1150203 meeting
前情提要
本次實驗同先前一樣使用 Weather2K 資料集,並測試在 $SSSD^{S4}$ 的訓練過程中,使其 epsilon_theta 預測值再次經過 $autoFRK$ 後才輸出。
sssd/training/utils.py training_loss
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輸入之資料集形狀為 (地點, 時間, 變數) ,並在輸入後對時間序列,也就是第 2 維度做標準化;輸入用於 $autoFRK$ 的地點座標形狀為 (地點, 座標) ,可為 (n, 1) 或 (n, 2) 或 (n, 3) ,本處採用的是緯度和經度,為 (n, 2) 。
在實驗的最後,為驗證對空間進行標準化是否會對 $autoFRK$ 的填補造成影響,故以下部分實驗包含:將時間序列還原後,對其地點進行標準化,經 $autoFRK$ 再還原回原資料尺度。
sssd/inference/generator.py DiffusionGenerator.generate()
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命名方式
以下各實驗命名方式遵照 XXX-XXXX-XX 的方式進行命名,其中 XXX 指的是是否有在訓練過程中使用 $autoFRK$ , XXXX 指的是訓練的迭代次數, XX 則是是否有對地點做標準化。如 NoFRK-4000-NoSP 指的是在訓練中未使用 $autoFRK$ ,迭代 4,000 次,且在填補時未對地點做標準化。
時間序列失真問題
經排查整體程式碼後,無發現異處。故推斷先前時間序列預測失真原因,可能為 $S4$ 層參數設定問題。故本次實驗設定修改如下:
model.yaml
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為提升時間序列準確率,本次主要調整 s4_state_dim 讓其高於 residual_layers ,並將 s4_dropout 由 0.0 更改為 0.1 ,以期 $S4$ 層能透過 dropout 而提升其在缺失值的預測能力,也或許未來可進一步提升 s4_state_dim 和 s4_dropout ,並透過拉高迭代次數使預測結果更加準確。
為釐清 diffusion 設定是否會影響實驗結果,本次實驗分別作了以下調整:
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
望藉二種實驗找出應調整的方向。
training.yaml
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inference.yaml
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在 training.yaml 和 inference.yaml 中,分別存有 autoFRK 的設定,未來希望將 AFRK_method 和 AFRK_tps_method 整合至 model.yaml 中進行統一設定。在 training.yaml 中, AFRK_method 和 AFRK_tps_method 目前暫未可供調整,皆使用預測值,這應於後續修正。
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 |
結論
擴散步數與參數調整 (T500 vs T200)
實驗數據顯示,適度增加擴散步數 T 與調整 beta 參數對於未來預測的穩定性有顯著影響:
- 預測精準度提升:在
Unknown Locs & Future的測試中,T500 配置(T500-beta_0.0008)相較於 T200 配置,在 MSPE 與 RMSPE 上展現了更優的收斂特性。例如,在 FRK-4000-SP 組合下,T500 的 MSPE 為 3.621,優於 T200 的 4.217。 - 未來趨勢擬合:較高的
s4_state_dim(128) 與s4_dropout(0.1) 有效改善了先前版本中時間序列失真的問題,使模型在面對未來未知區段時具備更強的泛化能力。
FRK 空間填補對未知地點的關鍵貢獻
無論是在已知地點或未知地點, FRK 空間填補似乎都無較大差異。最優的 MSPE 出現在 T500beta_00.0008beta_T0.08 的 FRK-4000-SP ;而最差的 MSPE 同樣也出現在 T500beta_00.0008beta_T0.08 的 FRK-4000-NoSP
空間標準化 (SP)
對空間進行標準化,對本次實驗結果而言也有些許不穩定,特別看到 T500 和 T200 的結果都不盡相同。
參考資料
- 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。參考自 https://openreview.net/forum?id=hHiIbk7ApW
- SSSD(2022)。GitHub。參考自 https://github.com/AI4HealthUOL/SSSD






