Unsupervised time sequence missing data filling method based on dynamic causal graph structure

Abstract

The invention discloses an unsupervised time sequence missing data filling method based on a dynamic cause and effect graph structure, which comprises the following steps: S1, collecting a data sample, and processing to obtain an initial filling complete data table; s2, clustering all the initial filling complete data tables, and selecting representative data tables; s3, constructing a sub-causal graph of each representative data table, and further constructing a total causal graph; s4, on the basis of a causal relationship in the total causal graph, constructing and training a corresponding weighted expandable depth time sequence convolutional network for the to-be-filled target feature column to obtain a missing value filling model, and further performing coarse filling on missing values; and S5, performing refined secondary filling on the target feature column by using the obtained missing value filling model to obtain a complete data table. The invention provides a filling method without real missing labels, optimization is carried out through a self-consistency or structure maintenance principle, the dynamic dependence and real causal relationship between the time series data can still be captured in a dynamic complex scene, and a better data filling effect is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of data processing technology, and specifically relates to an unsupervised time series missing data filling method based on dynamic causal structure. Background Art

[0002] The data collection process for multivariate time series often faces numerous difficulties and uncertainties across various fields. Incompleteness in a dataset can significantly undermine its reliability, leading to biases in forecasting tasks. However, in the real world, collected data is prone to missing values ​​for various reasons. These missing mechanisms are categorized into three types: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Each type reflects a different dependency between the missing data and the underlying data, which has important implications for modeling and imputation. This issue is particularly critical in medicine, where even minor imperfections can lead to serious consequences—and accurate imputation can potentially save lives. Therefore, finding a more accurate and efficient method to impute missing values ​​in multivariate time series data is a pressing and important research challenge.

[0003] In the MCAR (missing completely at random) setting, the probability of a data point being missing is independent of observed and unobserved variables. Therefore, missingness does not introduce systematic bias, and analyses performed on complete cases can draw valid inferences, albeit with some loss of statistical power. However, this strict randomness is rare in real-world datasets. The MAR mechanism is more common, assuming that missingness may depend on the observed data but not on the missing data themselves. For example, the probability of a patient missing a laboratory test may depend on age or prior diagnosis but not on unobserved test results. Under the MAR mechanism, unbiased estimates can still be obtained using likelihood-based methods or multiple imputation, as long as the observed variables associated with missingness are adequately modeled. MNAR (partial conditional random fields) is the most challenging case, where missingness is directly related to unobserved data. In this case, standard imputation techniques can lead to biased results unless the missing data mechanism is explicitly modeled. This requires strong assumptions or external information, and often sensitivity analysis.

[0004] Traditional methods for imputing missing data are usually divided into the following categories: (1) Statistical interpolation methods. Traditional methods for dealing with missing data have long been the foundation of statistical analysis, aiming to reduce bias and maintain data integrity. These methods include zero filling, mean substitution, or forward / backward imputation. These methods are easy to implement and computationally efficient, but often have difficulty capturing complex patterns in the data. Although these methods are simple and computationally inexpensive, they often underestimate the variability of the data and may introduce bias, especially when the data are not missing completely at random (MCAR).

[0005] (2) Model-based imputation methods treat missing values ​​as prediction targets and use models such as linear regression or random forests for inference. Techniques such as regression imputation or expectation maximization (EM) use statistical models to estimate missing values. For example, regression models predict missing data by observing relationships in the data. Although these methods are more accurate than simple imputation, they may overfit the data and fail to fully account for the uncertainty of the imputed values. There is also multiple imputation (MI), which reflects the uncertainty of missing data by creating multiple complete data sets with different imputed values. Each completed data set is analyzed and the results are then aggregated to produce more robust estimates. It is used in many applied research fields, especially epidemiology and health sciences.

[0006] (3) Deep learning-based methods use neural networks to model temporal and structural dependencies in time series. These methods utilize Transformers, variational autoencoders, generative adversarial networks (GANs), diffusion models, pre-trained base models (PFMs), and large language models (LLMs) to capture the underlying structure and complex temporal dynamics of time series data. By learning the true data distribution extracted from the observations, deep learning interpolation methods can generate more reliable and contextual estimates for missing data. (4) Joint learning methods can simultaneously optimize data filling and downstream tasks such as classification or prediction. By integrating these two objectives, these models not only improve performance but also make more effective use of incomplete data. However, joint learning frameworks are usually complex to train and very sensitive to task balance, which makes optimization and convergence more difficult.

[0007] While existing imputation algorithms can estimate missing values ​​based on observed data, their accuracy is often limited by the correlation between the data and the type of missingness mechanism. Missing data can cause a deviation between the observed data distribution and the target complete data distribution. This deviation can be explicitly modeled as a "missing indicator variable" in the underlying causal model. However, mining the complex causal relationships hidden among a large number of high-dimensional variables poses a significant challenge to algorithm design. Based on the principles of causal inference, the missing values ​​of a given variable can be inferred from its causal parent variables, a process that can be formalized as a robust optimization problem. Imputation based on a causal solution, i.e., utilizing the causal parent variable constructors of each missing variable in the underlying causal graph, is expected to bring new progress to missing value imputation. Furthermore, most existing imputation algorithms rely on supervised learning data, i.e., the true labels of missing values ​​are known, which is often difficult to obtain in the real world. Therefore, semi-supervised or unsupervised imputation methods applicable to unlabeled data are urgently needed. Summary of the Invention

[0008] In response to the above-mentioned deficiencies in the prior art, the unsupervised time series missing data filling method based on a dynamic causal graph structure provided by the present invention solves the problem that traditional missing data filling methods are difficult to capture the dynamic dependencies of time series data. Although the joint optimization method can simultaneously discover causal results, the strong constraints may cause the original data distribution to be distorted and rely on real value supervision, thereby affecting the accuracy of missing data filling.

[0009] In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: an unsupervised time series missing data filling method based on a dynamic causal graph structure, comprising the following steps: S1. Collect data samples from multivariate time series, construct a data table to be filled and preprocess it to obtain an initial filled complete data table; The structure of the initially filled complete data table is unified and has the same feature dimension and time length; S2. Cluster all initially filled complete data tables, and select the initially filled complete data table close to the geometric center in each cluster as the representative data table; S3. Use the improved Granger causality discovery method to construct the sub-causal graphs of each representative data table, and then construct the total causal graph; S4. Based on the causal relationship in the total causal graph, a corresponding weighted scalable deep temporal convolutional network is constructed and trained to initially fill in the target feature column to be filled in the complete data table, thereby obtaining a missing value filling model, and using it to roughly fill in the missing values ​​of the target feature column; S5. Use the missing value filling model to perform a refined secondary filling on the roughly filled target feature column to obtain a complete data table.

[0010] Furthermore, the step S1 includes the following sub-steps: S11, processing each data sample into an independent two-dimensional data table, representing the observation results of the observation object within a set time period; S12, processing each two-dimensional data table into a data table to be filled with a unified data structure; S13, filling the data table to be filled, thereby obtaining an initial filled complete data table; For the data table with all empty columns to be filled, fill all empty columns with fixed value 0 and mark all missing columns; For data tables with non-empty columns to be filled, a column-level filling model based on a linear structure is used to fill in the missing columns one by one.

[0011] Furthermore, each of the data tables to be filled is independent of each other, and in each data table to be filled: Arrange time steps in rows and observation features in columns; Have the same number of observed features and the order of the observed features is consistent; Have the same number of time steps and a fixed length of time step sequences; The interval between the time points represented by two adjacent rows is fixed.

[0012] Furthermore, in step S13, the method of using the column-level filling model based on the linear structure to fill in the missing columns one by one is specifically as follows: S31-1. Identify the data table to be filled Missing columns All consecutive missing intervals in ; S14. For missing intervals The missing sequences , divided into unilateral observable missing series and bilateral observable missing series according to their boundary observability; S15. For each missing sequence , fill in missing values ​​according to its left and right boundary values: When the missing sequence is only the left boundary If the unilaterally observable sequence is Fill in ; When the missing sequence is only the right boundary If the unilaterally observable sequence is Fill in ;in, ; When the missing sequence is a bilaterally observable missing sequence, linear interpolation is used to fill in the missing values ​​in the missing sequence. Fill in , and satisfies , , .

[0013] Furthermore, in step S3, in the process of constructing the sub-causal graphs of each representative data table using the improved Granger causality discovery method, a dynamic lower bound threshold is set to screen the potential causal relationships in the representative data table, and a block perturbation optimization method based on data characteristics is used to verify the screened causal relationships; Among them, the dynamic lower threshold for: Where, Indicates the front of the data Quantile, represents the mean score, represents the standard deviation, represents the coefficient for adjusting the standard deviation weight, The coefficient representing the range of control scores; Among them, the block perturbation optimization method based on data characteristics is: Input the time series series in the causal relationship and the block size block_size. Divide the time series series into consecutive blocks according to block_size, randomly shuffle the blocks, and splice the shuffled blocks into the new order.

[0014] Furthermore, in step S3, the method for constructing the total causal graph based on the sub-causal graph is specifically as follows: S31. Add all the causal graphs element by element to get the cumulative causal support matrix , represents the i-th sub-causal graph, and N represents the total number of sub-causal graphs; The cumulative causal support matrix Elements Indicates that in all the data tables to be filled, Is the feature The cumulative support strength of the causal parent of each feature; S32. Cumulative Causal Support Matrix For each column in the Positions, and set their corresponding values ​​to 1, and the values ​​of the remaining positions to 0, thus obtaining a binary causal graph As a total causal diagram.

[0015] Furthermore, the step S4 includes the following sub-steps: S41, for the initially filled complete data table, selecting the target feature column to be filled; S42. Determine the corresponding causal parent feature based on the causal relationship of each target feature listed in the overall causal graph; S43. Concatenate the target feature column with its corresponding causal parent feature to form an input sub-table, and use the target feature column as a prediction label to construct a training dataset. S44. Using the training data set, the constructed weighted expandable deep temporal convolutional network is trained to obtain a missing value filling model; S45. Use the missing value filling model to roughly fill in the missing values ​​of the target feature column.

[0016] Furthermore, the step S5 includes the following sub-steps: S51, calling the missing value filling model corresponding to the target feature column of the rough filling; S52. Input the target feature column and its three causal parent feature columns in the total causal graph into the missing value filling model, and output the complete prediction sequence of the target feature column; S53, identifying the original missing position in the target feature column according to the missing position mark in the data table to be filled; S54. For the original missing position in the target feature column, the initial filling value in the initial filling complete data table is replaced with the corresponding prediction value in the complete prediction sequence, thereby obtaining a complete data table.

[0017] The beneficial effects of the present invention are: 1. This paper adopts a structured two-stage filling strategy in the initial pre-filling stage, proposes a column-level missing pattern recognition scheme, implements zero-value filling and masking for completely empty columns to prevent noise propagation, and intelligently selects linear interpolation or mode filling based on boundary observability to improve the accuracy and robustness of initial filling.

[0018] 2. This paper proposes a method for selecting the center prototype of the initial data table to be completed based on K-Means clustering. By clustering the consistency of the time series data matrix, various geometric center samples are selected as causal learning prototypes, which effectively alleviates the data dimension explosion problem in the causal learning stage and enhances the stability of subsequent causal inference.

[0019] 3. This paper designs a temporal causal discovery method that integrates dynamic lower bound threshold setting and block perturbation optimization strategy. The introduction of dynamic lower bound threshold and block perturbation verification mechanism optimizes the recognition accuracy of temporal causal relationships, making the causal discovery process more adaptable and reliable.

[0020] 4. This paper adopts a self-consistent unsupervised filling strategy, which performs joint optimization using only the missing data itself without the need for real-value reference. During the filling process, the causal structure and trend of the data are explicitly maintained, and the causal graph structure is iteratively optimized to ultimately form a globally robust causal representation, ensuring that the filling results have both data consistency and causal interpretability. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a flow chart of the unsupervised time series missing data filling method based on the dynamic causal graph structure provided by the present invention.

[0022] Figure 2 This is a structural diagram of the unsupervised time series infill framework SCIT provided by the present invention. DETAILED DESCRIPTION

[0023] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0024] The embodiment of the present invention provides an unsupervised time series missing data filling method based on a dynamic causal graph structure, such as Figure 1 As shown, the following steps are included: S1. Collect data samples from multivariate time series, construct a data table to be filled and preprocess it to obtain an initial filled complete data table; The structure of the initially filled complete data table is unified and has the same feature dimension and time length; S2. Cluster all initially filled complete data tables, and select the initially filled complete data table close to the geometric center in each cluster as the representative data table; S3. Use the improved Granger causality discovery method to construct the sub-causal graphs of each representative data table, and then construct the total causal graph; S4. Based on the causal relationship in the total causal graph, a corresponding weighted scalable deep temporal convolutional network is constructed and trained to initially fill in the target feature column to be filled in the complete data table, thereby obtaining a missing value filling model, and using it to roughly fill in the missing values ​​of the target feature column; S5. Use the missing value filling model to perform a refined secondary filling on the roughly filled target feature column to obtain a complete data table.

[0025] Based on the above missing data filling method, an unsupervised temporal filling framework (Self-ConsistentImputation with Temporal causality, referred to as SCIT) is proposed. Figure 2 shown.

[0026] Step S1 of the embodiment of the present invention includes the following sub-steps: S11, processing each data sample into an independent two-dimensional data table, representing the observation results of the observation object within a set time period; S12, processing each two-dimensional data table into a data table to be filled with a unified data structure; S13, filling the data table to be filled, thereby obtaining an initial filled complete data table; For the data table with all empty columns to be filled, fill all empty columns with fixed value 0 and mark all missing columns; For data tables with non-empty columns to be filled, a column-level filling model based on a linear structure is used to fill in the missing columns one by one.

[0027] In this embodiment, each of the to-be-filled data tables is independent of each other, and in each to-be-filled data table: Arrange time steps by rows and observation features by columns, that is, the number of rows = the number of observation time steps, the number of columns = the number of observation features; Have the same number of observation features (consistent number of columns) and the order of observation features is consistent; They have the same number of time steps (consistent number of rows) and a fixed length of time step sequences, i.e. the time span between any two samples is equal; The interval between the time points represented by two adjacent rows is fixed, that is, the sampling period is an evenly spaced time step (such as every hour, every minute, etc.), and non-uniform sampling is not allowed.

[0028] To meet the above structural requirements, the sampled raw data is preprocessed, including filling in missing time steps or truncating them to a uniform time length; completing or deleting missing feature dimensions; and using a missing mask matrix to simultaneously record the filled positions for model use. Furthermore, tables that do not meet the above structural consistency or have serious missing data should be filtered out or cropped and not retained in the model training process.

[0029] In step S13 of this embodiment, the method of using the column-level filling model based on the linear structure to fill in the missing columns one by one is specifically as follows: S31-1. Identify the data table to be filled Missing columns All consecutive missing intervals in ; in, Indicates the feature vector (i.e., the first feature vector in the data table to be filled List), Indicates the No. The observation value of the row, that is, The characteristic value of each time step It is called atomic observation point. The entire data table to be filled has feature dimensions (columns), time steps (rows); S14. For missing intervals The missing sequences , divided into unilateral observable missing series and bilateral observable missing series according to their boundary observability; S15. For each missing sequence , fill in missing values ​​according to its left and right boundary values: When the missing sequence is only the left boundary If the unilaterally observable sequence is Fill in ; When the missing sequence is only the right boundary If the unilaterally observable sequence is Fill in ;in, ; When the missing sequence is a bilaterally observable missing sequence, linear interpolation is used to fill in the missing values ​​in the missing sequence. Fill in , and satisfies , , .

[0030] In a specific example of the present invention, taking the monitoring data of patients hospitalized in the ICU as an example, the original data records the continuous physiological indicators of the patients in the ICU, including heart rate, blood pressure, respiratory rate, body temperature, blood oxygen saturation, etc.

[0031] The specific process of processing the initial filled complete data table is as follows: One ICU hospitalization for each patient constituted an independent sample; The selected features include heart rate (HR), systolic blood pressure (SBP), diastolic blood pressure ( DBP), SpO2, etc., totaling d variables; If the sampling period is once per hour and the observation time is 24 hours, each sample forms a two-dimensional table of 24 × d; For individual patients with missing time or feature data, they were uniformly supplemented by interpolation, model prediction, or forward filling according to the above methods; Finally, an initial filled complete data table is formed with a unified structure consisting of n samples, the same feature dimension and time length.

[0032] In step S2 of the embodiment of the present invention, all the initial data tables to be filled are clustered using the K-Means algorithm into k clusters (the specific value can be customized according to the size characteristics of the data set), and then the initial filled complete data table closest to the geometric center is selected from each cluster as the representative data table.

[0033] In an embodiment of the present invention, inferring causal relationships from multivariate time series data and constructing a temporal causal graph is one of the core tasks of understanding the dynamic interaction mechanism of complex systems. Granger causality (GC) is a basic method for temporal causal discovery. Its core idea is to infer causal relationships by comparing the improvement in the prediction accuracy of the target variable. Specifically, if adding historical information of the cause variable can significantly reduce the prediction error when predicting the future value of the target variable, then it is considered that there is a causal relationship. The present invention improves a Granger causal relationship discovery method based on a temporal convolutional network (Temporal Causal Discovery Framework, abbreviated as TCDF) to construct the causal relationship between time series data in this task. TCDF trains a specific neural network model to fit and predict the future state of the target variable, and evaluates the causal influence of each input feature through feature perturbation testing, thereby identifying the potential causal structure between variables in the time series without the need for strong prior assumptions (such as linearity, stationarity, etc.).

[0034] In this embodiment of the present invention, TCDF constructs a causal graph structure that includes time delays. By combining the attention mechanism with causal verification steps, it can effectively identify direct and indirect causal relationships and is compatible with the existence of confounding factors and transient effects. Its core process is divided into three parts: time series prediction, attention interpretation, and causal verification.

[0035] During the attention interpretation phase, TCDF uses a fixed threshold to screen potential causal variables. This design is prone to false negatives (FNs) in the following scenarios: for example, weak signals are missed in dense causal networks. In dense networks such as brain functional connectivity, the attention score of a true causal relationship may fall below the threshold due to weak signals or noise interference, leading to the incorrect exclusion of key connections. For example, the functional connection between the prefrontal cortex and the hippocampus may be missed due to skewed score distributions that do not reach the threshold, directly affecting recall. It also lacks adaptability to non-stationary time series. For example, in non-stationary data such as finance, the strength of variable influence changes dynamically over time (e.g., the effect of policy windows increases). Static thresholds cannot be adjusted adaptively, and may incorrectly filter out true causal relationships during periods of high variance (such as market volatility).

[0036] During the causal verification phase, TCDF relies on a global random permutation strategy. While this strategy effectively eliminates short-term spurious correlations, it suffers from several drawbacks: The loss of macrocyclical patterns. In data with significant long-term trends (such as economic cycles and seasonal fluctuations), global permutation completely disrupts the time series structure, making it impossible to assess long-term causal effects between variables. For example, the impact of the Federal Reserve's interest rate hikes typically persists for several months, and global permutation fails to effectively capture their cross-quarter effects, resulting in missed causal associations. Furthermore, the permutation of event windows can lead to the dispersal of causal relationships driven by short-term events (such as financial report releases and breaking news) into random time periods, weakening the causal signal. For example, the persistent impact of variable A on variable B during the event window may be misclassified as noise.

[0037] In step S3 of the embodiment of the present invention, based on the shortcomings of traditional TCDF, the present invention proposes an improved Granger causality discovery method (TCDF with Dynamic Thresholding and Validation, abbreviated as DTV-TCDF). In the process of constructing the causal graph of each representative data table, a dynamic lower bound threshold is set to screen the potential causal relationship in the representative data table, and a block perturbation optimization method based on data characteristics is used to verify the screened causal relationship.

[0038] In this embodiment, a dual statistical strategy combining quantiles and mean-standard deviation (Mean+SD) is proposed for the dynamic lower bound threshold. The maximum value of the two is taken as the final lower bound (i.e., the dynamic lower bound is calculated). The formula is expressed as follows: Among them, the dynamic lower threshold for: Where, Indicates the front of the data Quantiles (such as , take the first 85% quantile). represents the mean score, represents the standard deviation, represents the coefficient for adjusting the standard deviation weight, represents the coefficient that controls the range of the score; where Mean plus times the standard deviation (for example, when β=1, it is the mean + 1 times the standard deviation).

[0039] Specifically, the calculation process for determining the dynamic lower bound threshold is as follows: (1) Target variable Attention score sequence , adjustment coefficient (control quantile range) and (Adjust standard deviation weight); (2) Calculation Quantile , filter high score intervals. For example, The top 20% of high-scoring nodes are retained to ensure that weak signals in sparse networks are not missed. , that is, the score is not less than The minimum index position of .

[0040] (3) Mean-standard deviation method: Calculate the mean score and standard deviation , dynamically expand the threshold to . Determine the lower bound of the standard deviation , that is, the score exceeds The minimum index position of .

[0041] (4) Threshold fusion: take and and constrain its minimum value to 1 to avoid the risk of an empty set.

[0042] In this embodiment, the above-mentioned dynamic setting of the lower threshold replaces the manual setting of the fixed threshold, which is automatically adjusted according to the data distribution to adapt to the characteristics of different data sets; the quantile and the mean-standard deviation are jointly optimized to take into account both position and dispersion information.

[0043] In this embodiment, a block perturbation optimization method based on data characteristics is proposed during the causal verification phase. The core idea is to preserve the macro structure of the data through block perturbation while destroying local pseudo-correlations, thereby improving the accuracy and interpretability of causal verification. Specifically, the implementation process of the block perturbation algorithm is as follows: (1) Input time series series, block size block_size.

[0044] (2) Block operation: divide the sequence into continuous blocks according to block_size, and retain the data that is not enough at the end; for example: for data of length, block it according to 80 days to obtain 50 complete blocks.

[0045] (3) Block permutation: randomly disrupting the order of blocks, destroying the temporal structure within the blocks but maintaining the macro trend between blocks.

[0046] (4) Sequence reorganization: Splice the replaced blocks into the new order and append the tail data (if any).

[0047] In this embodiment, based on the above-mentioned improved Granger causality discovery method, the causal strength between each feature of the k representative data tables obtained by clustering is calculated respectively, and a causal matrix is ​​created with a size of the number of features * the number of features. If the corresponding position is set to 1, it means that the corresponding row feature has a causal pointing relationship with the corresponding column feature, and the row is the causal parent node of the column. If the corresponding position is set to 0, it means that there is no causal relationship, and then a causal graph of each representative data table is obtained.

[0048] In step S3 of an embodiment of the present invention, in order to extract a stable and universal inter-feature causal graph from multiple independent representative data tables, the present invention proposes a global causal graph construction method based on "causal information cumulative weighting", which aggregates the independently estimated causal graphs in each representative data table to eliminate individual differences while enhancing the credibility of the causal structure.

[0049] Based on this, step S3 of this embodiment is specifically as follows: S31. Add all the causal graphs element by element to get the cumulative causal support matrix , represents the i-th sub-causal graph, N represents the total number of sub-causal graphs, and the matrix size of each sub-causal graph is represents the causal strength between features, where is the number of features; The cumulative causal support matrix Elements Indicates that in all the data tables to be filled, Is the feature The cumulative support strength of the causal parent of each feature. The larger the value, the more data in the table believes that there is causal direction; S32. Cumulative Causal Support Matrix For each column (i.e. each target feature), select the top column with the largest value. positions, and set their corresponding values ​​to 1, and the values ​​of the remaining positions to 0, thus obtaining the dimension Binary causal graph of As a total causal diagram.

[0050] In an embodiment of the present invention, in order to more effectively utilize the causal relationship between features to model and fill missing values, this embodiment adopts a strategy of independently training the Temporal Convolutional Network (TCN) by feature. TCN is suitable for a deep neural network structure for time series modeling and causal relationship identification.

[0051] This paper proposes a weighted scalable deep temporal convolutional network (ICTCN), based on causal convolution and channel-wise attention mechanisms, to effectively capture key causal factors in multivariate time series and enhance model interpretability. The ICTCN consists of two core modules: a deep scalable temporal convolutional network (DepthwiseNet), which employs multi-level dilated convolutions to build causal modeling capabilities; and a channel-wise attention weighting mechanism, which introduces channel weights as learnable parameters to measure the contribution of different input variables to the target output. The final output is then compressed using pointwise convolution to achieve target variable prediction.

[0052] In causal reasoning tasks, ICTCN is used to construct a prediction model for each target variable. By analyzing the values ​​of the attention mechanism parameters, the degree of influence of the input variables on the target can be obtained. Combined with perturbation testing, input variables that have a significant impact on the prediction accuracy after perturbation can be screened out and considered to be causal. Finally, this method integrates the causal parent set of all target variables into a causal adjacency matrix to achieve causal structure learning of multivariate time series systems.

[0053] The above-mentioned network structure proposed in the present invention seamlessly integrates time series modeling and causal reasoning. It not only has the powerful expressive ability of deep networks, but also introduces a structural interpretability mechanism, providing an efficient, scalable and physically reasonable solution for multivariate time series causal discovery.

[0054] Based on the above ICTCN network structure, step S4 of the embodiment of the present invention includes the following sub-steps: S41, for the initially filled complete data table, selecting the target feature column to be filled; Specifically, if the initial filling of the complete data table requires filling multiple features, the subsequent steps need to be performed separately for each target feature column; S42. Based on the causal relationship of the target feature listed in the overall causal graph, determine its corresponding causal parent feature; S43. Concatenate each target feature column with its corresponding causal parent feature to form an input sub-table, and use the target feature column as a prediction label to construct a training dataset. S44. Using the training data set, the constructed weighted expandable deep temporal convolutional network is trained to obtain a missing value filling model; S45. Use the missing value filling model to roughly fill in the missing values ​​of the target feature column.

[0055] In this embodiment, during the training of the constructed weighted scalable deep temporal convolutional network using the training set, the model parameters are optimized by backpropagating the loss (mean square error MSE or mean absolute error MAE) calculated by its predicted output and the true label.

[0056] In this embodiment, a corresponding missing value filling model is trained for each target feature column.

[0057] In the embodiment of the present invention, step S5 includes the following sub-steps: S51, calling the missing value filling model corresponding to the target feature column of the rough filling; S52. Input the target feature column and its three causal parent feature columns in the total causal graph into the missing value filling model, and output the complete prediction sequence of the target feature column; S53, identifying the original missing position in the target feature column according to the missing position mark in the data table to be filled; S54. For the original missing position in the target feature column, the initial filling value in the initial filling complete data table is replaced with the corresponding prediction value in the complete prediction sequence, thereby obtaining a complete data table; In this embodiment, during the above-mentioned secondary refined filling process of missing values, the original observation values ​​of non-missing positions are kept unchanged to ensure that the model does not cover the existing real observation information; the above-mentioned filling process is executed for each target feature column in turn, and finally all the target feature columns corrected by the model are integrated to form a complete data table.

[0058] In an embodiment of the present invention, an experimental test example of the above-mentioned missing data filling method is provided.

[0059] In this example, experiments were conducted on three public medical datasets: MIMIC-III, PhysioNet Challenge 2012, and PhysioNet Challenge 2019. MIMIC-III contains de-identified clinical data from patients in the emergency department and ICU at Beth Israel Deaconess Medical Center in Boston, USA. The publicly available MIMIC-III (version 1.4) dataset from Beth Israel Deaconess Medical Center covers patient data from 2001 to 2012. In the MIMIC III dataset, in-hospital mortality was selected as the downstream prediction task. The included death samples consisted of 3,265 records and the survival samples consisted of 27,579 records. Experiments with the original full data for PhysioNet Challenge 2012 and 2019 were conducted.

[0060] In this embodiment, the evaluation of the missing value filling results and the evaluation of the downstream task prediction using the filled data are designed respectively. The experimental results are shown in Tables 1 to 3.

[0061] Table 1: Evaluation of missing value imputation results for the MIMIC III dataset Table 2: Evaluation of missing value filling results for the PhysioNet Challenge 2012 dataset Table 3: Evaluation of missing value filling results for the dataset PhysioNet Challenge 2019 As can be seen from Tables 1-3 above, the proposed SCIT method demonstrates excellent performance in the missing value imputation task, significantly outperforming various traditional imputation methods on the three datasets. Compared to the next-best backward imputation method, SCIT still significantly improves performance. In a horizontal comparison, SCIT also shows steady improvement over statistical methods (median imputation and mean imputation), maintains improvement over time series methods (forward imputation and backward imputation), and significantly outperforms machine learning methods (KNN and MICE). These data fully demonstrate that the SCIT method effectively overcomes the extreme bias, distribution dependence, cumulative error, and computational complexity inherent in traditional methods. Through its innovative intelligent imputation strategy, it better preserves the data's structural characteristics while maintaining its statistical properties, demonstrating its significant advantages as a next-generation imputation method.

[0062] In this embodiment, the results of imputing the MIMIC III dataset using different data imputation methods and using them for predicting in-hospital mortality are shown in Table 4; Table 4: Comparison of prediction results based on different data filling methods As shown in Table 4, the experimental data fully demonstrates the comprehensive advantages of the SCIT method in the in-hospital mortality prediction task. In terms of key evaluation metrics, SCIT significantly outperforms other methods with an accuracy of 75.00% ± 1.75% (the best comparison method has mean padding of 73.30% ± 0.59%). It also maintains top performance in several key metrics, including precision (75.62% ± 4.60%), recall (74.29% ± 5.89%), F1 score (74.66% ± 2.85%), and AUROC (0.8249 ± 0.0183). In particular, its stable standard deviation (1.75%-5.89%) is significantly smaller than that of other methods, demonstrating SCIT's superior robustness. SCIT demonstrates a more balanced and reliable performance advantage. Compared with traditional methods, SCIT not only comprehensively surpasses basic methods such as zero-padding and median padding, but also outperforms more complex methods such as KNN and mean padding. In particular, it achieves an optimal balance between high precision and recall. These results demonstrate that the SCIT method, through its innovative filling mechanism, better preserves the key feature information in the data while maintaining the data distribution characteristics, thereby demonstrating stable and comprehensive performance advantages in various prediction tasks.

[0063] Specific embodiments are used in the present invention to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

[0064] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. An unsupervised time series missing data filling method based on dynamic causal graph structure, characterized by: The following steps are involved: S1. Collect data samples from multivariate time series, construct a data table to be filled and preprocess it to obtain an initial filled complete data table; The structure of the initially filled complete data table is unified and has the same feature dimension and time length; S2. Cluster all initially filled complete data tables, and select the initially filled complete data table close to the geometric center in each cluster as the representative data table; S3. Use the improved Granger causality discovery method to construct the sub-causal graphs of each representative data table, and then construct the total causal graph; S4. Based on the causal relationship in the total causal graph, a corresponding weighted scalable deep temporal convolutional network is constructed and trained to initially fill in the target feature column to be filled in the complete data table, thereby obtaining a missing value filling model, and using it to roughly fill in the missing values ​​of the target feature column; S5. Use the missing value filling model to perform a refined secondary filling on the roughly filled target feature column to obtain a complete data table.

2. The unsupervised time series missing data filling method based on dynamic causal graph structure according to claim 1 is characterized in that: The step S1 includes the following sub-steps: S11, processing each data sample into an independent two-dimensional data table, representing the observation results of the observation object within a set time period; S12, processing each two-dimensional data table into a data table to be filled with a unified data structure; S13, filling the data table to be filled, thereby obtaining an initial filled complete data table; For the data table with all empty columns to be filled, fill all empty columns with fixed value 0 and mark all missing columns; For data tables with non-empty columns to be filled, a column-level filling model based on a linear structure is used to fill in the missing columns one by one.

3. The unsupervised time series missing data filling method based on dynamic causal graph structure according to claim 1 is characterized in that: Each of the data tables to be filled is independent of each other, and in each data table to be filled: Arrange time steps in rows and observation features in columns; Have the same number of observed features and the order of the observed features is consistent; Have the same number of time steps and a fixed length of time step sequences; The interval between the time points represented by two adjacent rows is fixed.

4. The unsupervised time series missing data filling method based on dynamic causal graph structure according to claim 2 is characterized in that: In step S13, the method of filling missing columns one by one using the column-level filling model based on the linear structure is specifically as follows: S31-1. Identify the data table to be filled Missing columns All consecutive missing intervals in ; S14. For missing intervals The missing sequences , divided into unilateral observable missing series and bilateral observable missing series according to their boundary observability; S15. For each missing sequence , fill in missing values ​​according to its left and right boundary values: When the missing sequence is only the left boundary If the unilaterally observable sequence is Fill in ; When the missing sequence is only the right boundary If the unilaterally observable sequence is Fill in ;in, ; When the missing sequence is a bilaterally observable missing sequence, linear interpolation is used to fill in the missing values ​​in the missing sequence. Fill in , and satisfies , , .

5. The unsupervised time series missing data filling method based on dynamic causal graph structure according to claim 1 is characterized in that: In step S3, in the process of constructing the sub-causal graphs of each representative data table using the improved Granger causality discovery method, a dynamic lower bound threshold is set to screen the potential causal relationships in the representative data table, and a block perturbation optimization method based on data characteristics is used to verify the screened causal relationships; Among them, the dynamic lower threshold for: Where, Indicates the front of the data Quantile, represents the mean score, represents the standard deviation, represents the coefficient for adjusting the standard deviation weight, The coefficient representing the range of control scores; Among them, the block perturbation optimization method based on data characteristics is: Input the time series series in the causal relationship and the block size block_size. Divide the time series series into consecutive blocks according to block_size, randomly shuffle the blocks, and splice the shuffled blocks into the new order.

6. The unsupervised time series missing data filling method based on dynamic causal graph structure according to claim 1 is characterized in that: In step S3, the method for constructing the total causal graph based on the sub-causal graph is specifically as follows: S31. Add all the causal graphs element by element to get the cumulative causal support matrix , represents the i-th sub-causal graph, and N represents the total number of sub-causal graphs; The cumulative causal support matrix Elements Indicates that in all the data tables to be filled, Is the feature The cumulative support strength of the causal parent of each feature; S32. Cumulative Causal Support Matrix For each column in the Positions, and set their corresponding values ​​to 1, and the values ​​of the remaining positions to 0, thus obtaining a binary causal graph As a total causal diagram.

7. The method for filling missing data of a time series without deceleration based on a dynamic causal graph structure according to claim 1 is characterized in that: The step S4 comprises the following sub-steps: S41, for the initially filled complete data table, selecting the target feature column to be filled; S42. Determine the corresponding causal parent feature based on the causal relationship of each target feature listed in the overall causal graph; S43. Concatenate the target feature column with its corresponding causal parent feature to form an input sub-table, and use the target feature column as a prediction label to construct a training dataset. S44. Using the training data set, the constructed weighted expandable deep temporal convolutional network is trained to obtain a missing value filling model; S45. Use the missing value filling model to roughly fill in the missing values ​​of the target feature column.

8. The unsupervised time series missing data filling method based on dynamic causal graph structure according to claim 1 is characterized in that: The step S5 comprises the following sub-steps: S51, calling the missing value filling model corresponding to the target feature column of the rough filling; S52. Input the target feature column and its three causal parent feature columns in the total causal graph into the missing value filling model, and output the complete prediction sequence of the target feature column; S53, identifying the original missing position in the target feature column according to the missing position mark in the data table to be filled; S54. For the original missing position in the target feature column, the initial filling value in the initial filling complete data table is replaced with the corresponding prediction value in the complete prediction sequence, thereby obtaining a complete data table.

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