Missing value robust multivariable time sequence prediction system and method
By constructing an adaptive feature fusion mechanism with a reversible observation normalization module and a cross-time step and variable fusion module, the problems of information loss and high computational complexity caused by missing values in multivariate time series forecasting are solved, and efficient and stable forecasting under missing value conditions is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHWEST JIAOTONG UNIV
- Filing Date
- 2026-01-12
- Publication Date
- 2026-04-10
AI Technical Summary
Existing technologies for multivariate time series forecasting with missing values suffer from problems such as inconsistent optimization objectives between the imputation and forecasting stages, accumulation of imputation errors, loss of key forecast information, and high computational complexity, especially in scenarios with block-like missing values.
The system employs a reversible observation normalization module, a cross-time step fusion module, and a cross-variable fusion module. Through an adaptive gating mechanism, it optimizes historical reconstruction and future prediction within a unified framework. It uses observation data indicated by a mask matrix to calculate statistics, captures spatiotemporal dependencies, and achieves feature fusion through lightweight linear units.
It significantly improves prediction accuracy and robustness under missing value conditions, reduces computational complexity, solves the problems of distribution drift and information loss, and ensures stable prediction in dynamic environments.
Smart Images
Figure CN121836032A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of time series prediction, in particular to a multivariate time series prediction system and method robust to missing values. BACKGROUND
[0002] In the multivariate time series forecasting (MTSF) tasks of real-world scenarios such as traffic flow, weather monitoring, energy load and finance, factors such as sensor failure, communication link jitter, acquisition delay or system maintenance can cause random point missing or continuous block missing in the observed sequence, thereby destroying the time dependence and correlation between variables, and significantly reducing the accuracy and robustness of the prediction model in an open environment. Therefore, how to stably complete the prediction under the condition of complex missing mode and large missing rate change is a key problem that has been concerned for a long time.
[0003] Currently, the technical solutions for this problem mainly include two categories. The first category is the two-stage method of first interpolation and then prediction. This kind of method regards interpolation and prediction as two independent sequential steps. That is, first, use statistical interpolation or deep learning-based interpolation models such as BRITS, PriSTI and SAITS to fill in the missing values, and then apply the prediction model on the complete sequence. However, this fragmented process has significant defects. Since the optimization objectives of the interpolation stage and the prediction stage are inconsistent, and the errors generated by interpolation will propagate and accumulate to the prediction stage, resulting in suboptimal final prediction effect. And this kind of method usually discards the mask matrix indicating the missing position after interpolation. According to the data processing inequality principle, this cuts off the Markov chain continuity between the prediction window and the original missing pattern, causing the loss of key prediction information. The second category is the end-to-end or single-stage method, which tries to handle missing values in a unified framework. For example, RNN-based variants such as GRU-D, neural differential equation-based methods (Neural ODEs), diffusion model-based methods such as CSDI, and the latest graph neural network methods such as BiTGraph and state space model S4M. Although these methods try to model incomplete data directly, there are many defects. For example, GRU-D lacks a clear prediction optimization objective; Neural ODEs have high computational complexity and limited use of time patterns; CSDI has differences between training and inference stages; BiTGraph uses mask information, but it lacks sufficient use of time information, and it relies too much on local spatial correlation, lacks sufficient modeling of cross-time step and cross-variable interaction, and has high computational cost. Prediction models designed for complete data, such as iTransformer, AGCRN, MTGNN, DLinear, PatchTST, GPT4TS, often degenerate into two-stage patterns that rely on simple preprocessing such as mean filling when facing missing data, and cannot effectively handle complex scenarios such as block missing. SUMMARY
[0004] The present application provides a missing value robust multivariate time series prediction system and method to solve the problems in the prior art.
[0005] The technical scheme adopted by the present application is: a missing value robust multivariate time series prediction method, comprising the following steps: Step 1: constructing a prediction model, the prediction model comprising a reversible observation value normalization module, a cross-time step fusion module and a cross-variable fusion module; Step 2: obtaining data, including multivariate time series and mask, time index truncated historical backtracking window data and prediction window data, synchronously truncated corresponding mask matrix, and timestamp feature sequence of the window; Step 3: inputting the data into the prediction model for multivariate time series prediction; the process is as follows: The backtracking window data and the corresponding mask matrix are input into the reversible observation value normalization module to perform normalization processing on the backtracking window data by using the mean and variance to obtain normalized data; time embedding is generated according to the timestamp feature, the time embedding, the normalized data and the mask matrix are spliced in the feature dimension to obtain a composite input tensor; The composite input tensor is input into the cross-time step fusion module to perform feature fusion along the time dimension to obtain time-dependent features; The time-dependent features are input into the cross-variable fusion module to perform feature fusion along the variable dimension to obtain spatial-dependent features across variables; The spatial-dependent features across variables are projected back to the time dimension space of the multivariate time series, and the reversible observation value normalization module is used for reverse normalization to obtain the interpolation reconstruction value of the historical backtracking window and the prediction value of the future window.
[0006] Further, the composite input tensor calculation process is as follows: According to the backtracking window data And the mask matrix Calculate the mean And variance ;
[0007]
[0008] In the formula: is the mask vector at time t, L is the length of the historical backtracking window, t is the time; The normalized data is:
[0009] In the formula: gamma Andβ All are parameters. For hyperparameters, For element-wise multiplication; Composite input tensor as follows:
[0010] In the formula: tau For timestamp features, This represents concatenation along the feature dimension, where D is the variable dimension and C is the feature dimension. For the real number field, Embedded for time.
[0011] Furthermore, the time-dependent feature calculation process is as follows: Temporal evolution features are extracted from the composite input tensor, and gating weights are generated using the Sigmoid activation function. The temporal evolution features and gating weights are multiplied element-wise to obtain the temporal fusion features. Temporally dependent features are obtained by applying Dropout regularization and a linear projection layer to the temporally fused features.
[0012] Furthermore, the temporal fusion feature The calculation process is as follows:
[0013] In the formula: It is the Sigmoid activation function. and These are all linear layer weight matrices of the cross-timestep fusion module. and All are bias vectors of the cross-time step fusion module; Time-dependent features The calculation process is as follows:
[0014] In the formula: It is a random deactivation function. For matrix multiplication, For the weight matrix of the linear projection layer of the cross-time step fusion module, This is the bias matrix of the linear projection layer of the cross-time step fusion module.
[0015] Furthermore, the calculation process for the cross-variable spatial dependency features is as follows: The time-dependent features are extracted to form variable dimension evolution features, and the Sigmoid activation function is used to generate gate weights. The variable dimension evolution features and the gate weights are multiplied element by element to obtain the variable fusion features. The variable fusion features are then subjected to Dropout regularization and a linear projection layer to obtain cross-variable spatial dependency features.
[0016] Furthermore, the variable fusion feature The calculation process is as follows:
[0017] In the formula: and These are all linear layer weight matrices of the cross-variable fusion module. and All are bias vectors of the cross-variable fusion module; Spatial dependency features across variables The calculation process is as follows:
[0018] In the formula: The linear projection layer weight matrix of the cross-variable fusion module. This is the bias matrix of the linear projection layer of the cross-variable fusion module.
[0019] Furthermore, the calculation process for the interpolated reconstructed value of the historical backtracking window and the predicted value of the future window is as follows: Spatial dependency characteristics across variables Projecting back to the original data space:
[0020] In the formula; The interpolated and reconstructed values for the historical backtracking window. For the predicted value of the future window, For learnable parameters, These are learnable parameters; Perform inverse normalization, and Align the statistical information to the original data distribution: .
[0021] Furthermore, it also includes a loss function, through which the prediction model parameters are updated via backpropagation:
[0022] In the formula: For the interpolation loss of the historical window, Forecast loss for future windows; in: ,
[0023] In the formula: For historical backtracking window data at time t, Let be the interpolated reconstructed value of the historical backtracking window at time t, and H be the prediction window length. Let h be the prediction window and the mask matrix of the data. The prediction window data is at time h. Let h be the predicted value for the future window at time h.
[0024] A multivariate time series forecasting system robust to missing values includes a reversible observation normalization module, a cross-time step fusion module, and a cross-variable fusion module; The reversible observation normalization module is used to normalize the backtracking window data and the corresponding mask matrix by means and variance to obtain normalized data; a time embedding is generated based on the timestamp feature, and the time embedding, normalized data and mask matrix are concatenated along the feature dimension to obtain a composite input tensor; The cross-time step fusion module is used to fuse features of composite input tensors along the time dimension to obtain time-dependent features; The cross-variable fusion module is used to fuse time-dependent features along the variable dimension to obtain cross-variable spatial dependency features; The reversible observation normalization module projects the cross-variable spatial dependency features back to the time dimension space of the multivariate time series, and performs inverse normalization to obtain the interpolated reconstruction values of the historical backtracking window and the predicted values of the future window.
[0025] The beneficial effects of this invention are: This invention utilizes the RevON (Reversible Observation Normalization) module to calculate statistics based solely on observation data indicated by the mask matrix, thereby eliminating distribution drift in incomplete time series. Through sequentially connected cross-time-step fusion CTF and cross-variable fusion CVF modules, observations, mask matrices, and timestamps are embedded as input, and robust spatiotemporal dependencies are captured using an adaptive gating mechanism. By weighted combining imputation and prediction losses, the reconstruction of historical data and future predictions are simultaneously optimized within a unified framework, maximizing the retention of key information required for prediction. Attached Figure Description
[0026] Figure 1 This is a schematic diagram of the framework structure of the prediction system of the present invention. Detailed Implementation
[0027] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.
[0028] like Figure 1 As shown, a multivariate time series prediction system robust to missing values includes a reversible observation normalization module, a cross-time step fusion module, and a cross-variable fusion module; The reversible observation normalization module is used to normalize the backtracking window data and the corresponding mask matrix by means and variance to obtain normalized data; a time embedding is generated based on the timestamp feature, and the time embedding, normalized data and mask matrix are concatenated along the feature dimension to obtain a composite input tensor; The cross-time step fusion module is used to fuse features of composite input tensors along the time dimension to obtain time-dependent features; The cross-variable fusion module is used to fuse time-dependent features along the variable dimension to obtain cross-variable spatial dependency features; The reversible observation normalization module projects the cross-variable spatial dependency features back to the time dimension space of the multivariate time series, and performs inverse normalization to obtain the interpolated reconstruction values of the historical backtracking window and the predicted values of the future window.
[0029] A method for predicting multivariate time series data with missing values includes the following steps: Step 1: Construct a prediction model, which includes a reversible observation normalization module, a cross-time step fusion module, and a cross-variable fusion module; Step 2: Acquire data, including historical backtracking window data and prediction window data extracted by time index from multivariate time series and mask, synchronously extract the corresponding mask matrix, and the timestamp feature sequence of the window; Step 3: Input the data into the prediction model to perform multivariate time series prediction; the process is as follows: The backtracking window data and the corresponding mask matrix are input into the invertible observation normalization module. The backtracking window data is normalized using the mean and variance to obtain normalized data. A time embedding is generated based on the timestamp feature. The time embedding, normalized data, and mask matrix are concatenated along the feature dimension to obtain a composite input tensor. The calculation process of the composite input tensor is as follows: Based on the backtracking window data and mask matrix Calculate the mean and variance ;
[0030]
[0031] In the formula: Let be the mask vector at time t. L The length of the historical backtracking window. t For time; Normalized data for:
[0032] In the formula: gamma andβ All are parameters. For hyperparameters, For element-wise multiplication; Composite input tensor as follows:
[0033] In the formula: tau For timestamp features, This represents concatenation along the feature dimension, where D is the variable dimension and C is the feature dimension. For the real number field, Embedded for time.
[0034] The composite input tensor is input across time steps into the fusion module, and features are fused along the time dimension to obtain time-dependent features. The calculation process for time-dependent features is as follows: Temporal evolution features are extracted from the composite input tensor, and gating weights are generated using the Sigmoid activation function. The temporal evolution features and gating weights are multiplied element-wise to obtain the temporal fusion features. Temporally dependent features are obtained by applying Dropout regularization and a linear projection layer to the temporally fused features.
[0035] Temporal fusion features The calculation process is as follows:
[0036] In the formula: It is the Sigmoid activation function. and These are all linear layer weight matrices of the cross-timestep fusion module. and All are bias vectors of the cross-time step fusion module; Time-dependent features The calculation process is as follows:
[0037] In the formula: It is a random deactivation function. For matrix multiplication, For the weight matrix of the linear projection layer of the cross-time step fusion module, This is the bias matrix of the linear projection layer of the cross-time step fusion module.
[0038] The time-dependent features are input into the cross-variable fusion module, and feature fusion is performed along the variable dimension to obtain the cross-variable spatial dependency features. The calculation process for cross-variable spatial dependency features is as follows: The time-dependent features are extracted to form variable dimension evolution features, and the Sigmoid activation function is used to generate gate weights. The variable dimension evolution features and the gate weights are multiplied element by element to obtain the variable fusion features. The variable fusion features are then subjected to Dropout regularization and a linear projection layer to obtain cross-variable spatial dependency features.
[0039] Variable fusion features The calculation process is as follows:
[0040] Where: Where: and These are all linear layer weight matrices of the cross-variable fusion module. and All are bias vectors of the cross-variable fusion module; Spatial dependency features across variables The calculation process is as follows:
[0041] In the formula: The linear projection layer weight matrix of the cross-variable fusion module. This is the bias matrix of the linear projection layer of the cross-variable fusion module.
[0042] The spatial dependency features across variables are projected back into the time dimension space of the multivariate time series, and inverse normalization is performed through the reversible observation normalization module to obtain the interpolated reconstructed values of the historical backtracking window and the predicted values of the future window.
[0043] The calculation process for the interpolated reconstructed value of the historical backtracking window and the predicted value of the future window is as follows: Spatial dependency characteristics across variables Projecting back to the original data space:
[0044] In the formula; The interpolated and reconstructed values for the historical backtracking window. For the predicted value of the future window, For learnable parameters, These are learnable parameters; Perform inverse normalization, and Align the statistical information to the original data distribution: .
[0045] It also includes a loss function, which is used to backpropagate and update the prediction model parameters:
[0046] In the formula: For the interpolation loss of the historical window, Forecast loss for future windows; in: ,
[0047] In the formula: For historical backtracking window data at time t, Let be the interpolated reconstructed value of the historical backtracking window at time t, and H be the prediction window length. Let h be the prediction window and the mask matrix of the data. The prediction window data is at time h. Let h be the predicted value for the future window at time h.
[0048] Example In actual use, A method for predicting multivariate time series data with missing values includes the following steps: First, a prediction model is constructed, which includes a reversible observation normalization module, a cross-time step fusion module, and a cross-variable fusion module. The model's input includes multivariate time series data. Where T is the time step and D is the variable dimension; missing mask matrix Where 1 represents an observed value and 0 represents a missing value; timestamp feature Information such as time (hours, days of the week); balancing weight hyperparameters .
[0049] S1: Initialize all learnable parameters This includes the affine transformation parameters in the RevON module. The weights of the timestamp embedding layer; the linear layer weight matrix W and bias vector b in the CTF, CVF modules and projection layers.
[0050] Then iterative training is performed: S2: Acquire data from multivariate time series data. With mask Extracting historical backtracking window data by time index and prediction window data Where L is the historical backtracking window length and H is the prediction window length. The corresponding mask matrix is extracted synchronously. and Simultaneously extract the timestamp feature sequence of this window. .
[0051] S3: Backtrack window data and mask matrix Input the RevON module to calculate the mean based on the observations (i.e., the parts with a mask of 1). and variance The backtracking window data is then normalized. This helps alleviate the distribution drift problem caused by non-stationarity.
[0052]
[0053]
[0054] In the formula: Let be the mask vector at time t. It is 1 if the corresponding variable is observed, and 0 otherwise. L The length of the historical backtracking window. t For time;
[0055] In the formula: gamma and β All are parameters (learnable affine transformation parameters). For hyperparameters, This is for element-wise multiplication.
[0056] Based on timestamp characteristics Generate Embedded This is then concatenated with the normalized data and the mask matrix along the feature dimension to construct a composite input tensor:
[0057] In the formula: tau For timestamp features, This represents concatenation along the feature dimension, where D is the variable dimension and C is the feature dimension. For the real number field, For time embedding; where, , , For feature dimensions.
[0058] S4: Input the composite input tensor into the CTF module, which performs feature fusion along the time dimension. It uses a lightweight linear layer and a sigmoid gating mechanism to adaptively filter out missing value noise and capture the time-dependent features within a single variable.
[0059] The specific process is as follows: The composite input tensor is fed into two parallel linear branches. One branch extracts the original temporal evolution features, while the other generates 0-1 gating weights using a sigmoid activation function. The two branches are then multiplied element-wise to obtain the temporal fusion features. The fused features are then regularized using Dropout and a linear projection layer to output time-dependent features. Then Perform transpose operation to obtain .
[0060]
[0061] In the formula: It is the Sigmoid activation function. and These are all linear layer weight matrices of the cross-timestep fusion module. and All are bias vectors of the cross-time step fusion module; .
[0062]
[0063] In the formula: It is a random deactivation function. For matrix multiplication, For the weight matrix of the linear projection layer of the cross-time step fusion module, The bias matrix for the linear projection layer of the cross-time step fusion module; , h is the dimension of the hidden layer.
[0064] S5: Input time-dependent features into the CVF module. This module performs feature fusion along the variable dimension, similar to the CTF module, and dynamically captures spatial dependency features across variables.
[0065] The calculation process for cross-variable spatial dependency features is as follows: The time-dependent features are extracted to form variable dimension evolution features, and the Sigmoid activation function is used to generate gate weights. The variable dimension evolution features and the gate weights are multiplied element by element to obtain the variable fusion features. The cross-variable spatial dependency features are obtained by applying Dropout regularization and a linear projection layer to the fused variable features, and then the obtained cross-variable spatial dependency features are transposed.
[0066] Variable fusion features The calculation process is as follows:
[0067] In the formula: and These are all linear layer weight matrices of the cross-variable fusion module. and All are bias vectors of the cross-variable fusion module;
[0068] Spatial dependency features across variables The calculation process is as follows:
[0069] In the formula: The linear projection layer weight matrix of the cross-variable fusion module. This is the bias matrix of the linear projection layer of the cross-variable fusion module. , , , .
[0070] Transpose the spatial dependency feature across variables to obtain .
[0071] S6: Project the cross-variable spatial dependency features back into the time dimension space of the multivariate time series, and perform inverse normalization through the reversible observation normalization module to obtain the interpolated reconstruction value of the historical backtracking window and the predicted value of the future window.
[0072] Spatial dependency characteristics across variables Projecting back to the original data space:
[0073] In the formula; The interpolated and reconstructed values for the historical backtracking window. For the predicted value of the future window, For learnable parameters, These are learnable parameters; Denormalization is performed using the RevON module. Align the statistical information to the original data distribution: .
[0074] In the formula: ,
[0075] S7: Parameter update, calculate the interpolation loss of the historical window and the prediction loss of the future window, construct the loss function, and perform joint backpropagation to update the prediction model parameters.
[0076]
[0077] In the formula: For the interpolation loss of the historical window, For the predicted loss of the future window, For hyperparameters, .
[0078] in: ,
[0079] In the formula: For historical backtracking window data at time t, Let be the interpolated reconstructed value of the historical backtracking window at time t, and H be the prediction window length. Let h be the prediction window and the mask matrix of the data. The prediction window data is at time h. Let h be the predicted value for the future window at time h.
[0080] This invention addresses the information loss and distribution drift issues of two-stage methods by unifying the joint optimization objective of interpolation and prediction, designing a robust lightweight spatiotemporal feature fusion mechanism, and a reversible observation normalization module, thereby significantly improving prediction accuracy and computational efficiency.
[0081] The prediction model constructed in this invention includes a reversible observation normalization module, a cross-time-step fusion module, and a cross-variable fusion module. The reversible observation normalization module uses a mask matrix to filter only valid observations to calculate the mean and variance in real time. This eliminates data distribution distortion caused by filling missing values, enabling the model to adaptively handle changes in statistical characteristics over different time periods, significantly enhancing the model's generalization ability and robustness in dynamic environments and under non-stationary data. It effectively solves the problems of time series non-stationarity and distribution drift in environments with missing data. Specifically, at the input end, a mask matrix is used... Only valid observations are selected to calculate the mean in real time. and variance This avoids the distortion of the statistical distribution caused by filler values (such as 0). At the output, the same statistics and learnable affine parameters are used to inversely normalize the prediction results. This ensures the model can adapt to the distribution drift of the time series and guarantees statistical consistency and prediction stability even with a high proportion of missing data. The sequentially connected cross-time-step fusion module and cross-variable fusion module, through a unique linear gating mechanism, achieve robust modeling of the spatiotemporal dependencies of sparse data, effectively reducing noise interference from missing values. Adaptive weights are generated using the Sigmoid activation function, which can automatically identify and suppress invalid signals caused by missing values, while highlighting and retaining key observation information. This mechanism not only captures periodic evolution patterns through temporal embedding but also achieves spatial information complementarity through strong correlations between variables, thus accurately inferring the system state through non-missing associated variables even in extreme scenarios such as continuous block missing values. This method abandons the computationally expensive self-attention mechanism and instead uses a two-branch linear unit: one branch is used for feature extraction, and the other branch is generated through the Sigmoid function. The gating coefficients are fused using element-wise multiplication (Hadamard product). The CTF module adaptively suppresses noise caused by missing values while preserving key observation information in the time dimension. Then, through dimension transposition, the CVF module captures the spatial complementarity between sensors in the variable dimension. This lightweight and robust spatiotemporal modeling mechanism significantly reduces computational complexity while improving model performance on sparse data.
[0082] This invention constructs a joint optimization objective for collaborative interpolation and prediction, simultaneously minimizing historical reconstruction errors and future prediction errors within a unified framework. This not only blocks the propagation of noise from the interpolation stage to the prediction stage but also theoretically maximizes the lower bound of the mutual information between the predicted value and the true distribution. It ensures that the "missing pattern" information implied in the mask matrix is fully preserved and used to assist prediction; overcoming the shortcomings of traditional two-stage methods of "interpolation first, prediction later," such as error accumulation and loss of key prediction information.
Claims
1. A method for predicting multivariate time series data robust to missing values, characterized in that, Includes the following steps: Step 1: Construct a prediction model, which includes a reversible observation normalization module, a cross-time step fusion module, and a cross-variable fusion module; Step 2: Acquire data, including historical backtracking window data and prediction window data extracted by time index from multivariate time series and masks, synchronously extracting the corresponding mask matrix, and the timestamp feature sequence of the window; Step 3: Input the data into the prediction model to perform multivariate time series prediction; the process is as follows: The backtracking window data and the corresponding mask matrix are input into the invertible observation normalization module. The backtracking window data is normalized by the mean and variance to obtain normalized data. A time embedding is generated based on the timestamp feature. The time embedding, normalized data and mask matrix are concatenated along the feature dimension to obtain a composite input tensor. The composite input tensor input cross-time step fusion module performs feature fusion along the time dimension to obtain time-dependent features; The time-dependent features are input into the cross-variable fusion module, and feature fusion is performed along the variable dimension to obtain the cross-variable spatial dependency features. The spatial dependency features across variables are projected back into the time dimension space of the multivariate time series, and inverse normalization is performed through the reversible observation normalization module to obtain the interpolated reconstructed values of the historical backtracking window and the predicted values of the future window.
2. The method for robust multivariate time series prediction with missing values according to claim 1, characterized in that, The calculation process for the composite input tensor is as follows: Based on the backtracking window data and mask matrix Calculate the mean and variance ; In the formula: Let be the mask vector at time t. L The length of the historical backtracking window. t For time; Normalized data for: In the formula: γ and β All are parameters. For hyperparameters, For element-wise multiplication; Composite input tensor as follows: In the formula: τ For timestamp features, This represents concatenation along the feature dimension, where D is the variable dimension and C is the feature dimension. For the real number field, Embedded for time.
3. The method for robust multivariate time series prediction with missing values according to claim 2, characterized in that, The time-dependent feature calculation process is as follows: Temporal evolution features are extracted from the composite input tensor, and gating weights are generated using the Sigmoid activation function. The temporal evolution features and gating weights are multiplied element-wise to obtain the temporal fusion features. Temporally dependent features are obtained by applying Dropout regularization and a linear projection layer to the temporally fused features.
4. The method for robust multivariate time series prediction with missing values according to claim 3, characterized in that, The time fusion feature The calculation process is as follows: In the formula: It is the Sigmoid activation function. and These are all linear layer weight matrices of the cross-timestep fusion module. and All are bias vectors of the cross-time step fusion module; Time-dependent features The calculation process is as follows: In the formula: It is a random deactivation function. For matrix multiplication, For the weight matrix of the linear projection layer of the cross-time step fusion module, This is the bias matrix of the linear projection layer of the cross-time step fusion module.
5. The method for robust multivariate time series prediction with missing values according to claim 4, characterized in that, The calculation process for the cross-variable spatial dependency features is as follows: The time-dependent features are extracted to form variable dimension evolution features, and the Sigmoid activation function is used to generate gate weights. The variable dimension evolution features and the gate weights are multiplied element by element to obtain the variable fusion features. The variable fusion features are then subjected to Dropout regularization and a linear projection layer to obtain cross-variable spatial dependency features.
6. The method for robust multivariate time series prediction with missing values according to claim 5, characterized in that, The variable fusion feature The calculation process is as follows: In the formula: and These are all linear layer weight matrices of the cross-variable fusion module. and All are bias vectors of the cross-variable fusion module; Spatial dependency features across variables The calculation process is as follows: In the formula: The linear projection layer weight matrix of the cross-variable fusion module. This is the bias matrix of the linear projection layer of the cross-variable fusion module.
7. The method for robust multivariate time series prediction with missing values according to claim 6, characterized in that, The calculation process for the interpolated reconstructed value of the historical backtracking window and the predicted value of the future window is as follows: Spatial dependency characteristics across variables Projecting back to the original data space: In the formula; The interpolated and reconstructed values for the historical backtracking window. For the predicted value of the future window, For learnable parameters, These are learnable parameters; Perform inverse normalization, and Align the statistical information to the original data distribution: 。 8. The method for robust multivariate time series prediction with missing values according to claim 7, characterized in that, It also includes a loss function, which is used to backpropagate and update the prediction model parameters: In the formula: For the interpolation loss of the historical window, Forecast loss for future windows; in: , In the formula: For historical backtracking window data at time t, Let be the interpolated reconstructed value of the historical backtracking window at time t, and H be the prediction window length. Let h be the prediction window and the mask matrix of the data. The prediction window data is at time h. Let h be the predicted value for the future window at time h.
9. A multivariate time series prediction system robust to missing values using any one of the prediction methods described in claims 1 to 8, characterized in that, It includes a reversible observation normalization module, a cross-time step fusion module, and a cross-variable fusion module; The reversible observation normalization module is used to normalize the backtracking window data and the corresponding mask matrix by means and variance to obtain normalized data; a time embedding is generated based on the timestamp feature, and the time embedding, normalized data and mask matrix are concatenated along the feature dimension to obtain a composite input tensor; The cross-time step fusion module is used to fuse features of composite input tensors along the time dimension to obtain time-dependent features; The cross-variable fusion module is used to fuse time-dependent features along the variable dimension to obtain cross-variable spatial dependency features; The reversible observation normalization module projects the cross-variable spatial dependency features back to the time dimension space of the multivariate time series, and performs inverse normalization to obtain the interpolated reconstruction values of the historical backtracking window and the predicted values of the future window.