20260203 meeting
Background
This experiment uses the Weather2K dataset, identical to prior work, and evaluates whether, during the training process of $SSSD^{S4}$, the predicted value epsilon_theta should pass through $autoFRK$ again before being output.
sssd/training/utils.py training_loss
| |
The input dataset has shape (locations, time, variables). After loading, the time-series dimension (2nd dimension) is standardized. The location coordinates used by $autoFRK$ have shape (n, coords), where coords $\in$ {1, 2, 3}. Here, latitude and longitude are used, i.e., (n, 2).
At the end of the experiment, to verify whether spatial standardization affects the imputation results of $autoFRK$, additional experiments are conducted by first restoring the time series, standardizing only the spatial coordinates, applying $autoFRK$, and finally restoring the data back to the original scale.
sssd/inference/generator.py DiffusionGenerator.generate()
| |
Naming Scheme
Experiments are named using the format XXX-XXXX-XX, where XXX means whether $autoFRK$ is used during training; XXXX for number of training iterations; XX means whether spatial standardization is applied. For example, NoFRK-4000-NoSP means no $autoFRK$ during training, 4,000 iterations, no spatial normalization during inference.
Time-Series Distortion Issue
After a full inspection of the code, no abnormality was found. Thus, the earlier distortion in time-series prediction is suspected to originate from S4 layer parameter settings. The following modifications are applied:
model.yaml
| |
To improve temporal prediction accuracy, the main adjustment increases s4_state_dim, making it larger than residual_layers, and introduces s4_dropout = 0.1 instead of 0.0.
The intuition is that dropout may improve robustness to missing values. Future work may further increase s4_state_dim, s4_dropout, and the number of iterations.
To understand whether diffusion hyperparameters impact performance, two settings are tested:
T200beta_00.0001beta_T0.01
- T: 200
- beta_0: 0.0001
- beta_T: 0.01
T500beta_00.0008beta_T0.08
- T: 500
- beta_0: 0.0008
- beta_T: 0.08
These two settings aim to provide direction for model tuning.
training.yaml
| |
inference.yaml
| |
Both files contain autoFRK configuration.
In future work, AFRK_method and AFRK_tps_method should be merged into model.yaml for unified configuration.
In training.yaml, these two parameters are not yet adjustable and currently always use prediction values; this should be corrected later.
T200beta_00.0001beta_T0.01
FRK-4000-SP
| ALL Locs & All Time | Known Locs & All Time | Unknown Locs & All Time | ALL Locs & Future | Known Locs & Future | Unknown Locs & Future | ALL Locs & Past | Known Locs & Past | Unknown Locs & Past | |
|---|---|---|---|---|---|---|---|---|---|
| MSPE | 3.673955e+00 | 1.044696 | 2.691385 | 11.692819 | 3.482321 | 4.216817 | 2.372992e-01 | 4.597242e-08 | 2.037628 |
| RMSPE | 1.916756e+00 | 1.022104 | 1.640544 | 3.419476 | 1.866098 | 2.053489 | 4.871336e-01 | 2.144118e-04 | 1.427455 |
| MSPE% | 4.622483e+08 | 0.037858 | 0.099724 | 0.627227 | 0.126193 | 0.158012 | 6.603546e+08 | 2.081493e-09 | 0.074743 |
| RMSPE% | 2.149996e+04 | 0.194571 | 0.315791 | 0.791977 | 0.355237 | 0.397507 | 2.569737e+04 | 4.562338e-05 | 0.273392 |
| MAPE | 8.162235e-01 | 0.449798 | 1.145363 | 2.535552 | 1.498969 | 1.427123 | 7.936824e-02 | 1.531350e-04 | 1.024609 |
| MAPE% | 7.451615e+07 | 0.016351 | 0.041299 | 0.125651 | 0.054487 | 0.051297 | 1.064516e+08 | 6.598459e-06 | 0.037015 |
FRK-4000-NoSP
| ALL Locs & All Time | Known Locs & All Time | Unknown Locs & All Time | ALL Locs & Future | Known Locs & Future | Unknown Locs & Future | ALL Locs & Past | Known Locs & Past | Unknown Locs & Past | |
|---|---|---|---|---|---|---|---|---|---|
| MSPE | 3.683970e+00 | 1.076751 | 2.560667 | 11.714867 | 3.589169 | 4.042310 | 2.421567e-01 | 6.761885e-08 | 1.925678 |
| RMSPE | 1.919367e+00 | 1.037666 | 1.600209 | 3.422699 | 1.894510 | 2.010550 | 4.920942e-01 | 2.600363e-04 | 1.387688 |
| MSPE% | 5.535801e+08 | 0.039082 | 0.092555 | 0.628924 | 0.130273 | 0.148356 | 7.908287e+08 | 3.082764e-09 | 0.068640 |
| RMSPE% | 2.352828e+04 | 0.197691 | 0.304228 | 0.793048 | 0.360933 | 0.385170 | 2.812168e+04 | 5.552264e-05 | 0.261992 |
| MAPE | 8.178309e-01 | 0.461213 | 1.104491 | 2.539616 | 1.537005 | 1.424604 | 7.992314e-02 | 1.600120e-04 | 0.967299 |
| MAPE% | 8.074776e+07 | 0.016766 | 0.039164 | 0.125762 | 0.055870 | 0.050449 | 1.153539e+08 | 6.924418e-06 | 0.034328 |
NoFRK-4000-SP
| ALL Locs & All Time | Known Locs & All Time | Unknown Locs & All Time | ALL Locs & Future | Known Locs & Future | Unknown Locs & Future | ALL Locs & Past | Known Locs & Past | Unknown Locs & Past | |
|---|---|---|---|---|---|---|---|---|---|
| MSPE | 3.913162e+00 | 0.952113 | 2.773699 | 12.480633 | 3.166137 | 4.512771 | 2.413884e-01 | 0.003245 | 2.028383 |
| RMSPE | 1.978171e+00 | 0.975763 | 1.665443 | 3.532794 | 1.779364 | 2.124328 | 4.913130e-01 | 0.056968 | 1.424213 |
| MSPE% | 4.778024e+08 | 0.034727 | 0.103089 | 0.683527 | 0.115452 | 0.169912 | 6.825749e+08 | 0.000131 | 0.074450 |
| RMSPE% | 2.185869e+04 | 0.186352 | 0.321074 | 0.826757 | 0.339783 | 0.412204 | 2.612613e+04 | 0.011436 | 0.272855 |
| MAPE | 8.732765e-01 | 0.448829 | 1.169394 | 2.621475 | 1.391152 | 1.510315 | 1.240487e-01 | 0.044976 | 1.023285 |
| MAPE% | 7.806765e+07 | 0.016514 | 0.042264 | 0.131471 | 0.050783 | 0.054626 | 1.115252e+08 | 0.001827 | 0.036966 |
NoFRK-4000-NoSP
| ALL Locs & All Time | Known Locs & All Time | Unknown Locs & All Time | ALL Locs & Future | Known Locs & Future | Unknown Locs & Future | ALL Locs & Past | Known Locs & Past | Unknown Locs & Past | |
|---|---|---|---|---|---|---|---|---|---|
| MSPE | 3.942854e+00 | 0.947710 | 3.333118 | 12.516242 | 3.151153 | 5.188118 | 2.685454e-01 | 0.003377 | 2.538118 |
| RMSPE | 1.985662e+00 | 0.973504 | 1.825683 | 3.537830 | 1.775149 | 2.277744 | 5.182137e-01 | 0.058109 | 1.593147 |
| MSPE% | 6.130173e+08 | 0.034590 | 0.120954 | 0.685074 | 0.114983 | 0.190949 | 8.757390e+08 | 0.000137 | 0.090956 |
| RMSPE% | 2.475919e+04 | 0.185985 | 0.347785 | 0.827692 | 0.339091 | 0.436978 | 2.959289e+04 | 0.011687 | 0.301589 |
| MAPE | 8.781141e-01 | 0.446807 | 1.310592 | 2.624647 | 1.382412 | 1.635597 | 1.296001e-01 | 0.045833 | 1.171304 |
| MAPE% | 8.724114e+07 | 0.016465 | 0.046693 | 0.131566 | 0.050527 | 0.058264 | 1.246302e+08 | 0.001866 | 0.041733 |
T500beta_00.0008beta_T0.08
FRK-4000-SP
| ALL Locs & All Time | Known Locs & All Time | Unknown Locs & All Time | ALL Locs & Future | Known Locs & Future | Unknown Locs & Future | ALL Locs & Past | Known Locs & Past | Unknown Locs & Past | |
|---|---|---|---|---|---|---|---|---|---|
| MSPE | 3.623991e+00 | 1.083529 | 2.487596 | 11.545750 | 3.611759 | 3.621018 | 2.289513e-01 | 2.038718e-06 | 2.001843 |
| RMSPE | 1.903678e+00 | 1.040927 | 1.577211 | 3.397904 | 1.900463 | 1.902897 | 4.784885e-01 | 1.427837e-03 | 1.414865 |
| MSPE% | 3.975542e+08 | 0.039586 | 0.090990 | 0.616765 | 0.131953 | 0.134522 | 5.679346e+08 | 9.251824e-08 | 0.072333 |
| RMSPE% | 1.993876e+04 | 0.198962 | 0.301645 | 0.785344 | 0.363254 | 0.366773 | 2.383138e+04 | 3.041681e-04 | 0.268947 |
| MAPE | 8.185870e-01 | 0.447891 | 1.105351 | 2.542192 | 1.490310 | 1.325118 | 7.989899e-02 | 1.140664e-03 | 1.011165 |
| MAPE% | 6.858757e+07 | 0.016339 | 0.039440 | 0.125369 | 0.054350 | 0.047174 | 9.798224e+07 | 4.903483e-05 | 0.036126 |
FRK-4000-NoSP
| ALL Locs & All Time | Known Locs & All Time | Unknown Locs & All Time | ALL Locs & Future | Known Locs & Future | Unknown Locs & Future | ALL Locs & Past | Known Locs & Past | Unknown Locs & Past | |
|---|---|---|---|---|---|---|---|---|---|
| MSPE | 3.658965e+00 | 0.966137 | 3.058320 | 11.609590 | 3.220452 | 4.799263 | 2.515544e-01 | 2.038718e-06 | 2.312201 |
| RMSPE | 1.912842e+00 | 0.982923 | 1.748805 | 3.407285 | 1.794562 | 2.190722 | 5.015520e-01 | 1.427837e-03 | 1.520592 |
| MSPE% | 5.324177e+08 | 0.035367 | 0.111554 | 0.619298 | 0.117888 | 0.176998 | 7.605967e+08 | 9.251824e-08 | 0.083506 |
| RMSPE% | 2.307418e+04 | 0.188060 | 0.333996 | 0.786955 | 0.343349 | 0.420711 | 2.757892e+04 | 3.041681e-04 | 0.288974 |
| MAPE | 8.238042e-01 | 0.429766 | 1.254655 | 2.551795 | 1.429892 | 1.577962 | 8.323673e-02 | 1.140664e-03 | 1.116094 |
| MAPE% | 7.873417e+07 | 0.015684 | 0.044845 | 0.125726 | 0.052164 | 0.056313 | 1.124774e+08 | 4.903483e-05 | 0.039930 |
NoFRK-4000-SP
| ALL Locs & All Time | Known Locs & All Time | Unknown Locs & All Time | ALL Locs & Future | Known Locs & Future | Unknown Locs & Future | ALL Locs & Past | Known Locs & Past | Unknown Locs & Past | |
|---|---|---|---|---|---|---|---|---|---|
| MSPE | 3.949662e+00 | 1.047118 | 2.772684 | 12.555850 | 3.441994 | 4.511609 | 2.612950e-01 | 0.020743 | 2.027430 |
| RMSPE | 1.987376e+00 | 1.023288 | 1.665138 | 3.543424 | 1.855261 | 2.124055 | 5.111702e-01 | 0.144023 | 1.423879 |
| MSPE% | 4.903674e+08 | 0.038852 | 0.103059 | 0.685541 | 0.127553 | 0.169649 | 7.005249e+08 | 0.000837 | 0.074521 |
| RMSPE% | 2.214424e+04 | 0.197109 | 0.321028 | 0.827974 | 0.357146 | 0.411884 | 2.646743e+04 | 0.028938 | 0.272985 |
| MAPE | 9.255151e-01 | 0.521930 | 1.169730 | 2.631151 | 1.468595 | 1.509787 | 1.945285e-01 | 0.116216 | 1.023991 |
| MAPE% | 8.165531e+07 | 0.019474 | 0.042267 | 0.131905 | 0.053917 | 0.054554 | 1.166504e+08 | 0.004712 | 0.037001 |
NoFRK-4000-NoSP
| ALL Locs & All Time | Known Locs & All Time | Unknown Locs & All Time | ALL Locs & Future | Known Locs & Future | Unknown Locs & Future | ALL Locs & Past | Known Locs & Past | Unknown Locs & Past | |
|---|---|---|---|---|---|---|---|---|---|
| MSPE | 3.950400e+00 | 1.019267 | 2.684636 | 12.537292 | 3.348497 | 4.416978 | 2.703033e-01 | 0.021026 | 1.942204 |
| RMSPE | 1.987561e+00 | 1.009588 | 1.638486 | 3.540804 | 1.829890 | 2.101661 | 5.199070e-01 | 0.145002 | 1.393630 |
| MSPE% | 6.183450e+08 | 0.037956 | 0.098216 | 0.686796 | 0.124534 | 0.164116 | 8.833500e+08 | 0.000850 | 0.069974 |
| RMSPE% | 2.486654e+04 | 0.194822 | 0.313395 | 0.828731 | 0.352894 | 0.405113 | 2.972120e+04 | 0.029160 | 0.264525 |
| MAPE | 9.257683e-01 | 0.517047 | 1.158709 | 2.629134 | 1.449343 | 1.529362 | 1.957544e-01 | 0.117492 | 0.999858 |
| MAPE% | 9.063959e+07 | 0.019332 | 0.041542 | 0.131896 | 0.053325 | 0.054903 | 1.294851e+08 | 0.004764 | 0.035816 |
Conclusion
Diffusion Steps and Parameter Adjustments (T500 vs T200)
Experimental results indicate that moderately increasing the diffusion steps T and tuning the beta parameters have a significant impact on the stability of future predictions:
Improved Prediction Accuracy: In the evaluation of
Unknown Locs & Future, the T500 configuration (T500-beta_0.0008) demonstrates better convergence compared to T200. For example, under the FRK-4000-SP setup, the MSPE of T500 is 3.621, outperforming T200’s 4.217.Better Future Trend Modeling: The increase in
s4_state_dim(128) along withs4_dropout(0.1) effectively mitigates the temporal distortion observed in earlier versions. These adjustments enhance the model’s generalization capability for future unseen segments.
Contribution of FRK Spatial Imputation to Unknown Locations
Across both known and unknown locations, FRK spatial imputation does not exhibit large differences. The best MSPE appears in the T500beta_0.0008beta_T0.08 – FRK-4000-SP configuration, while the worst MSPE similarly appears in the T500beta_0.0008beta_T0.08 – FRK-4000-NoSP configuration.
This suggests that while FRK contributes meaningfully to spatial consistency, its effectiveness is sensitive to preprocessing choices, particularly spatial normalization.
Spatial Standardization (SP)
Spatial standardization shows mild instability in this experiment. Results differ notably between T500 and T200 configurations, indicating that SP may introduce additional variance and does not consistently enhance model performance.
References
- Zhu X, Xiong Y, Wu M, et al. Weather2K: A Multivariate Spatio-Temporal Benchmark Dataset for Meteorological Forecasting Based on Real-Time Observation Data from Ground Weather Stations[C]//International Conference on Artificial Intelligence and Statistics. PMLR, 2023: 2704-2722.
- Juan Lopez Alcaraz, Nils Strodthoff (2022). Diffusion-based time series imputation and forecasting with structured state space models. Transactions on Machine Learning Research. Retrieved from https://openreview.net/forum?id=hHiIbk7ApW
- SSSD (2022). GitHub. Retrieved from https://github.com/AI4HealthUOL/SSSD


![[Thought] Historical Earthquake Locations Around Taiwan](https://Josh-test-lab.github.io/posts/Historical%20Earthquake%20Locations%20Around%20Taiwan/cover%20image.webp)






