SpaceTime 🌌⏱️

Code for SpaceTime, a neural net architecture for time series. Named after state-space models for time series forecasting and classification.

Cousin of S4, S4D, DSS, and H3. Descendent of LSSL. Expressive autoregressive modeling + fast flexible decoding (i.e., forecasting) ftw.

Proposed in Effectively Modeling Time Series with Simple Discrete State Spaces, ICLR 2023.

Paper links:

• ArXiv
• OpenReview

Setup

Dependencies

A list of dependencies is provided in environment.yaml. We recommend creating a virtual environment with conda:

conda env create -f environment.yaml
conda activate spacetime

Data

Data for the Informer benchmark can be downloaded from https://github.com/zhouhaoyi/ETDataset. The data exists as CSV files, which should be saved in the directory ./dataloaders/data/informer/, e.g.,

./dataloaders/data/informer/etth/ETTh1.csv
./dataloaders/data/informer/etth/ETTh2.csv
./dataloaders/data/informer/ettm/ETTm1.csv
./dataloaders/data/informer/ettm/ETTm2.csv

Usage

Colab demo

We include an example Colab notebook walking through how to train and forecast a SpaceTime model on financial time series. For fun, we also provide a quick demo on how to power a trading bot with SpaceTime forecasts (probably with some bugs). Feel free to extend it and have fun. None of this is financial advice!

Training scripts

Sample scripts for training models on the Informer benchmark are provided below. For a complete set of arguments, please see ./setup/args.py. For an overview of key command-line arguments, please see the Experiment arguments section below.

# ETTh1 720  
python main.py --dataset etth1 --lag 336 --horizon 720 --embedding_config embedding/repeat --encoder_config encoder/default --decoder_config decoder/default --output_config output/default --n_blocks 1 --kernel_dim 64 --norm_order 1 --batch_size 50 --dropout 0.25 --lr 1e-3 --weight_decay 1e-4 --max_epochs 500 --early_stopping_epochs 20 --data_transform mean --loss informer_rmse --val_metric informer_rmse --criterion_weights 1 1 1 --seed 0 --no_wandb

# ETTh2 720   
python main.py --dataset etth2 --lag 336 --horizon 720 --embedding_config embedding/repeat --encoder_config encoder/default --decoder_config decoder/default --output_config output/default --n_blocks 1 --kernel_dim 64 --norm_order 1 --batch_size 50 --dropout 0.25 --lr 1e-3 --weight_decay 1e-4 --max_epochs 500 --early_stopping_epochs 20 --data_transform mean --loss informer_rmse --val_metric informer_rmse --criterion_weights 1 1 1 --seed 0 --no_wandb

# ETTm1 720  
python main.py --dataset ettm1 --lag 336 --horizon 720 --embedding_config embedding/repeat --encoder_config encoder/default --decoder_config decoder/default --output_config output/default --n_blocks 1 --kernel_dim 64 --norm_order 1 --batch_size 50 --dropout 0.25 --lr 1e-3 --weight_decay 1e-4 --max_epochs 500 --early_stopping_epochs 20 --data_transform mean --loss informer_rmse --val_metric informer_rmse --criterion_weights 1 1 1 --seed 0 --no_wandb

# ETTm2 720  
python main.py --dataset ettm2 --lag 336 --horizon 720 --embedding_config embedding/repeat --encoder_config encoder/default --decoder_config decoder/default --output_config output/default --n_blocks 1 --kernel_dim 64 --norm_order 1 --batch_size 50 --dropout 0.25 --lr 1e-3 --weight_decay 1e-4 --max_epochs 500 --early_stopping_epochs 20 --data_transform mean --loss informer_rmse --val_metric informer_rmse --criterion_weights 1 1 1 --seed 0 --no_wandb

More details

SpaceTime architecture and configs

To build a SpaceTime model, we specify a series of config files responsible for individual model components (determined via the config arguments, e.g., --embedding_config embedding/<config_name>). Default config files are located in ./configs/model. Please find more information on the directory structure via the config paths and descriptions below.

Config Path (./configs/model/)	Description
embedding/	Configs for the input layer, which maps from the input sample dimension (1 for univariate data) to the model dimension (hidden-layer width).
encoder/	Configs for the encoder blocks ("SpaceTime layers" in the paper). - Each config specifies the configs behind the preprocessing, open-loop, and closed-loop SSMs, the MLPs, and the skip connections in each block.
decoder/	Configs for the decoder block. Same organization as encoder/
ssm/	Configs for open-loop (convolutional view) SSMs used in the encoder blocks. - Also contains subdirectories for preprocessing and closed-loop SSMs.
ssm/preprocess/	Configs for the preprocessing SSMs (e.g., differencing, moving average residual) used in the encoder blocks.
ssm/closed_loop/	Configs for the closed-loop (recurrent view) SSMs used in the decoder block.
mlp/	Configs for MLPs (FFNs) used in each block.
output/	Configs for the output layer, which maps from the model dimension to the target dimension.

Command-line arguments

Argument	Description
--dataset	The dataset name
--lag	Input sequence length, i.e., number of historical time-steps or lag terms taken as input to the model
--horizon	Output sequence length, i.e., number of future time-steps or horizon terms to predict
--embedding_config	Config file for model embedding layer
--encoder_config	Config file for model encoder blocks ("SpaceTime Layers" in the paper)
--decoder_config	Config file for model decoder blocks ("SpaceTime Layers" in the paper)
--output_config	Config file for model output layer
--n_blocks	Number of blocks (SpaceTime layers) in the model encoder. Overrides default specified in --encoder_config file
--kernel_dim	Dimension of SSM kernel used in each block. Overrides default specified in SSM config file (see section on SpaceTime Architecture for more details)
--norm_order	Normalization order applied to A, B and C / K matrices when computing SSM outputs
--early_stopping_epochs	Number of epochs to wait before early stopping. Training stops after validation metric (specified in --val_metric) does not improve after this many epochs.
--data_transform	Transformation applied to lag terms before being used as model inputs. We reverse this transformation for the predictions. Defaults to subtracting the mean over inputs.
--criterion_weights	List of 3 values that specify relative weight of loss components. Given --criterion_weights w0 w1 w2, w0 weights loss over horizon term model outputs, w1 weights loss over lag term model outputs, w2 weights loss over lag term closed-loop outputs (last-layer next-time-step inputs). Please see ./train/step/informer.py for additional details.
--no_wandb	If included, does not use Weights & Biases (wandb) to log experiment metrics (default logs to wandb)
--no_cuda	If included, does not use GPU for training and inference (default uses one GPU if available)

Citation

If you use our code or found our work valuable, please cite:

@article{,
  title={Effectively Modeling Time Series with Simple Discrete State Spaces},
  author={Zhang, Michael, and Saab, Khaled and Poli, Michael and Dao, Tri and Goel, Karan and R{\'e}, Christopher},
  journal={International Conference on Learning Representations},
  year={2023},
}