20250304 meeting

Discussion on the Input and Output of the $SSSD^{S4}$ Model.

Published 2025-02-28 Updated 2025-04-23 2401 words 12 minutes views

https://raw.githubusercontent.com/AI4HealthUOL/SSSD/main/reports/updated_architecture.png

Contents

The cover image is the operational process of the $SSSD^{S4}$ model, captured from Github on February 28, 2024.

$SSSD$ Model Dataset

I tried using the example provided by the original authors on Github, training with the Mujoco dataset. From the original author’s Github, we learn that the dataset was extracted from NRTSI. NRTSI offers a series of datasets suitable for training time-series models, and in addition to providing training and test set files packaged in .npy format, it also provides other methods for filling missing time-series data.

Regarding the $SSSD^{S4}$ input data train_mujoco.npy discussed in last week's meeting, we can see that

The data is in NumPy array format with dimensions $8000 \times 100 \times 14$.
Based on the config settings, the filled result is an array of size $500 \times 14 \times 100$.

Here’s the Python script and execution results used for testing.

Loading modules, setting functions, and parameters.

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# import modele
import numpy as np
import os
import pickle

# function
def check_dataset(file_path):
    data = np.load(file_path, allow_pickle=True)
    print(f'Type: {type(data)}, Shape: {data.shape}')
    print(f'{data}\n')
    return data

# main program
## parameter
output_dir_path = r'D:\Code\sssd_cp_learning_and_testing\learning_and_testing\SSSD\results\mujoco\90\T200_beta00.0001_betaT0.02'

Viewing the Mujoco Dataset Training Set

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## model input dataset (mujoco)
print(f'train_mujoco.npy')
file_path = r"D:\Code\sssd_cp_learning_and_testing\learning_and_testing\SSSD\datasets\Mujoco\train_mujoco.npy"
train_mujoco = check_dataset(file_path)

Execution results reference

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train_mujoco.npy
Type: <class 'numpy.ndarray'>, Shape: (8000, 100, 14)
[[[1.0188564  0.34472078 0.9193448  ... 1.5551598  0.8262319  1.449314  ]
  [1.0205188  0.34052694 0.92114544 ... 1.5594999  0.82539403 1.450077  ]
  [1.0221945  0.33620164 0.92290837 ... 1.563845   0.82457316 1.4503349 ]
  ...
  [1.0996897  0.09380768 0.91228646 ... 2.0254884  0.74934673 1.4205385 ]
  [1.0996888  0.093808   0.9123445  ... 2.0256474  0.7493937  1.421181  ]
  [1.0996878  0.09380717 0.91238856 ... 2.0259614  0.749325   1.4219254 ]]

 [[1.1299545  0.56555724 0.8105636  ... 2.0017648  0.7691426  1.3971107 ]
  [1.1328042  0.5636149  0.8118937  ... 2.001997   0.76909196 1.3971739 ]
  [1.1356547  0.5615865  0.81322247 ... 2.00223    0.7690404  1.397237  ]
  ...
  [1.3818084  0.04634438 0.8966854  ... 1.9546272  0.7980857  1.5649099 ]
  [1.3814888  0.04611954 0.8954035  ... 1.9563212  0.7971047  1.5648654 ]
  [1.3811697  0.04583227 0.89410746 ... 1.9577047  0.79626673 1.5648133 ]]

 [[0.9395856  0.26847756 0.8532757  ... 2.0925462  0.88624686 1.4330561 ]
  [0.9394652  0.26569197 0.85121363 ... 2.0933154  0.8870823  1.4280789 ]
  [0.9393492  0.26279953 0.84915906 ... 2.0925698  0.8863424  1.4268135 ]
  ...
  [0.93903416 0.06014196 0.7692848  ... 2.0294168  0.7476863  1.4105136 ]
  [0.93900484 0.06018732 0.769219   ... 2.0295722  0.7476749  1.4098489 ]
  [0.93897474 0.0602343  0.7691506  ... 2.0297213  0.74766856 1.4091637 ]]

 ...

 [[0.9482162  0.46353704 0.81380767 ... 1.0249602  1.2738136  1.350296  ]
  [0.94537544 0.46859425 0.81512964 ... 1.0194359  1.275639   1.3530833 ]
  [0.9427458  0.47382125 0.81637526 ... 1.0178125  1.2746325  1.3559105 ]
  ...
  [0.70087945 0.6286735  0.8703839  ... 2.1573842  0.6628122  1.4355185 ]
  [0.6981438  0.6258822  0.870551   ... 2.1580424  0.6628611  1.4355744 ]
  [0.6954119  0.6230053  0.87070715 ... 2.1587005  0.6629189  1.4356297 ]]

 [[1.084146   0.13920696 0.8108991  ... 2.304378   0.7502878  1.465541  ]
  [1.0859725  0.13577522 0.8078264  ... 2.4035823  0.7357796  1.4806526 ]
  [1.0877669  0.13278663 0.80474424 ... 2.4574542  0.7256363  1.4895606 ]
  ...
  [1.1298585  0.15936916 0.84470177 ... 2.0286796  0.7642296  1.4276175 ]
  [1.1294307  0.1585352  0.8442135  ... 2.029027   0.7654774  1.4275758 ]
  [1.1290065  0.15761633 0.8437144  ... 2.0292292  0.76694435 1.4277219 ]]

 [[0.8497951  0.628934   1.0146345  ... 2.0245514  0.81360376 1.431919  ]
  [0.84885335 0.6278094  1.0138252  ... 2.0257835  0.8132482  1.4319915 ]
  [0.84791064 0.6265908  1.0130211  ... 2.0270183  0.81288934 1.4320644 ]
  ...
  [0.7533675  0.12601541 1.0557469  ... 2.0797296  0.7346148  1.4350158 ]
  [0.752361   0.11651292 1.0562434  ... 2.0798457  0.73452085 1.4350255 ]
  [0.7513538  0.10692114 1.0567361  ... 2.0799599  0.73442733 1.4350348 ]]]

View the model imputation result `imputation0.npy`

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## model output
### imputation
print(f'imputation0.npy')
file_path = os.path.join(output_dir_path, 'imputation0.npy')
imputation0 = check_dataset(file_path)

Execution results reference

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imputation0.npy
Type: <class 'numpy.ndarray'>, Shape: (500, 14, 100)
[[[0.9779899  0.98437977 1.0914965  ... 1.1645157  0.92187357 0.9408777 ]
  [0.45340696 0.45619234 0.45239526 ... 0.09200554 0.09504005 0.09845223]
  [1.0418788  1.0411524  1.0791966  ... 1.0726292  1.0911459  1.0768353 ]
  ...
  [1.9333378  1.9531232  1.9822652  ... 1.9063805  1.9313103  1.9919088 ]
  [0.7332712  0.7334014  0.72775054 ... 0.79629755 0.74248964 0.77277774]
  [1.3981225  1.3949718  1.4293809  ... 1.3827648  1.4142646  1.4201723 ]]

 [[0.8017445  0.8029894  0.7908626  ... 0.715918   0.6784949  0.691612  ]
  [0.28352863 0.27537826 0.2731     ... 0.05175451 0.03815852 0.04471585]
  [1.1245177  1.1291656  1.1952096  ... 1.182712   1.1503464  1.1865829 ]
  ...
  [1.8880249  1.8927475  1.8664936  ... 1.9198602  1.8935788  1.971485  ]
  [0.66902924 0.66292894 0.67104393 ... 0.74909174 0.7419653  0.7354708 ]
  [1.3671505  1.3676192  1.4229809  ... 1.448961   1.4355994  1.447378  ]]

 [[1.035299   1.0503275  1.1367137  ... 1.2797318  1.0733584  1.0659832 ]
  [0.41497543 0.4130687  0.42461908 ... 0.08333386 0.05842083 0.0736234 ]
  [1.0304348  1.0206361  1.0440897  ... 1.0806819  1.0630673  1.0686685 ]
  ...
  [1.8276113  1.8258247  1.8390502  ... 1.9030184  1.9482071  1.9963055 ]
  [0.72919995 0.71213514 0.72257394 ... 0.7469197  0.7098038  0.71767974]
  [1.374692   1.3816208  1.4401623  ... 1.3709145  1.3681242  1.3561548 ]]

 ...

 [[1.0017495  1.0141724  1.030208   ... 1.1663914  1.0523969  1.0220131 ]
  [0.3814863  0.39106598 0.3751795  ... 0.03352571 0.04184113 0.0321909 ]
  [0.82935625 0.8351018  0.84719926 ... 0.78193384 0.79715204 0.8116017 ]
  ...
  [1.9513766  1.9874988  1.9917512  ... 1.6337692  1.6832944  1.7768489 ]
  [0.9911371  0.86839604 0.8214125  ... 0.7012732  0.62618077 0.6505313 ]
  [1.3318325  1.3209419  1.3354611  ... 1.4256169  1.4097162  1.4321613 ]]

 [[0.8313655  0.8345677  0.8353071  ... 0.7665064  0.69832975 0.70574576]
  [0.15491015 0.1849071  0.19601335 ... 0.04784474 0.05161434 0.04703766]
  [0.78100544 0.7520876  0.7652805  ... 0.7345611  0.7311005  0.7375943 ]
  ...
  [1.9338595  1.9964237  2.0456364  ... 1.8495271  1.8366884  1.9121118 ]
  [0.76967365 0.7433044  0.72210073 ... 0.7822682  0.7486641  0.7456464 ]
  [1.3081641  1.3280656  1.3773645  ... 1.4195722  1.4250567  1.4304402 ]]

 [[0.8578036  0.8595259  0.8822513  ... 0.81210816 0.75448877 0.75732774]
  [0.26452947 0.24751675 0.24756058 ... 0.07032993 0.0835114  0.08039934]
  [1.0795563  1.0977736  1.1368525  ... 1.1014563  1.1016102  1.0979248 ]
  ...
  [1.5444437  1.5485339  1.5500091  ... 1.9859809  2.0041018  2.034277  ]
  [0.76173866 0.74596816 0.74051833 ... 0.7301484  0.71769965 0.7053322 ]
  [1.3084735  1.3045095  1.2793151  ... 1.4134452  1.411825   1.424677  ]]]

View the model mask `mask0.npy`

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print(f'mask0.npy')
file_path = os.path.join(output_dir_path, 'mask0.npy')
mask0 = check_dataset(file_path)

Execution results reference

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mask0.npy
Type: <class 'numpy.ndarray'>, Shape: (500, 14, 100)
[[[0. 0. 1. ... 1. 0. 0.]
  [0. 0. 0. ... 0. 0. 1.]
  [0. 0. 1. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 1.]
  [1. 0. 0. ... 1. 0. 0.]
  [0. 0. 1. ... 0. 0. 0.]]

 [[0. 0. 1. ... 1. 0. 0.]
  [0. 0. 0. ... 0. 0. 1.]
  [0. 0. 1. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 1.]
  [1. 0. 0. ... 1. 0. 0.]
  [0. 0. 1. ... 0. 0. 0.]]

 [[0. 0. 1. ... 1. 0. 0.]
  [0. 0. 0. ... 0. 0. 1.]
  [0. 0. 1. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 1.]
  [1. 0. 0. ... 1. 0. 0.]
  [0. 0. 1. ... 0. 0. 0.]]

 ...

 [[0. 0. 1. ... 1. 0. 0.]
  [0. 0. 0. ... 0. 0. 1.]
  [0. 0. 1. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 1.]
  [1. 0. 0. ... 1. 0. 0.]
  [0. 0. 1. ... 0. 0. 0.]]

 [[0. 0. 1. ... 1. 0. 0.]
  [0. 0. 0. ... 0. 0. 1.]
  [0. 0. 1. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 1.]
  [1. 0. 0. ... 1. 0. 0.]
  [0. 0. 1. ... 0. 0. 0.]]

 [[0. 0. 1. ... 1. 0. 0.]
  [0. 0. 0. ... 0. 0. 1.]
  [0. 0. 1. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 1.]
  [1. 0. 0. ... 1. 0. 0.]
  [0. 0. 1. ... 0. 0. 0.]]]

View the `original0.npy` file.

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print(f'original0.npy')
file_path = os.path.join(output_dir_path, 'original0.npy')
original0 = check_dataset(file_path)

Execution results reference

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original0.npy
Type: <class 'numpy.ndarray'>, Shape: (500, 14, 100)
[[[1.1403443  1.1419119  1.1434577  ... 1.2344646  1.2355565  1.2366652 ]
  [0.44503313 0.44048095 0.43586108 ... 0.09895922 0.09892198 0.09881818]
  [1.1080282  1.1087638  1.1094663  ... 1.2303919  1.2330028  1.2356437 ]
  ...
  [2.0913386  2.0889924  2.0888383  ... 1.9993011  1.9984908  1.9976755 ]
  [0.73612225 0.7470203  0.7525134  ... 0.8020001  0.80041975 0.7988277 ]
  [1.4327983  1.4327874  1.4329102  ... 1.4458942  1.4462585  1.4466181 ]]

 [[0.7846492  0.78152096 0.7783957  ... 0.7394441  0.73993295 0.7404261 ]
  [0.18229088 0.17586255 0.16937983 ... 0.04270957 0.04123447 0.03970251]
  [1.2447149  1.245681   1.2466406  ... 1.2939184  1.2957157  1.2975751 ]
  ...
  [2.0702024  2.0702455  2.0702934  ... 1.9835824  1.9814789  1.9794396 ]
  [0.66228145 0.66188604 0.6615124  ... 0.74620795 0.745842   0.74548316]
  [1.4399137  1.4400566  1.4401985  ... 1.4306774  1.4308321  1.430989  ]]

 [[1.1801645  1.1829025  1.185635   ... 1.353138   1.3533303  1.3534759 ]
  [0.42506483 0.42107233 0.41697702 ... 0.08018772 0.08011684 0.08016345]
  [1.0592788  1.060556   1.061817   ... 1.1660019  1.16614    1.1663134 ]
  ...
  [2.0391326  2.0405219  2.0418937  ... 2.0199184  2.0142357  2.01137   ]
  [0.7274884  0.7268261  0.72616607 ... 0.7510811  0.7506006  0.75041914]
  [1.4546845  1.4547614  1.4548372  ... 1.4172906  1.4174985  1.4176484 ]]

 ...

 [[1.041035   1.0441163  1.0472333  ... 1.2278599  1.2281811  1.2284214 ]
  [0.34285313 0.33905002 0.3351447  ... 0.02366458 0.02423722 0.02502784]
  [0.872797   0.87108004 0.86942434 ... 0.8618627  0.86235774 0.8627792 ]
  ...
  [2.2161305  2.2242827  2.2318084  ... 1.7459784  1.7671947  1.7800756 ]
  [1.0148592  1.0114378  1.0082384  ... 0.71554226 0.71559244 0.71584934]
  [1.314138   1.314857   1.3155673  ... 1.4610794  1.4615589  1.4618688 ]]

 [[0.8292507  0.8287961  0.8283144  ... 0.817418   0.8179071  0.8183963 ]
  [0.03687635 0.03981134 0.04268485 ... 0.05158203 0.05035937 0.0491191 ]
  [0.79548436 0.7929163  0.790848   ... 0.7809997  0.7824856  0.7840376 ]
  ...
  [2.2418637  2.240296   2.1343472  ... 1.9140354  1.9133472  1.9098523 ]
  [0.7737858  0.77333015 0.78193784 ... 0.7994397  0.7997823  0.79999524]
  [1.3916144  1.3917903  1.3927475  ... 1.4365767  1.4376484  1.4388508 ]]

 [[0.891903   0.8903191  0.8887091  ... 0.86425775 0.86428493 0.8643113 ]
  [0.1616086  0.15369551 0.1457126  ... 0.08562256 0.085611   0.08560599]
  [1.1634592  1.1706057  1.1778103  ... 1.2142228  1.2142922  1.2143536 ]
  ...
  [1.6939791  1.6989081  1.7037703  ... 2.0460596  2.0468404  2.0475001 ]
  [0.77711374 0.7763163  0.77555615 ... 0.73519385 0.7354764  0.73573035]
  [1.2510566  1.2510723  1.251081   ... 1.4290721  1.4289652  1.4288527 ]]]

Compare Test Set

The matrix information for the test set is as follows.

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print(f'test_mujoco.npy')
file_path = r"D:\Code\sssd_cp_learning_and_testing\learning_and_testing\SSSD\datasets\Mujoco\test_mujoco.npy"
train_mujoco = check_dataset(file_path)

Execution results reference

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test_mujoco.npy
Type: <class 'numpy.ndarray'>, Shape: (2000, 100, 14)
[[[1.1403443  0.44503313 1.1080282  ... 2.0913386  0.73612225 1.4327983 ]
  [1.1419119  0.44048095 1.1087638  ... 2.0889924  0.7470203  1.4327874 ]
  [1.1434577  0.43586108 1.1094663  ... 2.0888383  0.7525134  1.4329102 ]
  ...
  [1.2344646  0.09895922 1.2303919  ... 1.9993011  0.8020001  1.4458942 ]
  [1.2355565  0.09892198 1.2330028  ... 1.9984908  0.80041975 1.4462585 ]
  [1.2366652  0.09881818 1.2356437  ... 1.9976755  0.7988277  1.4466181 ]]

 [[0.7846492  0.18229088 1.2447149  ... 2.0702024  0.66228145 1.4399137 ]
  [0.78152096 0.17586255 1.245681   ... 2.0702455  0.66188604 1.4400566 ]
  [0.7783957  0.16937983 1.2466406  ... 2.0702934  0.6615124  1.4401985 ]
  ...
  [0.7394441  0.04270957 1.2939184  ... 1.9835824  0.74620795 1.4306774 ]
  [0.73993295 0.04123447 1.2957157  ... 1.9814789  0.745842   1.4308321 ]
  [0.7404261  0.03970251 1.2975751  ... 1.9794396  0.74548316 1.430989  ]]

 [[1.1801645  0.42506483 1.0592788  ... 2.0391326  0.7274884  1.4546845 ]
  [1.1829025  0.42107233 1.060556   ... 2.0405219  0.7268261  1.4547614 ]
  [1.185635   0.41697702 1.061817   ... 2.0418937  0.72616607 1.4548372 ]
  ...
  [1.353138   0.08018772 1.1660019  ... 2.0199184  0.7510811  1.4172906 ]
  [1.3533303  0.08011684 1.16614    ... 2.0142357  0.7506006  1.4174985 ]
  [1.3534759  0.08016345 1.1663134  ... 2.01137    0.75041914 1.4176484 ]]

 ...

 [[1.0392356  0.08581756 0.7099395  ... 2.0302138  0.79023373 1.3759874 ]
  [1.0393484  0.08554491 0.7099324  ... 2.0082736  0.7879161  1.3767979 ]
  [1.0394112  0.08544233 0.70994276 ... 1.9963381  0.7867339  1.377317  ]
  ...
  [1.0310189  0.08667419 0.6916089  ... 2.0218747  0.75082636 1.4282196 ]
  [1.030978   0.08667409 0.6915245  ... 2.0217166  0.75112975 1.4281985 ]
  [1.0309373  0.08667286 0.69144064 ... 2.0216012  0.7514324  1.4281791 ]]

 [[1.0522602  0.14923434 0.8988266  ... 2.4332573  0.7175308  1.4357938 ]
  [1.0528201  0.14891274 0.8963647  ... 2.4315226  0.71667176 1.4355559 ]
  [1.0533336  0.14862238 0.89461184 ... 2.2289753  0.72654146 1.4373304 ]
  ...
  [1.0292536  0.06743535 0.77494836 ... 2.0265324  0.74734867 1.4283221 ]
  [1.0285449  0.06419316 0.77352923 ... 2.0248575  0.74751395 1.4282281 ]
  [1.0278436  0.06086201 0.77209336 ... 2.023194   0.7475705  1.4281812 ]]

 [[0.8054271  0.38287213 0.7195578  ... 2.0518327  0.6804158  1.4449072 ]
  [0.8015366  0.38034502 0.71702343 ... 2.0528839  0.6800664  1.444928  ]
  [0.7976455  0.3777312  0.7144991  ... 2.053944   0.6797198  1.4449484 ]
  ...
  [0.4756081  0.11156489 0.5117482  ... 2.3870192  0.80451727 1.3886195 ]
  [0.47334316 0.11220536 0.50762016 ... 2.4114656  0.8274635  1.3821098 ]
  [0.47113514 0.11276194 0.50347656 ... 2.4220142  0.8363771  1.379714  ]]]

Plotting Prediction Graph

From the NRTSI paper, we learn that the MuJoCo dataset contains 14 feature dimensions, 100 time points, and 2,000 experiments.

https://raw.githubusercontent.com/Josh-test-lab/website-assets-repository/refs/heads/main/posts/1140304%20meeting/mujoco%20dataset%20description.jpg — Description of the MuJoCo dataset in the NRTSI paper.

Therefore, we can plot the data as shown below.

https://raw.githubusercontent.com/Josh-test-lab/website-assets-repository/refs/heads/main/posts/1140304%20meeting/Figure_1.png

The above plot shows the third feature value of the 10-th experiment, taking the first 100 data points.

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def plot_experiment_feature(test_mujoco, original0, imputation0, n, f):
    """
    Plot the variation of the f-th feature over time in the n-th experiment, including test_mujoco, original0, and imputation0.

    :param test_mujoco: A dataset of shape (2000, 100, 14)
    :param original0: A dataset of shape (500, 14, 100), which needs to be transposed to (500, 100, 14)
    :param imputation0: A dataset of shape (500, 14, 100), which needs to be transposed to (500, 100, 14)
    :param n: Specifies the experiment index
    :param f: Specifies the feature index
    """

    # Transpose original0 and imputation0 to shape (500, 100, 14)
    original0 = original0.transpose(0, 2, 1)
    imputation0 = imputation0.transpose(0, 2, 1)

    if min(original0.shape[1], imputation0.shape[1]) < n:
        n = min(original0.shape[1], imputation0.shape[1])

    if min(original0.shape[2], imputation0.shape[2]) < f:
        f = min(original0.shape[2], imputation0.shape[2])

    time_steps = np.arange(100)

    plt.figure(figsize=(12, 6))
    plt.plot(time_steps, test_mujoco[n, :, f], label="Test Mujoco", alpha=0.7, linestyle='-')
    plt.plot(time_steps, original0[n, :, f], label="Original0", alpha=0.7, linestyle='dotted')
    plt.plot(time_steps, imputation0[n, :, f], label="Imputation0", alpha=0.7, linestyle='dashed')

    plt.xlabel("Time Step")
    plt.ylabel(f"Feature {f} Value")
    plt.title(f"Experiment {n} - Feature {f} Over Time")
    plt.legend()
    plt.show()

n = 10  # 10th experiment
f = 3   # 3rd feature
plot_experiment_feature(test_mujoco, original0, imputation0, n, f)

Environment

Operating System: Windows 11 24H2
Programming Language: Python 3.12.9

Extended Learning

Reading and Writing Files with NumPy in Python
I tested the project at this Github repository.

References

Juan Lopez Alcaraz and 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
Shan, Siyuan and Li, Yang and Oliva, Junier B. (2023). Nrtsi: Non-recurrent time series imputation. ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 1–5. IEEE.
NRTSI. (2023). GitHub. Retrieved from https://github.com/lupalab/NRTSI/tree/main/codes_regularly-sampled

Contents

20250304 meeting

Discussion on the Input and Output of the $SSSD^{S4}$ Model.

$SSSD$ Model Dataset

Viewing the Mujoco Dataset Training Set

View the model imputation result imputation0.npy

View the model mask mask0.npy

View the original0.npy file.

Compare Test Set

Plotting Prediction Graph

Environment

Extended Learning

References

Related Posts

View the model imputation result `imputation0.npy`

View the model mask `mask0.npy`

View the `original0.npy` file.