Ultra-high-dimensional data model-free variable selection method based on sufficient dimension reduction

Abstract

The invention relates to the technical field of variable selection, and discloses an ultra-high-dimensional data model-free variable selection method based on sufficient dimension reduction, which comprises the following steps of: searching an optimal regularization parameter for each column of an SAVE sufficient dimension reduction space, performing Lasso estimation on each column of the SAVE sufficient dimension reduction space to obtain an estimated matrix, and selecting the optimal regularization parameter for each column of the SAVE sufficient dimension reduction space; norms of all rows of the metabolite of the subject in the corrected matrix are extracted and arranged from large to small according to the norms, and a previous effective variable is obtained. According to the method, the difference between a metabolite covariance matrix and a slice covariance matrix is calculated through a full sample, signals of core effective variables are converted into features with extremely high identification degree in a U matrix, a preposition is stabilized on a lithotripsy map, interference of noise and dimension expansion is avoided, and a foundation is laid for TPR improvement and FPR reduction.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of variable selection, in particular to a model-free variable selection method for super-high-dimensional data based on sufficient dimension reduction. BACKGROUND

[0002] In the field of precision medicine, variable selection of metabolomics data is the key to cracking the mechanism of disease. From the early detection of 50 core metabolites (p=50), to the intermediate screening of 500 broad-spectrum metabolites (p=500), to the current 2000 full-spectrum metabolomics analysis (p=2000), the continuous increase in data dimensions makes it more urgent to capture non-linear interaction variables. The target variables (such as type 2 diabetes risk score, blood glucose control level, and metabolic disorder degree) are all continuous variables, which further highlights the limitations of traditional methods: The existing mainstream variable selection methods (such as SIR, Lasso, etc.) face double bottlenecks: on the one hand, interaction variable capture fails - SIR can only handle linear main effects, and cannot see the core interaction signals such as metabolite A x metabolite B metabolite C 2 x metabolite D that drive the changes in continuous target variables; on the other hand, dimension adaptation and evaluation are misaligned - traditional Lasso is prone to over-regularization in low-dimensional (p=50) scenarios, leading to the omission of interaction signals, and in medium-high-dimensional (p=500) scenarios, global λ cannot adapt to the heterogeneity between columns, introducing a lot of noise. In the super-high-dimensional (p=2000) scenario, either the sample size (n=300) is much smaller than the dimension, leading to model overfitting, or the split training / validation set completely loses the scarce interaction signals; more importantly, traditional methods are mostly adapted to binary classification tasks, and it is difficult to accurately measure the selection effect with core evaluation indicators (TPR, FPR) in continuous variable scenarios.

[0003] The experience of a certain medical research team is highly representative: they began tracking metabolomics data for type 2 diabetes in 2018, with the target variable being a continuous glycemic control score (0-10, with higher scores indicating worse control). The data dimension was gradually upgraded from the initial p=50 to p=2000, and through previous basic experiments, they had identified 10 core effective variables (including 4 key interaction terms) as the core drivers of changes in glycemic levels. However, traditional methods consistently failed to reliably capture these variables—at p=50, SIR only identified 3 linear variables, completely missing the 10 core effective variables. Of the 7 candidates, the TPR was only 30% and the FPR was as high as 45%. At p=500, the traditional Lasso method screened out 47 candidate variables, of which only 2 of the 10 core variables were included, the TPR dropped to 20% and the FPR was still 38%. In the full spectrum analysis stage at p=2000, the existing method completely failed: none of the 10 core variables appeared in the screening results, the TPR approached 0 and the FPR soared to 52%, and the ranking of effective variables on the scree plot was masked by a lot of noise. The study fell into the dilemma that the higher the dimension, the more difficult it was to identify the core signal and the worse the evaluation effect. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a model-free variable selection method for ultra-high dimensional data based on sufficient dimensionality reduction, which has advantages such as being unaffected by noise and dimensionality expansion, and solves the aforementioned technical problems.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a model-free variable selection method for ultra-high dimensional data based on sufficient dimensionality reduction, comprising the following steps: S1: Obtain the global covariance matrix of metabolites from all subjects and The covariance matrix of each blood glucose level slice was obtained and concatenated with auxiliary variables. Based on auxiliary variables Constructing a fully dimensionality-reduced SAVE space ; S2: Dimensionally reduce the space of SAVE in S1. Find the optimal regularization parameter for each column ; S3: Optimal regularization parameters obtained in S2 Fully reduce the dimensionality of SAVE Lasso estimation is performed on each column to obtain the estimated matrix. ; S4: Extracting subject metabolites from the corrected matrix All rows norm, and based on Arrange the norms from largest to smallest; S5: Based on the RRE algorithm, extract subject metabolites into the corrected matrix. All rows The norm is used for filtering to obtain the first... One effective variable.

[0006] As a preferred technical solution of the present invention, the SAVE fully reduces the dimensionality space. The specific expression is as follows:

[0007] in, Represents the global covariance matrix. Let the covariance matrix of the h-th blood glucose level slice be denoted as . A set representing slices of blood glucose levels. This represents the inverse of the global covariance matrix.

[0008] As a preferred embodiment of the present invention, step S2 includes the following steps: S2.1: Optimize the dimensionality reduction space of SAVE by the number of slices based on blood glucose levels. Divided into Different groups; S2.2: For The mean of the same column in each group is aggregated to obtain the comprehensive training signal; S2.3: Traversal The candidate set is used to train the columns to be estimated by integrating the training signals, and the fitting loss is calculated for the groups in S2.2 that did not participate in the mean aggregation. S2.4: Select the one with the minimum loss as the optimal regularization parameter. .

[0009] As a preferred embodiment of the present invention, the specific expression for mean aggregation in S2.2 is as follows:

[0010] in, The segment represents the first Columns in the same position, This represents the aggregated training signal after mean aggregation.

[0011] As a preferred technical solution of the present invention, the traversal in S2.2 The candidate set, trained by integrating training signals, is specifically expressed as follows:

[0012] in, The column to be estimated is indicated by the superscript. Indicates transpose. express The 1 norm, The global covariance matrix is ​​represented and solved using the ADMM algorithm.

[0013] As a preferred embodiment of the present invention, the specific expression for the fitting loss in S2.3 is as follows:

[0014] in, Indicates the fitting loss, superscript Indicates transpose. Represents the global covariance matrix. express The corresponding column.

[0015] As a preferred technical solution of the present invention, the S3 method fully reduces the dimensionality of SAVE. Lasso estimation is performed on each column to obtain the estimated matrix. The expression is as follows:

[0016] in, express The List, Represents an auxiliary variable, and , This indicates that SAVE represents the full dimensionality reduction space. The List, This represents the estimation result obtained by minimization. This represents the estimate of the sample covariance matrix. express 3D space.

[0017] Compared with existing technologies, this invention provides a model-free variable selection method for ultra-high-dimensional data based on sufficient dimensionality reduction, which has the following beneficial effects: 1. This invention calculates the difference between the metabolite covariance matrix and the slice covariance matrix by the full sample, and transforms the signal of the core effective variable into a highly identifiable feature in the U matrix. No matter how the dimensionality increases, the signal strength of the variable always leads and remains at the top on the scree plot. It is not affected by noise and dimensionality expansion, which lays the foundation for improving TPR and reducing FPR.

[0018] 2. Unlike the global unified λ of traditional Lasso, this invention uses Group-CV, which is split according to the signal dimension, to select the optimal regularization parameter column by column and automatically adapt the core effective variables to mild regularization, thus preserving their interaction signals; it automatically strengthens regularization for massive noise variables to suppress redundant information; at the same time, the batch processing mechanism greatly improves the computational efficiency of ultra-high dimensional data. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of a low-dimensional scene according to the present invention; Figure 3 This is a schematic diagram of a high-dimensional scene in this invention; Figure 4 This is a schematic diagram of the ultra-high-dimensional scene of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Please see Figures 1-4 A model-free variable selection method for ultra-high dimensional data based on sufficient dimensionality reduction includes the following steps: S1: Obtain the global covariance matrix of metabolites from all subjects and The covariance matrix of each blood glucose level slice was obtained and concatenated with auxiliary variables. Based on auxiliary variables Constructing a fully dimensionality-reduced SAVE space ; S2: Dimensionally reduce the space of SAVE in S1. Find the optimal regularization parameter for each column ; S3: Optimal regularization parameters obtained in S2 Fully reduce the dimensionality of SAVE Lasso estimation is performed on each column to obtain the estimated matrix. ; S4: Extracting subject metabolites from the corrected matrix All rows norm, and based on Arrange the norms from largest to smallest; S5: Based on the RRE algorithm, extract subject metabolites into the corrected matrix. All rows The norm is used for filtering to obtain the first... There are one valid variable, and the specific expression is as follows:

[0022] in, This represents the index corresponding to the minimum value. express, Indicates the first row norm, To indicate that the variable is a constant, the specific expression is as follows:

[0023] in, Indicates the noise variance. Indicates the dimension of the variable. This represents the total number of samples.

[0024] SAVE provides ample dimensionality reduction space. The specific expression is as follows:

[0025] in, Represents the global covariance matrix. Let the covariance matrix of the h-th blood glucose level slice be denoted as . A set representing slices of blood glucose levels. This represents the inverse of the global covariance matrix.

[0026] S2 includes the following steps: S2.1: Optimize the dimensionality reduction space of SAVE by the number of slices based on blood glucose levels. Divided into Different groups; S2.2: For The mean of the same column in each group is aggregated to obtain the comprehensive training signal; S2.3: Traversal The candidate set is used to train the columns to be estimated by integrating the training signals. The fitting loss is calculated for the groups in S2.2 that did not participate in mean aggregation. For this fixed slice grouping in the traversal process, only the parameter candidate set is traversed. For example, if there are 5 candidate parameters, the loss under 5 different candidate parameters is calculated, and the parameter with the smallest loss is selected. The logic of this fixed grouping is to first determine which slice and column the column to be estimated belongs to. For example, if the column to be estimated belongs to the 3rd column of the 2nd slice, the 3rd columns of the other slices are used for mean aggregation. The column to be estimated is used to calculate the fitting loss. S2.4: Select the one with the minimum loss as the optimal regularization parameter. .

[0027] The specific expression for mean aggregation in S2.2 is as follows:

[0028] in, The segment represents the first Columns in the same position, This represents the aggregated training signal after mean aggregation.

[0029] Traversal in S2.2 The candidate set, trained by integrating training signals, is specifically expressed as follows:

[0030] in, The superscript indicates the column to be estimated, i.e., the column that needs to be estimated. Indicates transpose. express The 1 norm, Let the global covariance matrix be represented in the above equation. The solution is obtained using the ADMM algorithm.

[0031] The specific expression for the fitting loss in S2.3 is as follows:

[0032] in, Indicates the fitting loss, superscript Indicates transpose. Represents the global covariance matrix. express The corresponding column.

[0033] S3 provides a sufficient dimensionality reduction space for SAVE. Lasso estimation is performed on each column to obtain the estimated matrix. The expression is as follows:

[0034] in, express The List, Represents an auxiliary variable, and , This indicates that SAVE represents the full dimensionality reduction space. The List, This represents the estimate obtained by minimizing this expression. This represents the estimate of the sample covariance matrix. express 3D space.

[0035] The embodiments of this application are as follows: Adapting to the evaluation requirements of continuous variables, its innovative design allows the algorithm to accurately anchor 10 core effective variables across the entire range of p=50 to p=2000, and achieves quantitative verification through TPR and FPR, specifically addressing the three core shortcomings of traditional methods: Precise identification of core effective variables (applicable to all dimensions): The algorithm does not require a preset interaction form. It calculates the difference between the metabolite covariance matrix and the Y-slice covariance matrix of the whole sample (constructing the U matrix), and transforms the signals of 10 core effective variables (including interaction terms) into highly recognizable features in the U matrix. No matter how the dimensionality increases, the signal strength of these 10 variables always leads and remains at the top of the scree map. They are not affected by noise and dimensionality expansion, laying the foundation for TPR improvement and FPR reduction. Inter-column heterogeneity and dimensionality adaptation (seamless transition from p=50 to p=2000): Unlike the globally uniform λ of traditional Lasso, this algorithm selects the optimal regularization parameter column by column through Group-CV splitting by signal dimension—automatically adapting mild regularization for 10 core effective variables to preserve their interaction signals; automatically strengthening regularization for massive noise variables to suppress redundant information; at the same time, the batch processing mechanism greatly improves the computational efficiency of ultra-high dimensional data; Small Sample Signal Preservation and Continuous Variable Adaptation (Loss-Free in All Dimensions): Innovatively adopting CV logic that splits only the signal dimension without sample splitting, regardless of the dimensionality, the U matrix and covariance matrix are constructed using full sample data, avoiding the core signal loss caused by splitting small samples (n=300) in high-dimensional scenarios; at the same time, by aggregating the mean of multiple columns of the training group, the signal strength of the 10 core variables is further amplified, making them more significant in the prediction association of continuous variables, ensuring the stability of TPR and FPR evaluation.

[0036] Additional results: From p=50 to p=2000, the core effective variable identification remained stable and leading (reasonable decay under increased dimensionality). In the full-dimensional application of continuous variable data in type 2 diabetes metabolomics, this algorithm breaks through the dilemma that core signals completely disappear with increasing dimensionality. Within the range of p=50 to p=2000, it consistently maintains the leading position of 10 core effective variables in the scree plot. Although the effect slightly decreases with increasing dimensionality, the total renal rate (TPR) remains stable above 90%, a breakthrough that traditional methods cannot achieve. 1. Low-dimensional scenario (p=50): No core variables are omitted, TPR is maximized, FPR is zeroed; The algorithm accurately selected all 10 core effective variables, including 4 key interaction terms such as insulin × glucose triglycerides × high-density lipoprotein, without any omissions or redundancies. On the scree plot, the weight values ​​of the 10 core variables are significantly higher than those of the other 40 noise variables, ranking consistently in the top 1-10, with clear boundaries; In the validation experiment: TPR=100% (all 10 core variables were screened out), FPR=0% (no noise variables were mixed in), which is a qualitative leap compared with the traditional Lasso (TPR=20%, FPR=38%); the MAE of the prediction model is significantly reduced compared with the SIR model. 2. Mid-to-high dimensional scenarios (p=500): Core variables consistently rank highly, and TPR remains above 90%; (correspond Figure 1 Scree plot: The weights of the 10 core effective variables are still concentrated in the top 20 of the scree plot, with only a few variables slightly shifted in rank. In the validation experiment: TPR=90% (9 out of 10 core variables were identified), FPR=5% (only 2 noisy variables were mixed in, which can be quickly removed in subsequent validation), which is far better than the traditional Lasso (TPR=20%, FPR=38%). 3. Ultra-high dimensional scenario (p=2000) (the figure only shows the case of the first 1000 variables): anchoring the core in noise, TPR is maintained at 90%; corresponding Figure 2 Scree plot: The weights of the 8 core effective variables are concentrated at the top of the scree plot, while some variables are ranked lower but still lead the vast majority of noise. In the validation experiment: TPR=80%, FPR=8% (which can be removed after clinical validation), far exceeding the industry average of TPR and FPR>40% in ultra-high dimensional scenarios; The algorithm's controllable decay across all scenarios enabled the team to upgrade their research in a new dimension, ensuring that core signals did not disappear: from precise targeting at p=50, to slight decay at p=500, and then to stable leadership at p=2000, the 10 core variables remained head signals in the scree plot. Based on these 9 identified core variables, the team successfully validated 80% of the metabolic pathway mechanisms, providing core targets for subsequent intervention studies.

[0037] From p=50 to p=2000, this algorithmic innovation is not without its flaws, but it has achieved stable identification of core effective variables in high-dimensional scenarios for the first time. Even with a 40-fold increase in dimensionality, the core variables can still maintain their leading position in the scree plot, with the total potential response rate (TPR) remaining above 90%. This has enabled variable selection in high-dimensional biomedical data to move from random screening to controllable identification, promoting the feasibility of precision medicine research in the high-dimensional era.

[0038] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A model-free variable selection method for ultra-high dimensional data based on sufficient dimensionality reduction, characterized by: Includes the following steps: S1: Obtain the global covariance matrix of metabolites from all subjects and The covariance matrix of each blood glucose level slice was obtained and concatenated with auxiliary variables. Based on auxiliary variables Constructing a fully dimensionality-reduced SAVE space ; S2: Dimensionally reduce the space of SAVE in S1. Find the optimal regularization parameter for each column ; S3: Optimal regularization parameters obtained in S2 Fully reduce the dimensionality of SAVE Lasso estimation is performed on each column to obtain the estimated matrix. ; S4: Extracting subject metabolites from the corrected matrix All rows norm, and based on Arrange the norms from largest to smallest; S5: Based on the RRE algorithm, extract subject metabolites into the corrected matrix. All rows The norm is used for filtering to obtain the first... There are one valid variable, and the specific expression is as follows: ； in, This represents the index corresponding to the minimum value. express, Indicates the first row norm, Indicates the first row norm, This indicates a variable selection constant.

2. The method for selecting model-free variables for ultra-high-dimensional data based on sufficient dimensionality reduction according to claim 1, characterized in that: The SAVE fully reduces dimensionality space. The specific expression is as follows: ； in, Represents the global covariance matrix. Let the covariance matrix of the h-th blood glucose level slice be denoted as . A set representing slices of blood glucose levels. This represents the inverse of the global covariance matrix.

3. The method for selecting model-free variables for ultra-high-dimensional data based on sufficient dimensionality reduction according to claim 2, characterized in that: S2 includes the following steps: S2.1: Optimize the dimensionality reduction space of SAVE by the number of slices based on blood glucose levels. Divided into Different groups; S2.2: For The mean of the same column in each group is aggregated to obtain the comprehensive training signal; S2.3: Traversal The candidate set is used to train the columns to be estimated by integrating the training signals, and the fitting loss is calculated for the groups in S2.2 that did not participate in the mean aggregation. S2.4: Select the one with the minimum loss as the optimal regularization parameter. .

4. The method for selecting model-free variables for ultra-high-dimensional data based on sufficient dimensionality reduction according to claim 3, characterized in that: The specific expression for mean aggregation in S2.2 is as follows: ； in, The segment represents the first Columns in the same position, This represents the aggregated training signal after mean aggregation.

5. The method for selecting model-free variables for ultra-high-dimensional data based on sufficient dimensionality reduction according to claim 3, characterized in that: The traversal in S2.2 The candidate set, trained by integrating training signals, is specifically expressed as follows: ； in, The column to be estimated is indicated by the superscript. Indicates transpose. express The 1 norm, The global covariance matrix is ​​represented and solved using the ADMM algorithm.

6. The method for selecting model-free variables for ultra-high-dimensional data based on sufficient dimensionality reduction according to claim 5, characterized in that: The specific expression for the fitting loss in S2.3 is as follows: ； in, Indicates the fitting loss, superscript Indicates transpose. Represents the global covariance matrix. express The corresponding column.

7. The method for selecting model-free variables for ultra-high-dimensional data based on sufficient dimensionality reduction according to claim 6, characterized in that: The S3 section provides a sufficient dimensionality reduction space for SAVE. Lasso estimation is performed on each column to obtain the estimated matrix. The expression is as follows: ； in, express The List, Represents an auxiliary variable, and , This indicates that SAVE represents the full dimensionality reduction space. The List, This represents the estimation result obtained by minimization. This represents the estimate of the sample covariance matrix. express 3D space.

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