A spatio-temporal prediction method based on PCMCI prior anchorable learnable causal graph
Patent Information
- Application Number
- CN202611051448.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-15
- Publication Date
- 2026-11-03
AI Technical Summary
Existing spatiotemporal prediction models for airport delays cannot capture non-spatial dependencies, lack causal interpretability, cannot perform counterfactual reasoning, have unreliable prediction intervals, and are difficult to quantify the propagation effects of intervention measures.
A learnable causal graph spatiotemporal prediction method based on PCMCI prior anchoring is adopted. By constructing a learnable causal graph model, the directed edges extracted by the PCMCI algorithm are used as prior knowledge. Combined with GRU temporal coding and multi-head GAT spatial coding, a joint loss function is designed. The model is trained by expanding window cross-validation to achieve conformal prediction intervals and counterfactual intervention.
It improves prediction accuracy, enhances causal interpretability, possesses counterfactual reasoning capabilities, outputs reliable prediction intervals, supports airport delay prediction and traffic flow prediction, and is suitable for high-risk spatiotemporal decision-making scenarios.
Smart Images
Figure CN123031771A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of deep learning technology, and specifically to a learnable causal graph spatiotemporal prediction method based on PCMCI prior anchoring. Background Technology
[0002] Spatiotemporal prediction of airport network delays is a core supporting technology for air traffic control and flight operation optimization. Accurately quantifying the propagation patterns of delays between airports and achieving reliable delay duration predictions have critical engineering value for flight scheduling, extreme congestion early warning, and control strategy formulation. With the rapid application of Graph Neural Networks (GNNs) in temporal modeling, spatiotemporal prediction methods based on GNNs have become the mainstream technical approach in airport delay prediction. Currently, mainstream GNN spatiotemporal prediction models construct airport association topology graphs in two main ways: one is a fixed topology graph based on prior physical rules, where adjacency matrices are predefined manually based on spatial distance information such as airport geographical location and route mileage; the other is a purely data-driven adaptive graph learning scheme, which automatically mines airport associations from historical operational data and dynamically generates adjacency matrices based on learnable parameters of the model. The two types of mapping approaches mentioned above are widely used in existing spatiotemporal prediction models, supporting the basic prediction of airport delay points. However, in practical applications aimed at refined air traffic control decision-making, the existing technical architecture still suffers from several inherent technical defects that are difficult to avoid, hindering the implementation of models in areas of critical engineering needs such as causal interpretability, counterfactual inference, and uncertainty quantification. These methods have the following technical problems:
[0003] 1. Physical distance graphs cannot capture non-spatial dependencies because airports that are far apart have strong delay propagation relationships due to flight route connections, resulting in the missing edge in the physical distance graph.
[0004] 2. While purely data-driven graph learning can uncover implicit dependencies, the edges it learns lack interpretability and are prone to overfitting to spurious correlations in the training data.
[0005] 3. Lack of counterfactual reasoning ability: Existing models can only make "observational predictions" and cannot answer causal intervention questions such as "If upstream airport delays are reduced by 20%, how much will downstream airport delays decrease?" These questions are crucial for the formulation of delay mitigation strategies.
[0006] Unreliable prediction intervals: Most models only output point predictions (single values) and cannot provide prediction intervals with confidence levels, resulting in unknown decision-making risks. Summary of the Invention
[0007] The purpose of this invention is to provide a learnable causal graph spatiotemporal prediction method based on PCMCI prior anchoring. By constructing a learnable causal graph spatiotemporal prediction model, this invention addresses the problem that existing models lack endogenous counterfactual reasoning capabilities and cannot quantitatively assess the propagation effect of intervention measures, thereby improving prediction accuracy.
[0008] To achieve the above objectives, this invention provides a spatiotemporal prediction method for learnable causal graphs based on PCMCI prior anchoring, comprising the following steps:
[0009] Step 1: Obtain the set of prior directed edges extracted from historical data by the PCMCI algorithm. and its causal strength weight ;
[0010] Step 2: Construct a learnable cause-effect graph module and initialize it:
[0011] For each prior edge ,set up
[0012] ;
[0013] For non-prior edges, set ;
[0014] Step 3: Construct a learnable causal graph spatiotemporal prediction model, inputting multi-lag features. From GRU temporal coding to learnable graph A+ multi-head GAT spatial coding, the final output is... ;
[0015] Step 4: Design the joint loss function ;
[0016] Step 5: Train the model using expanded window cross-validation and calculate the residual quantiles on the calibration set to construct the conformal prediction interval;
[0017] Step 6: Conduct counterfactual intervention and designate the target airport for intervention. and the intensity of intervention Modify the intermediate features of the model, perform forward propagation again, and calculate the average treatment effect. ;
[0018] Step 7: Output the learned graph adjacency matrix Model evaluation metrics, counterfactual effect curves, and prediction interval coverage.
[0019] The learnable causal graph spatiotemporal prediction model is composed of a data input and preprocessing module, a temporal coding module, a learnable causal graph module, a spatial coding module, an output module, a training and optimization module, a counterfactual intervention module, and a conformal prediction module connected in sequence.
[0020] The data input and preprocessing module is responsible for receiving multivariate time series data and constructing multi-lag feature windows.
[0021] The output module outputs the Gaussian distribution parameters of the predicted target: mean μ and logarithm of variance log(σ). 2 It supports probability prediction.
[0022] The temporal coding module consists of a linear projection layer and two gated recurrent units, used to extract high-dimensional temporal features of each node.
[0023] The spatial coding module employs a multi-head graph attention network, using the learnable graph A as the structural prior for attention computation, and introduces residual connections and layer normalization.
[0024] The learnable causal graph module maintains the learnable parameter edge_raw, which is then processed by the Sigmoid function to obtain the graph adjacency matrix. The PCMCI prior anchoring mechanism mandates that the weight of the prior edge is greater than or equal to a preset lower bound. Instead of learning prior edges starting from the minimum value, it learns them from the minimum value.
[0025] The training optimization module jointly optimizes the negative log-likelihood loss, sparse regularization loss, and attention diversity loss.
[0026] The counterfactual intervention module intervenes in the input features of a specified upstream node during the inference phase, re-propagates forward, calculates the counterfactual prediction changes of the downstream node, and supports Bootstrap confidence interval estimation.
[0027] The conformal prediction module generates prediction intervals with specified coverage for the predicted values based on the residual quantiles of the calibration set.
[0028] This invention provides a spatiotemporal prediction method for learnable causal graphs based on PCMCI prior anchoring. It integrates causal discovery and deep learning into a spatiotemporal prediction framework, constructing a PCMCI-based learnable causal graph spatiotemporal prediction model for airport delay prediction and traffic flow prediction. Specifically, directed causal edges mined from historical data by the PCMCI algorithm are used as prior knowledge, and the parameter space of the learnable graph structure is constrained by anchoring. This ensures that the final learned graph retains the causal prior framework while allowing data-driven fine-tuning of edge weights. Furthermore, a counterfactual intervention module enables causal inference. This invention integrates probabilistic prediction, counterfactual reasoning, and adaptive uncertainty quantification capabilities, significantly improving model interpretability and decision reliability while maintaining high accuracy. It is particularly suitable for high-risk spatiotemporal decision-making scenarios such as airport delay prediction. Attached Figure Description
[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0030] Figure 1 This is a schematic diagram of the architecture and process of the learnable causal graph spatiotemporal prediction method based on PCMCI prior anchoring described in this invention.
[0031] Figure 2 This is a flowchart illustrating a single-task scenario using the Causal-STGRN prediction model in an embodiment of the present invention.
[0032] Figure 3 This is a schematic diagram illustrating the results of counterfactual intervention and causal effect analysis introduced in an embodiment of the present invention.
[0033] Figure 4 This is a schematic diagram illustrating the process of optimizing the model through conformal prediction intervals in an embodiment of the present invention. Detailed Implementation
[0034] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.
[0035] This invention provides a learnable causal graph spatiotemporal prediction method based on PCMCI prior anchoring, comprising the following steps:
[0036] Step 1: Obtain the set of prior directed edges extracted from historical data by the PCMCI algorithm. and its causal strength weight ;
[0037] Step 2: Construct a learnable cause-effect graph module and initialize it:
[0038] For each prior edge ,set up
[0039] ;
[0040] For non-prior edges, set ;
[0041] Step 3: Construct a learnable causal graph spatiotemporal prediction model, inputting multi-lag features. From GRU temporal coding to learnable graph A+ multi-head GAT spatial coding, the final output is... ;
[0042] Step 4: Design the joint loss function ;
[0043] Step 5: Train the model using expanded window cross-validation and calculate the residual quantiles on the calibration set to construct the conformal prediction interval;
[0044] Step 6: Conduct counterfactual intervention and designate the target airport for intervention. and the intensity of intervention Modify the intermediate features of the model, perform forward propagation again, and calculate the average treatment effect. ;
[0045] Step 7: Output the learned graph adjacency matrix Model evaluation metrics, counterfactual effect curves, and prediction interval coverage.
[0046] Please see Figure 1 This invention provides a learnable causal graph spatiotemporal prediction model based on PCMCI prior anchoring (Causal-STGRN). The core idea is to use directed causal edges mined from historical data by the PCMCI algorithm as prior knowledge, constraining the parameter space of the learnable graph structure through "anchoring." This ensures that the finally learned graph retains the causal prior framework while allowing data-driven fine-tuning of edge weights. Furthermore, a counterfactual intervention module enables causal inference. The Causal-STGRN model includes the following sequentially connected modules:
[0047] Data input and preprocessing module: Receives multivariate time series data (such as multi-airport delay, meteorological, and traffic data) and constructs multi-lag feature windows.
[0048] The temporal coding module consists of a linear projection layer and two gated recurrent units (GRUs), used to extract high-dimensional temporal features of each node (airport).
[0049] Learnable causal graph module: Maintains the learnable parameter edge_raw, and obtains the graph adjacency matrix through the Sigmoid function. The PCMCI prior anchoring mechanism mandates that the weight of the prior edge is greater than or equal to a preset lower bound. (e.g., 0.1), instead of learning prior edges starting from the minimum value.
[0050] Spatial encoding module: Employs Multi-Head Graph Attention Network (Multi-HeadGAT) with learnable graphs As a structural prior for attention computation, residual connections and layer normalization (LayerNorm) are introduced.
[0051] Output module: Simultaneously outputs the Gaussian distribution parameters of the predicted target (delay) – mean. and logarithm of variance This supports probabilistic prediction.
[0052] Training optimization module: jointly optimizes negative log-likelihood loss, sparse regularization loss (only penalizing non-prior edges) and attention diversity loss.
[0053] Counterfactual intervention module: During the inference phase, the input features of a specified upstream node are intervened (e.g., their delay values are artificially reduced), the forward propagation is restarted, the counterfactual prediction changes of the downstream node are calculated, and Bootstrap confidence interval estimation is supported.
[0054] Conformal prediction module: Based on the residual quantiles of the calibration set, it generates prediction intervals with a specified coverage (e.g., 95%) for the predicted values.
[0055] Furthermore, to further illustrate the advantages of this invention, specific embodiments are proposed, showcasing the core functions and technological innovations of the Causal-STGRN model from different dimensions through three implementation methods (see details). Figures 2 to 4 ):
[0056] Implementation Method 1: Standard Causal-STGRN Model Training and Prediction (Single Task Scenario)
[0057] This embodiment uses the task of predicting flight delays at 60 airports in China as an example to simulate the complete implementation process of the invention. The model simultaneously learns the graph structure and prediction parameters, and finally outputs the delay distribution of each airport at the next time step.
[0058] Step 1: Data Acquisition and Preprocessing
[0059] Based on minute-by-minute operational data from 60 airports, including six feature dimensions: takeoff delay, arrival delay, scheduled flight volume, and weather conditions (visibility, wind speed, thunderstorm intensity), the data was resampled at 15-minute intervals to construct a lag window. (Using data from the past 3 hours, with each time step being 15 minutes), predict the arrival delay for the next time step. Use an expanded window to divide the dataset into training, validation, calibration, and test sets for subsequent experiments.
[0060] Step 2: Run the PCMCI algorithm to obtain causal priors
[0061] For the training set data, for each target airport Historical delay sequences from other airports were used as candidate causes, and the PCMCI algorithm was run simultaneously (parameter: maximum time delay). significance level Extract all directed edges that pass the conditional independence test. and the strength of its causal relationship (weighted by the test statistic in the MCI test). ). Obtain the prior edge set. For example, “Zhengzhou Xinzheng Airport (CGO) → Wuhan Tianhe Airport (WUH)” and “Beijing Capital Airport (PEK) → Shanghai Hongqiao Airport (SHA)”.
[0062] Step 3: Construct a learnable cause-effect graph module
[0063] Initialize the learnable parameter matrix with a shape of (60, 60), setting the diagonals to 0. For each prior edge... ,calculate: , Normalization to Interval. For non-prior edges, set (correspond Forward computation graph adjacency matrix: Prior anchoring: Forced execution after each forward computation; then... ,in This operation is implemented using a mask and does not participate in gradient backpropagation, but it affects subsequent GAT calculations.
[0064] Step 4: Construct the Causal-STGRN prediction model
[0065] The model structure consists of the following sub-modules in sequence, such as Figure 2 :
[0066] Input layer: B represents the batch size.
[0067] Timing encoder: Linear projection: ,Will Dimensional mapping to hidden dimensions 2-layer GRU (bidirectional, last forward output is taken): Output .
[0068] Learnable causal graph module (build the learnable causal module in step 3, output) ).
[0069] Spatial encoder (multi-head GAT):
[0070] Number of attention heads Calculate for each head:
[0071] Attention coefficient .
[0072] Figure A is used as a multiplication mask in attention computation, i.e. This ensures that weak edges in A are unlikely to receive high attention. Each head output... After splicing multiple outputs, they are aggregated through a linear layer.
[0073] Residual connection: .
[0074] Output layer: Mean:
[0075] Logarithm of variance:
[0076] Prediction Delay Distribution
[0077] Step 5: Training Process and Loss Function
[0078] The loss function is designed as follows:
[0079]
[0080] in: The mean (Gaussian negative log-likelihood).
[0081] Here is the average weight of the non-prior edges, where The set of non-prior edges Prior edges are not subject to sparsity penalty.
[0082] ,in Let k be the node feature matrix output by the attention head. Calculate the mean absolute Pearson correlation coefficient between the column vectors of the two matrices, λ2=0.005.
[0083] Optimizer: The Adam optimizer was used for parameter optimization, with a learning rate of 0.001 and weight decay of 1e-5. There were 100 training epochs, with a waiting period of 15 epochs before early termination. Training was stopped if the validation set loss did not decrease for 15 consecutive epochs.
[0084] Step 6: Constructing Conformal Prediction Intervals
[0085] The trained model was run on the calibration set (July–September 2020) to obtain predictions. and the true value .
[0086] Calculate the inconsistency score: (i.e., standardized residuals).
[0087] Take the 95th percentile of the fractional distribution: .
[0088] For the test set, the prediction interval is: .
[0089] Step 7: Results Output and Evaluation
[0090] Output the learned graph adjacency matrix This can be compared with the PCMCI prior graph to statistically analyze the proportion of newly added and disappeared edges. (Test set) It is 0.05 higher than the fixed distance map; the actual coverage of the predicted interval is 94.7%, close to the nominal 95%.
[0091] In the case study, the temporal GRU captured the dynamic propagation lag characteristics of airport delays, while the spatial GAT utilized the learnable graph. Guided by this approach, attention is focused on upstream nodes with genuine causal relationships. The two work together: GRU provides temporal alignment, and GAT provides spatial selection, allowing the negative log-likelihood loss of the output layer to guide edge_raw to fine-tune edge weights and even uncover new dependencies (such as new propagation paths under extreme weather conditions) while preserving prior edges. Sparse regularization only applies to non-prior edges, ensuring the model doesn't add a large number of spurious edges for minimal fit improvement. The final model achieves both high-accuracy predictions and outputs an interpretable causal graph.
[0092] Implementation Method Two: Counterfactual Intervention and Causal Effect Analysis
[0093] This implementation case shares the same model structure and training parameters as Implementation Case 1, but introduces intervention operations during the inference phase, such as... Figure 3 This is used to answer the question, "If delays at a certain upstream airport decrease..." How much will downstream delays change? This example is applicable to the pre-evaluation of delay mitigation strategies.
[0094] Step 1: Load the pre-trained Causal-STGRN model
[0095] Load the model parameters (including edge_raw, GRU weights, GAT weights, etc.) saved in Implementation Method 1, freeze all parameters, and do not perform gradient calculation.
[0096] Step 2: Selecting Intervention Goals and Intervention Strategies
[0097] Designated upstream airport Zhengzhou Xinzheng International Airport (CGO), downstream target airport =Wuhan Tianhe Airport (WUH).
[0098] Intervention strategy: Multiply the historical delay sequence of CGO within a specific time window by a coefficient. ,in Indicates the intensity of intervention.
[0099] Step 3: Perform counterfactual forward propagation
[0100] Original forward pass: Input original features The Causal-STGRN model was used to obtain the downstream delay prediction. .
[0101] Counterfactual forward: copying Modify the delay feature of the CGO node to Other features remain unchanged. (Modified version) The same model is input to ultimately obtain counterfactual predictions.
[0102] Calculate the individual treatment effect: .
[0103] Step 4: Multi-intensity intervention and Bootstrap confidence interval
[0104] right Repeat step 3 to perform counterfactual forward propagation and obtain different results. .
[0105] The Bootstrap method was used: 500 random samples with replacement were taken from the test set, and the ITE distribution was calculated each time. The 2.5% and 97.5% quantiles were used as the 95% confidence intervals.
[0106] Step 5: Output the causal effect curve
[0107] Based on the obtained data, an intervention intensity vs. average treatment effect curve was plotted to show the impact of CGO delay reduction on WUH delay.
[0108] The results showed that when CGO delays decreased by 30%, WUH delays decreased by an average of 4.2 minutes (95% CI: 3.5–4.9 minutes); when CGO delays decreased by 60%, WUH delays decreased by 7.8 minutes (95% CI: 6.9–8.7 minutes), exhibiting an approximately linear relationship, which is consistent with common sense regarding aviation network communication.
[0109] Step 6: Edge Blocking Analysis
[0110] Humans will learn the graph edge weight Force it to 0 (blocking the causal path) and re-execute the counterfactual intervention. If ITE approaches 0 at this point, it proves that the edge did indeed transmit a causal effect, enhancing the interpretability of the model.
[0111] This embodiment achieves counterfactual inference because the model learns the causal structure of the real data generation mechanism during the training phase (through PCMCI prior anchoring and data fine-tuning). During the inference phase, we explicitly modify the input features (intervention) while keeping the model parameters unchanged, simulating a counterfactual scenario where "only the upstream delay is changed, all other conditions remaining constant." Internally, the temporal GRU encodes the modified upstream delay into different hidden states, and the GAT (Growth Atlas) uses the learnable graph... middle The attention weights are then propagated to the WUH representation, and the final output layer reflects this change. Above. The entire process does not require training an additional causal model, achieving "one model, two uses" (prediction + counterfactual).
[0112] Implementation Method 3: Conformal Prediction Interval Optimization (Adaptive Quantile Version)
[0113] This implementation case improves upon implementation method one by modifying the conformal prediction interval construction method, as follows: Figure 4 This allows it to adapt to the heteroscedasticity of input features (i.e., greater prediction uncertainty under high latency). This embodiment is suitable for scenarios with extremely high requirements for prediction reliability, such as air traffic control decision-making.
[0114] Step 1: Train the basic Causal-STGRN model
[0115] Step 2: Calculate the weighted residuals on the calibration set
[0116] The model outputs the value of each sample on the calibration set. .
[0117] Define the non-consistent score as: ,in It's an adjustment parameter. When When it degenerates into an absolute residual; when The time represents the standardized residual. This embodiment selects the residual through a grid search. .
[0118] Step 3: Quantile calibration and interval construction
[0119] Calculate fractions 95th percentile .
[0120] For test set sample t, the prediction interval is: .
[0121] Step 4: Coverage and Interval Width Assessment
[0122] Calculate the actual coverage on the test set and compare it to the nominal 95%. Also calculate the average interval width.
[0123] The results show that the interval width in this embodiment automatically widens in high-latency scenarios (because σ_t is large) and narrows in low-latency scenarios, achieving adaptive uncertainty quantification. Compared with the fixed scaling factor (q_0.95*σ_t) in Implementation Method 1, the interval in this embodiment is more economical (average width reduced by 12%), while the coverage remains at 94.5%.
[0124] Step 5: Output reliability diagnostic chart
[0125] Plot a scatter plot of "predicted mean vs. standardized residuals" and overlay a quantile regression curve to show the interval coverage under different delay levels.
[0126] Output the predicted range coverage probability ranking for each airport to identify airports that need data improvement.
[0127] Working principle analysis: Standard conformal prediction assumes that the score distribution is independent of the feature, but the variance of the delayed data usually increases with the delay value (heteroscedasticity). This embodiment introduces... An index that allows the scale of scores to vary with the predictive standard deviation. Adjustment to make the quantiles Different The coverage remains consistent even at the horizontal level. This is achieved through probabilistic predictions combined with the Causal-STGRN output. This embodiment further improves the reliability and economy of interval prediction. This effect is achieved by combining two steps: "probabilistic prediction output + adaptive conformal calibration," neither of which can be omitted.
[0128] In summary, compared with the prior art, the present invention has the following beneficial effects:
[0129] 1. The accuracy of single-point prediction in the model is significantly improved.
[0130] Existing fixed adjacency graphs based on geographic location cannot depict the real delay propagation relationships caused by flight transfers between long-distance airports, resulting in a disconnect between the topology and objective delay propagation patterns. Pure data-driven graph learning without causal prior constraints easily fits spurious correlations in the data, limiting its generalization ability. This invention leverages PCMCI causal discovery results to differentially initialize the parameters of the learnable causal graph and anchor prior edges. It embeds statistically validated objective causal relationships into the adjacency matrix generation process and constrains the spatial attention network to perform feature aggregation only between real causal links, allowing the graph topology to align with the real mechanisms of airport delay generation. On a real-world dataset of 60 domestic hub airports, the model's coefficient of determination R² is improved by 0.03-0.05 compared to the geographic distance-based graph baseline and by 0.01-0.02 compared to a pure adaptive graph neural network without prior knowledge. Under extreme test samples with unconventional disturbances such as thunderstorms and temporary airspace control, the model's generalization performance advantage is further highlighted, effectively improving the prediction bias problem caused by topological distortion in traditional models.
[0131] 2. The interpretability of causal topology is greatly enhanced, making it suitable for practical analysis of air traffic control operations.
[0132] Traditional fixed topology graphs and black-box adaptive graphs cannot distinguish the origin of airport-related edges. The learned links cannot determine whether they are due to objective causal effects or accidental data correlations, making it difficult to provide air traffic control personnel with a practical basis for delay tracing. This invention uses differentiated initialization rules for learnable causal graph parameters to naturally form two types of distinguishable edges in the trained causal graph: original prior causal edges obtained and anchored by the PCMCI algorithm, and newly added implicit related edges autonomously mined and supplemented by the model based on measured data. This allows for a direct comparison between the prior baseline graph and the learned graph, clearly identifying the retention of original causal dependencies and newly discovered delay propagation associations in the data, accurately locating key propagation hub airports, breaking through the bottleneck of "black-box modeling" in graph neural networks, and facilitating the analysis of delay cross-airport propagation mechanisms from a business perspective.
[0133] 3. The model has built-in native counterfactual reasoning capabilities, eliminating the need to build an additional independent causal simulation model.
[0134] Existing spatiotemporal prediction models only support observational post-event predictions. To conduct simulations of control measures and quantify intervention effects, additional causal models need to be trained separately, resulting in drawbacks such as inconsistent parameters across multiple models, high development costs, and the accumulation of simulation errors. This invention deeply integrates the causal adjacency matrix into the Causal-STGRN network architecture. After model training, all network parameters are frozen, and the delay input characteristics of the target upstream airport are specifically modified. Counterfactual simulation can be completed through a single forward propagation, directly calculating the change in downstream airport delays caused by upstream intervention (ITE individual treatment effect). This allows for rapid quantitative simulation of "a specific percentage reduction in upstream airport delays and how many minutes the downstream airport delays change," providing quantitative data support for pre-emptive decisions such as air traffic control flow restriction and flight schedule optimization.
[0135] 4. The adaptive conformal prediction interval balances reliability and economy, solving the interval failure problem in heteroscedastic scenarios.
[0136] Conventional prediction models only output single-point prediction values, failing to quantify prediction uncertainty. Traditional conformal prediction methods with fixed scaling factors ignore the inherent heteroscedasticity of civil aviation delays. In high-delay scenarios, prediction uncertainty is high, but the fixed interval width can lead to insufficient coverage; in low-delay scenarios, uncertainty is low, but the interval redundancy is too wide. This invention improves the conformal algorithm by introducing a weighted non-consistency score with a hyperparameter τ on top of the model's probability output layer, relying on the prediction standard deviation of the model output. Dynamically and adaptively adjusts the interval width to address high latency. Larger predictions, automatically widened prediction range, low latency correspondence The model exhibits relatively small intervals with automatic narrowing. On an independent, unseen test set, the measured coverage of the model interval remains stable at 94.5%, closely approaching the 95% nominal confidence level. At the same time, compared to the traditional fixed-coefficient interval, the average width is reduced by 12%, simplifying interval redundancy while ensuring statistical reliability. This effectively quantifies prediction uncertainty and reduces air traffic control decision-making risks.
[0137] 5. Differentiated sparsity constraints achieve sparsity and structural stability in causal graphs, preserving effective causal prior information.
[0138] Traditional global uniform sparse regularization indiscriminately compresses and penalizes all graph edge weights, easily leading to excessive sparsity of valuable true causal edges mined by the PCMCI algorithm, or even their removal from the topology, resulting in the loss of objective causal knowledge. Without regularization constraints, it easily breeds a large number of noisy and spurious edges, causing severe model training oscillations. This invention employs a targeted, differentiated sparse regularization strategy, applying sparsity penalties to non-causal original edges without PCMCI prior constraints, while prior causal edges protected by anchored lower bounds are not compressed by sparse regularization. This design filters out invalid redundant edges induced by data noise, achieving overall sparsity and lightweighting of the causal graph, while fully preserving the true propagation links verified by causality, effectively suppressing overfitting and improving the convergence stability of causal graph training.
[0139] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.
Claims
1. A learnable causal graph spatiotemporal prediction method based on PCMCI prior anchoring, characterized in that, Includes the following steps: Step 1: Obtain the set of prior directed edges extracted from historical data by the PCMCI algorithm. and its causal strength weight ; Step 2: Construct a learnable cause-effect graph module and initialize it: For each prior edge ,set up ； For non-prior edges, set ; Step 3: Construct a learnable causal graph spatiotemporal prediction model, inputting multi-lag features. From GRU temporal coding to learnable graph A+ multi-head GAT spatial coding, the final output is... ; Step 4: Design the joint loss function ; Step 5: Train the model using expanded window cross-validation and calculate the residual quantiles on the calibration set to construct the conformal prediction interval; Step 6: Conduct counterfactual intervention and designate the target airport for intervention. and the intensity of intervention Modify the intermediate features of the model, perform forward propagation again, and calculate the average treatment effect. ; Step 7: Output the learned graph adjacency matrix Model evaluation metrics, counterfactual effect curves, and prediction interval coverage.
2. The spatiotemporal prediction method for learnable causal graphs based on PCMCI prior anchoring as described in claim 1, characterized in that, The learnable causal graph spatiotemporal prediction model is composed of a data input and preprocessing module, a temporal coding module, a learnable causal graph module, a spatial coding module, an output module, a training and optimization module, a counterfactual intervention module, and a conformal prediction module connected in sequence.
3. The spatiotemporal prediction method for learnable causal graphs based on PCMCI prior anchoring as described in claim 2, characterized in that, The data input and preprocessing module is responsible for receiving multivariate time series data and constructing multi-lag feature windows. The output module outputs the Gaussian distribution parameters of the predicted target: mean μ and logarithm of variance log(σ). 2 It supports probability prediction.
4. The spatiotemporal prediction method for learnable causal graphs based on PCMCI prior anchoring as described in claim 2, characterized in that, The temporal coding module consists of a linear projection layer and two gated recurrent units, used to extract high-dimensional temporal features of each node; The spatial coding module employs a multi-head graph attention network, using the learnable graph A as the structural prior for attention computation, and introduces residual connections and layer normalization.
5. The spatiotemporal prediction method for learnable causal graphs based on PCMCI prior anchoring as described in claim 2, characterized in that, The learnable causal graph module maintains a learnable parameter edge_raw, which is then processed by the Sigmoid function to obtain the graph adjacency matrix. The PCMCI prior anchoring mechanism mandates that the weight of the prior edge is greater than or equal to a preset lower bound. Instead of learning prior edges starting from the minimum value, it learns them from the minimum value.
6. The spatiotemporal prediction method for learnable causal graphs based on PCMCI prior anchoring as described in claim 2, characterized in that, The training optimization module jointly optimizes the negative log-likelihood loss, sparse regularization loss, and attention diversity loss.
7. The spatiotemporal prediction method for learnable causal graphs based on PCMCI prior anchoring as described in claim 2, characterized in that, During the inference phase, the counterfactual intervention module intervenes in the input features of a specified upstream node, re-propagates forward, calculates the counterfactual prediction changes of downstream nodes, and supports Bootstrap confidence interval estimation. The conformal prediction module generates prediction intervals with specified coverage for the predicted values based on the residual quantiles of the calibration set.