sensitive to outliers or isolated points in the data and avoiding excessive influence on parameter estimation. Furthermore, the adjustable degrees of freedom of the t-distribution allow it to adapt to data distributions with varying degrees of fat tails, enhancing the model's fitting flexibility and applicability.

[0040] Step S4: Based on the posterior statistic, update the parameters of the t-mixed linear mixed effects model by maximizing a preset objective function. The preset objective function includes a penalty term acting on the mixing ratio parameter of the t-mixed linear mixed effects model. The strength of the penalty term increases as the value of the mixing ratio parameter decreases. In this embodiment, this step is the M-step in the EM algorithm, and its purpose is to maximize the conditional expectation of the complete data log-likelihood with a penalty term added. The preset objective function is a function used to guide parameter updates, consisting of the conditional expectation of the complete data log-likelihood and the penalty term. The penalty term acts on the mixing ratio vector. Functions on the above have the characteristic of being able to handle smaller values. Applying a greater penalty intensity reduces the mixing ratio of unimportant components to zero.

[0041] Optionally, refer to Figure 3 The steps to update model parameters by maximizing the objective function include the following: Step S410: Based on the posterior statistic, calculate the conditional expectation of the log-likelihood of the complete data; In this embodiment, the posterior statistic is calculated based on step S3. , Calculate the conditional expectation of the log-likelihood function of the complete data given the observed data and the current parameter estimates, which is... ,in This represents the set of parameters to be updated. The function is the objective function of the M-step EM algorithm, and its specific form is determined by the model definition and the calculated posterior statistics.

[0042] Step S420: Based on the conditional expectation, add a penalty term to the mixing ratio parameter of the t-mixed linear mixed effect model to form a preset objective function; In this embodiment, Based on the function, a penalty term acting on the mixing ratio parameter is introduced to form a penalized objective function. Specifically, it includes the following steps: Step S421: Obtain the penalty intensity adjustment parameters; In this embodiment, the penalty intensity adjustment parameter A positive number that controls the overall strength of the penalty. The larger the value, the stronger the driving force for sparsification of the mixing ratio, and the fewer effective components the final model may have.

[0043] Optionally, penalty intensity adjustment parameters This can be determined through the following adaptive process: providing a set of candidate values, for example, in the interval... Selected at logarithmic intervals Each value constitutes a set. For each candidate value By executing the complete process of the method of this invention, the corresponding model is obtained. Calculate each model Bayesian information criterion value Ultimately, the selection makes smallest This serves as the optimal penalty intensity adjustment parameter. This is an external selection process.

[0044] Specifically, a set of candidate values ​​is provided. For each candidate value Substitute it into the penalty item Then, complete steps S2 to S6 to obtain a corresponding evaluation model. Each model is calculated according to the Bayesian information criterion. BIC value: , in, Let be the number of free parameters for each component in the t-mixed linear mixed-effects model. Specifically, ,in The number of fixed effects coefficients. For the random effects dimension.

[0045] Candidate values ​​that will generate the minimum BIC value The optimal penalty intensity adjustment parameter was determined to be... .

[0046] Step S422: Based on the penalty intensity adjustment parameter, construct a penalty term function, wherein the output value of the penalty term function increases as the input mixing ratio parameter value decreases; In this embodiment, the penalty term applies a greater penalty intensity to the components with smaller values ​​in the mixing ratio parameter than it applies to the components with larger values. The penalty intensity is adjusted based on the penalty intensity parameter. Construct the penalty term function, as shown in the following equation: , in, The number of observed objects, The penalty intensity adjustment parameter, Let be the number of free parameters for each component in the t-mixed linear mixed-effects model. For a preset minimum positive number, The number of effective components in the current iteration. For the first The mixing ratio parameters of each component.

[0047] Step S423: Add the penalty term function to the conditional expectation to form the preset objective function.

[0048] In this embodiment, the penalty item is... The conditional expectation calculated in step S410 Adding them together forms the preset objective function to be maximized. : .

[0049] In this embodiment, a penalty term for the mixing ratio is introduced into the expectation of the log-likelihood of the complete data. This penalty term applies a stronger penalty to smaller mixing ratios, causing redundant components to shrink towards zero during iterations. This achieves model sparsity and automatically identifies and eliminates components that contribute little to the model. Combined with adaptive selection of the penalty strength parameter using the BIC criterion, it effectively balances model goodness of fit and complexity, improving the automation and consistency of model selection.

[0050] Step S430: By maximizing the preset objective function, obtain the updated parameters of the t-mixed linear mixed effect model; In this embodiment, by maximizing To update all parameters.

[0051] Optionally, the mixing ratio parameter Update value Determine by the following formula: , in, The first one calculated in step S3 The observation belongs to the first The posterior probability of each component. This represents the number of valid components at the start of this iteration. This calculation shows that if the sum of the posterior probabilities of all observations belonging to a certain component is less than a threshold... Its mixing ratio will be set to zero, thus enabling automatic removal during iteration.

[0052] Optionally, fixed effects parameters The update is determined by the following formula: ; Optionally, the error variance parameter The update is determined by the following formula: ; in, .

[0053] Optionally, the random effects covariance parameter Update using the following formula: ; Optionally, the t-distribution degree of freedom parameters Update using the following formula: , in, For the Digamma function, The conditional expectation of the scaling variable calculated in step S3. The value of the previous iteration. For the first The number of repeated observations of each observation object.

[0054] Step S5: Remove components whose mixing ratio parameter value is zero after the update, reorganize the parameter structure of the current parameter of the t-mixing linear mixture effect model, and update the number of effective components in the t-mixing linear mixture effect model; In this embodiment, after each M-step parameter update, the mixed components that become unimportant during the iteration process are dynamically identified and removed to gradually simplify the model and finally determine the correct number of components.

[0055] Optionally, based on the identification of zero-value components, to further improve the robustness of the removal process and avoid misjudging important components that are forming due to minor fluctuations in parameter updates, a monitoring mechanism for component change trends can be introduced as an auxiliary decision-making mechanism. Specifically, the decay trend of the mixing ratio parameters of each component can be monitored; when the mixing ratio of a certain component is detected to be continuously decaying and eventually reaching zero, removal is performed. (Refer to...) Figure 4 The specific execution steps are as follows: Step S510: Monitor the changing trend of the penalty intensity of each component in the t-mixed linear mixed effect model; In this embodiment, each current active ingredient is monitored in each iteration. The trend of changing penalty intensity can be observed by examining its mixing ratio. The evaluation is indirectly based on the changing behavior during continuous iterations.

[0056] Optionally, calculate The change, or rate of change, relative to the previous iteration is used to determine whether the component is being slowly compressed or suddenly becomes unimportant.

[0057] Step S520: If it is detected that the penalty intensity of a certain component continues to decrease in multiple consecutive iterations, and the mixing ratio parameter value becomes zero after the current iteration, then remove the component. In this embodiment, the mixing ratio parameter values ​​of all current active ingredients after the update in step S4 are checked. For any component If its If the value is 0, the component is considered redundant and is marked as to be removed from the current model.

[0058] Step S530: Based on the removal result, restructure the parameter structure of the current parameters of the t-mixed linear mixed effect model and update the number of effective components so that subsequent iterations can continue to be executed based on the updated model.

[0059] In this embodiment, based on the removal decision in step S520, redundant components are removed and the remaining component parameters are reorganized to update the model, so that subsequent iterations can continue to be executed based on the updated model.

[0060] Optionally, the ingredients to be marked and removed All corresponding parameters are removed from the current model parameter set, including their mixing ratio, fixed effects coefficient, random effects covariance, error variance, and t-distribution degrees of freedom.

[0061] Optionally, the mixing ratio parameters of the remaining components are readjusted so that the sum of the mixing ratio parameters of the remaining components is 1. At the same time, the parameter array of the remaining components is reorganized to ensure the continuity of parameter indices in subsequent iterations.

[0062] In this embodiment, by combining the aforementioned zero-value removal mechanism with the optional auxiliary strategy of trend monitoring, redundant components can be automatically and stably eliminated during the iteration process. This ensures that the removal decisions have clear data basis, and observing trends enhances the interpretability and robustness of the algorithm in actual operation. After removing redundant components, the mixing ratio of the remaining components is reorganized and normalized, and the parameter structure is reorganized to maintain model integrity. This operation ensures the consistency and continuity of the model structure after each iteration, providing a stable foundation for subsequent optimization. Simultaneously, reorganization avoids the calculation of removed components, optimizes memory and computing resource usage, and improves the overall computational efficiency of the algorithm.

[0063] Step S6: Iteratively execute steps S3 to S5 until the preset convergence condition is met; In this embodiment, step E of step S3, step M of step S4, and elimination step of step S5 are repeatedly executed to form a complete iterative loop.

[0064] Optionally, the preset convergence condition can be set as follows: the increment of the log-penalized likelihood function is less than the preset tolerance; parameters The change is less than the preset tolerance; the preset maximum number of iterations is reached. When any convergence condition is met, the iteration stops and proceeds to step S7.

[0065] Step S7: Output the number of effective components and parameter estimates of each component in the converged t-mixed linear mixed effect model.

[0066] In this embodiment, the final model obtained after convergence is output, including: the final number of effective components and the estimated parameters of each component. The estimated parameters of each component include the mixing ratio. Fixed effects random effects covariance Error variance and the degrees of freedom of the t-distribution .

[0067] This application constructs an efficient and automated framework for modeling and selecting t-mixture linear mixed-effects models by introducing a series of innovative techniques, including adaptive component number selection, multi-starting-point optimal initialization, and penalized likelihood sparsification estimation. This method can directly learn the optimal component structure from the data, effectively solving problems such as sensitivity to initial values, susceptibility to local optima, the need for pre-setting component numbers, and sensitivity to outliers in related techniques. Ultimately, it significantly improves the stability of parameter estimation, computational efficiency, and automation level in practical applications while ensuring model fitting accuracy and robustness, making it particularly suitable for longitudinal or repeated measures data analysis with complex heterogeneity, intra-group correlations, and outliers.

[0068] Example 2 To verify the effectiveness and robustness of the component selection method of the t-mixed linear mixed effect model in this application, the following simulation experiments are conducted.

[0069] 1. Experimental setup: Ten sets of simulation data were generated, covering Gaussian distribution, Student's t-distribution, and contaminated Gaussian mixture distribution, with balanced and unbalanced mixing ratios set. Each set of data was simulated 100 times. Comparison methods included: (1) BIC-GMLMM: Gaussian mixture linear mixture model based on BIC to select the number of components.

[0070] (2) BIC-tMLMM: A linear mixing model of t-mixing based on the selection of the number of components by BIC.

[0071] (3) Penalty-GMLMM: Gaussian mixture linear mixture model based on the penalized likelihood framework of this invention.

[0072] (4) Penalty-tMLMM: The method of this invention.

[0073] 2. Component selectivity: exist , Under the given settings, the key results are shown in Table 1. The method of this invention (Penalty-tMLMM) correctly identifies the number of components in data with heavy tails or outliers (such as Model 9, 10). The proportion of cases where the BIC method is used is significantly higher than that of cases where the Gaussian data is contaminated. In particular, the BIC method tends to overfit (in contaminated Gaussian data). The method of this invention can effectively suppress redundant components, achieving a selection accuracy close to 100%. (See reference...) Figure 5 , Figure 5 To estimate the component numbers using four different methods on simulated contaminated Gaussian distribution data (Model 9). The distribution histogram. The true number of groups is... The estimation results of the method of this invention (Penalty-tMLMM) (marked in the figure) are highly concentrated on the correct component number 3, demonstrating extremely high selection accuracy and stability. In contrast, the BIC-based t-mixture model (BIC-tMLMM), although also mainly selecting 3 components, has a slightly more dispersed distribution. Furthermore, the estimation results of the two methods based on the Gaussian assumption (Penalty-GMLMM and BIC-GMLMM) are severely dispersed, significantly overestimating the component number (…). >3) indicates that they are extremely sensitive to outliers in the data and tend to introduce redundant components to fit outliers, leading to overfitting.

[0074] Table 1. Correct selection of component proportions under some models using different methods ( ) 3. Parameter estimation performance: Provided that the components are correctly identified, the method of this invention achieves estimation accuracy (measured by median squared error) of fixed effects coefficients, error variance, and random effects covariance that is comparable to or even better than that of standard non-penalized methods. In particular, for t-distributed data, the estimation error of Penalty-tMLMM is significantly smaller than that of models based on the Gaussian assumption (Penalty-GMLMM).

[0075] 4. Predictive performance: In tests predicting new data, the mixed-effects model framework (including GMLMM and tMLMM) showed significantly lower prediction mean squared errors than mixed regression models that ignored random effects and single-component linear mixed models. This demonstrates the advantages of the mixed-effects framework upon which this invention is based in capturing data heterogeneity and within-group correlations. Specifically, Penalty-tMLMM achieved optimal or near-optimal prediction accuracy under most simulation settings.

[0076] Example 3 The method of this invention was applied to the World Health Organization (WHO) Life Expectancy dataset. This dataset contains longitudinal observations of 133 countries over 16 years. Modeling was performed using the steps described above, with life expectancy as the response variable, and incorporating random intercepts at the national level and random slopes for HIV / AIDS infection rates and populations.

[0077] 1. Model selection and subgroup discovery: The method of this invention (Penalty-tMLMM) automatically divides the data into two potential subgroups ( Subgroup 0: Contains 30 countries including Nigeria. Subgroup 1: Contains the remaining 103 countries.

[0078] Analysis revealed a key difference between the two subgroups: in subgroup 0, the composition of income resources had a weaker impact on life expectancy. =0.2822), while the influence of school education is stronger ( =2.3428); the opposite is true in subgroup 1 ( =7.8546, =-0.2578). This finding indicates that the dominant socioeconomic factors influencing life expectancy across different national populations are heterogeneous.

[0079] 2. Predictive performance comparison: The data was randomly divided into 80% training set and 20% test set according to country. Table 2 shows the comparison of the prediction performance of each model on the test set. The method of this invention (Penalty-tMLMM) achieved the lowest mean squared error (MSE=2.9250) and mean absolute error (MAE=0.9845), as well as an R-value closest to 1. 2 The index indicates that its predictive accuracy is superior to all the comparative models, including the BIC-based tMLMM, the single-component robust linear mixture model (tLMM), and the t-mixture regression model (tMR) that ignores random effects.

[0080] Table 2: Comparison of the predictive performance of WHO life expectancy data The simulation experiments and real data analysis described above demonstrate that the penalized likelihood-based t-mixed linear mixed-effects modeling and selection method provided in this invention can automatically and accurately determine the number of heterogeneous subgroups in the data, and achieve robust and accurate parameter estimation in the process. Ultimately, the model exhibits superior performance in predicting unknown data, and is particularly suitable for handling real-world data with complex hierarchical structures, heavy-tailed distributions, or outliers.

[0081] Example 4 In the embodiments of this application, a component selection device for a t-mixed linear mixing effect model is proposed.

[0082] Reference Figure 6 , Figure 6 This is a schematic diagram of the terminal structure of the hardware operating environment involved in one embodiment of this application.

[0083] like Figure 6 As shown, the control terminal may include: a processor 1001, such as a CPU, a network interface 1003, a memory 1004, and a communication bus 1002. The communication bus 1002 is used to enable communication between these components. The network interface 1003 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1004 may be high-speed RAM or stable non-volatile memory, such as disk storage. Alternatively, the memory 1004 may be a storage device independent of the aforementioned processor 1001.

[0084] Those skilled in the art will understand that Figure 6 The terminal structure shown does not constitute a limitation on the terminal and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0085] like Figure 6As shown, the memory 1004, which serves as a computer storage medium, may include an operating system, a network communication module, and a component selection program for a t-mixed linear mixed-effects model.

[0086] exist Figure 6 In the component selection device hardware structure of the t-mixed linear mixed-effects model shown, the processor 1001 can call the component selection program of the t-mixed linear mixed-effects model stored in the memory 1004 and perform the following operations: Step S1: Obtain observation data; Step S2: Initialize the t-mix linear mixture effect model, wherein the initial number of components of the t-mix linear mixture effect model is an integer greater than 1; Step S3: Calculate the posterior statistic of the observed data based on the current parameters of the t-mixed linear mixed effects model; Step S4: Based on the posterior statistic, update the parameters of the t-mixed linear mixed effects model by maximizing a preset objective function. The preset objective function includes a penalty term acting on the mixing ratio parameter of the t-mixed linear mixed effects model. The strength of the penalty term increases as the value of the mixing ratio parameter decreases. Step S5: Remove components whose mixing ratio parameter value is zero after the update, reorganize the parameter structure of the current parameter of the t-mixing linear mixture effect model, and update the number of effective components in the t-mixing linear mixture effect model; Step S6: Iteratively execute steps S3 to S5 until the preset convergence condition is met; Step S7: Output the number of effective components and parameter estimates of each component in the converged t-mixed linear mixed effect model.

[0087] Optionally, the processor 1001 may call the component selection program of the t-mixture linear mixed-effects model stored in the memory 1004, and further perform the following operations: Monitor the changing trends of the penalty intensity of each component in the t-mixed linear mixed effect model; If the mixing ratio parameter of a certain component is detected to decrease continuously in multiple iterations, and the value of the mixing ratio parameter becomes zero after the current iteration, then the component is removed. Based on the removal results, the parameter structure of the current parameters of the t-mixed linear mixed-effects model is restructured, and the number of effective components is updated so that subsequent iterations can continue to be performed based on the updated model.

[0088] Optionally, the processor 1001 may call the component selection program of the t-mixture linear mixed-effects model stored in the memory 1004, and further perform the following operations: Based on the current parameters, calculate the probability density of each observation data under each component in the t-mixed linear mixed effect model; Based on the probability density and the mixing ratio parameters of the current t-mixed linear mixed effect model, calculate the posterior probability of each observed data belonging to each component; Based on the posterior probability and the t-distribution degrees of freedom parameters of each component in the current t-mixed linear mixed effects model, calculate the conditional expectation of the scaling variable; Based on the posterior probability and the mixed-effects structure parameters of the current t-mixed linear mixed-effects model, the conditional expectation of the random effects is calculated.

[0089] Optionally, the processor 1001 may call the component selection program of the t-mixture linear mixed-effects model stored in the memory 1004, and further perform the following operations: Based on the posterior statistic, calculate the conditional expectation of the log-likelihood of the complete data; Based on the conditional expectation, a penalty term is added to the mixing ratio parameter of the t-mixed linear mixed effect model to form a preset objective function; By maximizing the preset objective function, the updated parameters of the t-mixed linear mixed effect model are obtained; Wherein, the penalty term applies a greater penalty intensity to the component with a smaller value in the mixing ratio parameter than it applies to the component with a larger value.

[0090] Optionally, the processor 1001 may call the component selection program of the t-mixture linear mixed-effects model stored in the memory 1004, and further perform the following operations: Obtain the penalty intensity adjustment parameters; Based on the penalty intensity adjustment parameter, a penalty term function is constructed, wherein the output value of the penalty term function increases as the input mixing ratio parameter value decreases; The penalty function is added to the conditional expectation to form the preset objective function.

[0091] Optionally, the processor 1001 may call the component selection program of the t-mixture linear mixed-effects model stored in the memory 1004, and further perform the following operations: Obtain a set of candidate values ​​for the penalty intensity adjustment parameters; Based on each candidate value, construct the penalty term function and execute steps S2 to S6 to obtain the corresponding evaluation model; Calculate the Bayesian information criterion value for each of the evaluation models based on the Bayesian information criterion. The candidate values ​​that generate the optimal Bayesian information criterion value will be used as the obtained penalty intensity adjustment parameters.

[0092] Optionally, the processor 1001 may call the component selection program of the t-mixture linear mixed-effects model stored in the memory 1004, and further perform the following operations: Multiple initial component allocation strategies are employed to generate multiple sets of initial cluster labels for the observed data; For each set of initial cluster labels, a set of parameters of the mixed-effects model are independently initialized to form multiple initial parameter sets; For each of the multiple initial parameter sets, the iterative optimization process from step S3 to step S6 is executed independently to obtain multiple candidate models; Based on the preset model selection criteria, an optimal model is selected from the multiple candidate models as the initialized t-mixed linear mixed effect model.

[0093] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0094] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0095] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0096] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0097] It should be noted that any reference signs placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. This application can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In a unit claim enumerating several means, several of these means may be embodied by the same item of hardware. The use of the words first, second, third, etc., does not indicate any order. These words can be interpreted as names.

[0098] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0099] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of the invention. Therefore, if these modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include these modifications and variations.

Claims

1. A component selection method of a t-mixture linear mixture effect model, characterized by, The method includes: Step S1: Obtain observation data; Step S2: Initialize the t-mix linear mixture effect model, wherein the initial number of components of the t-mix linear mixture effect model is an integer greater than 1; Step S3: Calculate the posterior statistic of the observed data based on the current parameters of the t-mixed linear mixed effects model; Step S4: Based on the posterior statistic, update the parameters of the t-mixed linear mixed effects model by maximizing a preset objective function. The preset objective function includes a penalty term acting on the mixing ratio parameter of the t-mixed linear mixed effects model. The strength of the penalty term increases as the value of the mixing ratio parameter decreases. Step S5: Remove components whose mixing ratio parameter value is zero after the update, reorganize the parameter structure of the current parameter of the t-mixing linear mixture effect model, and update the number of effective components in the t-mixing linear mixture effect model; Step S6: Iteratively execute steps S3 to S5 until the preset convergence condition is met; Step S7: Output the number of effective components and parameter estimates of each component in the converged t-mixed linear mixed effect model.

2. The method as described in claim 1, characterized in that, Step S5 includes: Monitor the changing trends of the penalty intensity of each component in the t-mixed linear mixed effect model; If the mixing ratio parameter of a certain component is detected to decrease continuously in multiple iterations, and the value of the mixing ratio parameter becomes zero after the current iteration, then the component is removed. Based on the removal results, the parameter structure of the current parameters of the t-mixed linear mixed-effects model is restructured, and the number of effective components is updated so that subsequent iterations can continue to be performed based on the updated model.

3. The method according to claim 1, characterized in that, Step S3 includes: Based on the current parameters, calculate the probability density of each observation data under each component in the t-mixed linear mixed effect model; Based on the probability density and the mixing ratio parameters of the current t-mixed linear mixed effect model, calculate the posterior probability of each observed data belonging to each component; Based on the posterior probability and the t-distribution degrees of freedom parameters of each component in the current t-mixed linear mixed effects model, calculate the conditional expectation of the scaling variable; Based on the posterior probability and the mixed-effects structure parameters of the current t-mixed linear mixed-effects model, calculate the conditional expectation of the random effects; The posterior probability, the conditional expectation of the scaling variable, and the conditional expectation of the random effect are the posterior statistics.

4. The method as described in claim 1, characterized in that, Step S4 includes: Based on the posterior statistic, calculate the conditional expectation of the log-likelihood of the complete data; Based on the conditional expectation, a penalty term is added to the mixing ratio parameter of the t-mixed linear mixed effect model to form a preset objective function; By maximizing the preset objective function, the updated parameters of the t-mixed linear mixed effect model are obtained; Wherein, the penalty term applies a greater penalty intensity to the component with a smaller value in the mixing ratio parameter than it applies to the component with a larger value.

5. The method as described in claim 4, characterized in that, The step of adding a penalty term to the mixing ratio parameter of the t-mixed linear mixed-effects model based on the expected condition to form a preset objective function includes: Obtain the penalty intensity adjustment parameters; Based on the penalty intensity adjustment parameter, a penalty term function is constructed, wherein the output value of the penalty term function increases as the input mixing ratio parameter value decreases; The penalty function is added to the conditional expectation to form the preset objective function.

6. The method as described in claim 5, characterized in that, The penalty intensity adjustment parameter is adaptively determined from a set of candidate values ​​using a Bayesian information criterion; wherein the candidate values ​​are a plurality of pre-set discrete values ​​greater than zero.

7. The method as described in claim 1, characterized in that, The step of initializing the t-mixed linear mixed-effects model in step S2 includes: Multiple initial component allocation strategies are employed to generate multiple sets of initial cluster labels for the observed data; For each set of initial cluster labels, a set of parameters of the mixed-effects model are independently initialized to form multiple candidate initial parameter sets; Based on a preset model selection criterion, an optimal parameter set is selected from the multiple candidate initial parameter sets as the initial parameters of the initial t-mixed linear mixed effect model.

8. The method as described in claim 5, characterized in that, The penalty term function is constructed as follows: ， Where n is the number of observed objects, The penalty intensity adjustment parameter, Let be the number of free parameters for each component in the t-mixed linear mixed-effects model. For a preset minimum positive number, The number of effective components in the current iteration. For the first The mixing ratio parameters of each component.

9. The method as described in claim 4, characterized in that, In the step of obtaining the updated parameters of the t-mixed linear mixed effects model, the first... Mixing ratio parameters of each component Update value Determine by the following formula: ， in, For the i-th observed object calculated in step S3, it belongs to the i-th observation object. The posterior probability of each component. This represents the number of effective components at the start of this iteration.

10. The method as described in claim 3, characterized in that, The t-distribution degree of freedom parameter of the first t-distribution degrees of freedom parameters of each component Update by solving the following equation: ， in, For the Digamma function, The conditional expectation of the scaling variable calculated in step S3. The value of the previous iteration. For the first The number of repeated observations of each observation object.

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