The official code repository for the paper SAITS: Self-Attention-based Imputation for Time Series (preprint on arXiv is here), which has been accepted by the journal Expert Systems With Applications (ESWA) [2022 IF 8.665, CiteScore 12.2, JCR-Q1, CAS-Q1 (中科院-1区), CCF-C]. You may never hear of ESWA, while this journal was ranked 1st in Google Scholar under the top publications of Artificial Intelligence in 2016 (info source), and here is the current ranking list for your information.

SAITS is the first work applying pure self-attention and without any recursive design in the algorithm for general time series imputation. Basically you can take it as a validated framework for time series imputation. More generally, you can use it for sequence imputation. Of course, it probably needs a bit of modification in the model structure or loss functions for specific purpose or data input. Therefore, you're welcome to modify SAITS for your own research purpose and domain applications.

Please cite SAITS in your publications if it helps your research. Please star🌟 this repo to help others notice SAITS if you think it is useful. It really means a lot to my open-source work. Thank you! BTW, you may also like PyPOTS for easily modeling your partially-observed time-series datasets.

‼️Kind reminder: This document can help you solve many common questions, please read it before you run the code 😊

📣 Attention please:
SAITS now is available in PyPOTS, a Python toolbox for data mining on POTS (Partially-Observed Time Series). An example of training SAITS for imputing dataset PhysioNet-2012 is shown below. With PyPOTS, easy peasy! 😉

# Install PyPOTS first: pip install pypots>=0.0.10
import numpy as np
from sklearn.preprocessing import StandardScaler
from pypots.data import load_specific_dataset, mcar, masked_fill
from pypots.imputation import SAITS
from pypots.utils.metrics import cal_mae
# Data preprocessing. Tedious, but PyPOTS can help. 🤓
data = load_specific_dataset('physionet_2012')  # For datasets in PyPOTS database, PyPOTS will automatically download and extract it.
X = data['X']
num_samples = len(X['RecordID'].unique())
X = X.drop(['RecordID', 'Time'], axis = 1)
X = StandardScaler().fit_transform(X.to_numpy())
X = X.reshape(num_samples, 48, -1)
X_intact, X, missing_mask, indicating_mask = mcar(X, 0.1) # hold out 10% observed values as ground truth
X = masked_fill(X, 1 - missing_mask, np.nan)
# Model training. This is PyPOTS showtime. 💪
saits = SAITS(n_steps=48, n_features=37, n_layers=2, d_model=256, d_inner=128, n_heads=4, d_k=64, d_v=64, dropout=0.1, epochs=10)
dataset = {"X": X}
saits.fit(dataset)  # train the model. Here I use the whole dataset as the training set, because ground truth is not visible to the model.
imputation = saits.impute(dataset)  # impute the originally-missing values and artificially-missing values
mae = cal_mae(imputation, X_intact, indicating_mask)  # calculate mean absolute error on the ground truth (artificially-missing values)

⦿ Motivation: SAITS is developed primarily to help overcome the drawbacks (slow speed, memory constraints, and compounding error) of RNN-based imputation models and to obtain the state-of-the-art (SOTA) imputation accuracy on partially-observed time series.

⦿ Performance: SAITS outperforms BRITS by 12% ∼ 38% in MAE (mean absolute error) and achieves 2.0 ∼ 2.6 times faster training speed. Furthermore, SAITS outperforms Transformer (trained by our joint-optimization approach) by 2% ∼ 19% in MAE with a more efficient model structure (to obtain comparable performance, SAITS needs only 15% ∼ 30% parameters of Transformer). Compared to another SOTA self-attention imputation model NRTSI, SAITS achieves 7% ∼ 39% smaller mean squared error (above 20% in nine out of sixteen cases), meanwhile, needs much fewer parameters and less imputation time in practice. Please refer to our full paper for more details about SAITS' performance.

Here we only show the two main components of our method: the joint-optimization training approach and SAITS structure. For the detailed description and explanation, please read our full paper.

Fig. 1: Training approach

Fig. 2: SAITS structure

The implementation of SAITS is in dir modeling. We give configurations of our models in dir configs, provide the dataset links and preprocessing scripts in dir dataset_generating_scripts. Dir NNI_tuning contains the hyper-parameter searching configurations.

All dependencies of our development environment are listed in file conda_env_dependencies.yml. You can quickly create a usable python environment with an anaconda command conda env create -f conda_env_dependencies.yml.

For datasets downloading and generating, please check out the scripts in dir dataset_generating_scripts.

Generate the dataset you need first. To do so, please check out the generating scripts in dir dataset_generating_scripts.

After data generation, train and test your model, for example,

# create a dir to save logs and results
mkdir NIPS_results

# train a model
nohup python run_models.py \
    --config_path configs/PhysioNet2012_SAITS_best.ini \
    > NIPS_results/PhysioNet2012_SAITS_best.out &

# during training, you can run the blow command to read the training log
less NIPS_results/PhysioNet2012_SAITS_best.out

# after training, pick the best model and modify the path of the model for testing in the config file, then run the below command to test the model
python run_models.py \
    --config_path configs/PhysioNet2012_SAITS_best.ini \
    --test_mode

❗️Note that paths of datasets and saving dirs may be different on personal computers, please check them in the configuration files.

If you find SAITS is helpful to your research, please cite our paper as below, ⭐️star this repository, and recommend it to others who you think may need it. 🤗

@article{DU2023SAITS,
title = {{SAITS: Self-Attention-based Imputation for Time Series}},
journal = {Expert Systems with Applications},
volume = {219},
pages = {119619},
year = {2023},
issn = {0957-4174},
doi = {https://doi.org/10.1016/j.eswa.2023.119619},
url = {https://www.sciencedirect.com/science/article/pii/S0957417423001203},
author = {Wenjie Du and David Cote and Yan Liu},
}

or

Wenjie Du, David Cote, and Yan Liu. SAITS: Self-Attention-based Imputation for Time Series. Expert Systems with Applications, 219:119619, 2023.

Thanks to Mitacs and NSERC (Natural Sciences and Engineering Research Council of Canada) for funding support. Thanks to Ciena for providing computing resources. Thanks to all our reviewers for helping improve the quality of this paper. And thank you all for your attention to this work! ❤️

If you have any additional questions or have interests in collaboration, please take a look at my GitHub profile and feel free to contact me😃.