DeformTime

This repository maintains the official implementation of methods and experiments presented in our paper titled "DeformTime: Capturing Variable Dependencies with Deformable Attention for Time Series Forecasting".

@article{shu2024deformtime,
    author    = {Yuxuan Shu and Vasileios Lampos},
    title     = {{\textsc{DeformTime}: Capturing Variable Dependencies with
                  Deformable Attention for Time Series Forecasting}},
    year      = {2024},
    journal   = {Preprint under review}
}

Abstract

In multivariate time series (MTS) forecasting, existing state-of-the-art deep learning approaches tend to focus on autoregressive formulations and overlook the information within exogenous indicators. To address this limitation, we present DeformTime, a neural network architecture that attempts to capture correlated temporal patterns from the input space, and hence, improve forecasting accuracy. It deploys two core operations performed by deformable attention blocks (DABs): learning dependencies across variables from different time steps (variable DAB), and preserving temporal dependencies in data from previous time steps (temporal DAB). Input data transformation is explicitly designed to enhance learning from the deformed series of information while passing through a DAB. We conduct extensive experiments on 6 MTS data sets, using previously established benchmarks as well as challenging infectious disease modelling tasks with more exogenous variables. The results demonstrate that DeformTime improves accuracy against previous competitive methods across the vast majority of MTS forecasting tasks, reducing the mean absolute error by 10% on average. Notably, performance gains remain consistent across longer forecasting horizons.

Highlights

We propose DeformTime, a novel MTS forecasting model that better captures inter- and intra-variate dependencies at different temporal granularities. It comprises two Deformable Attention Blocks (DAB) which allow the model to adaptively focus on more informative neighbouring attributes. The below figure shows how different dependencies are established:

(a) The inter-variable dependency is established across different variables over time. (b) The intra-variable dependency focuses on the important information of the specific variable across time. Both dependencies are adaptively established w.r.t. the input.

Setting Up the Environment

• Ensure you have Anaconda installed on your system. You can download and install it from here.

1. Create a Conda Environment

Our code was tested with Python 3.9. To create a Conda environment, run the following command in the terminal:

conda create --name dtime python=3.9

2. Activate the Conda Environment

Activate the environment using the following command:

conda activate dtime

3. Install the Requirements

Install the required packages using:

pip install -r requirements.txt

Prepare the data sets

Benchmark data sets

To prepare the benchmark data sets, you need to obtain the ETTh1, ETTh2, and weather data sets. Steps as below:

1. Download the ETTh1, ETTh2, and weather data sets from the Autoformer repository.

2. Organize the folders with the following structure:

   data/
   ├──dataset/
      ├── ETT/
      │   ├── ETTh1.csv
      │   ├── ETTh2.csv
      └── weather/
          └── weather.csv
   

ILI rates

Due to a restricted data sharing policy, we currently cannot provide the full version of the ILI data sets in our experiment. Alternatively, we provide the following instructions for anyone interested in obtaining the data.

CDC flu data

The ILI rates of the US HHS regions are obtained by the Centers for Disease Control and Prevention (CDC). You may access the data from their official website.

RCGP flu data

The ILI data for England in our experiment was obtained from the Royal College of General Practitioners (RCGP) with a fixed list of GP practices throughout England. Although we are unable to provide the original ILI data, you may access the officially reported influenza data here.

Google Health Trends

Queries used in our experiments can be found under the folder data/dataset/queries/. The full version of the base queries is provided in base.csv and the seed queries used to conduct semantic filtering are in seed.csv. We also provide the query lists after semantic filtering. The list for England is available in UK.csv (containing $4{,}396$ queries), and the list for US regions is available in US.csv (containing $2{,}479$ queries). Apply here to get access to Google Trends API.

Model training

To train the model(s) in the paper (for the benchmark data sets), run the below commands:

For ETTh1 tasks:

bash scripts/DeformTime/ETTh1.sh

For ETTh2 tasks:

bash scripts/DeformTime/ETTh2.sh

For weather tasks:

bash scripts/DeformTime/weather.sh

The results will be saved in a result.txt file.

Results

Our model achieves the following performance with MAE score. The best results are in bold font and the second best are underlined. We use iTrans. and Cross. as the abbreviation for iTransformer and Crossformer respectively. See full results in the paper.

---

Tasks	$H$	DeformTime	PatchTST	iTrans.	TimeMixer	Cross.	LightTS	DLinear
ETTh1	96	0.1941	0.2017	0.2052	0.2112	0.2126	0.2215	0.2599
	192	0.2116	0.2409	0.2429	0.2382	0.2820	0.2636	0.3798
	336	0.2158	0.2559	0.2593	0.2625	0.2947	0.2807	0.6328
	720	0.2862	0.3087	0.2886	0.3055	0.3350	0.5334	0.7563
ETTh2	96	0.3121	0.3145	0.3420	0.3454	0.3486	0.3507	0.3349
	192	0.3281	0.3839	0.4233	0.4183	0.4035	0.4022	0.4084
	336	0.3450	0.4018	0.4332	0.4380	0.4487	0.4425	0.4710
	720	0.3640	0.4960	0.4565	0.4729	0.5832	0.6252	0.7981
Weather	96	0.0244	0.0258	0.0277	0.0322	0.0271	0.0293	0.0251
	192	0.0260	0.0279	0.0277	0.0347	0.0308	0.0319	0.0270
	336	0.0291	0.0303	0.0308	0.0359	0.0345	0.0317	0.0305
	720	0.0363	0.0389	0.0395	0.0457	0.0395	0.0386	0.0352
ILI-ENG	7	1.6417	2.3115	2.3084	2.1748	1.8698	2.2397	2.8214
	14	2.2308	3.2547	3.2301	3.0209	2.6543	2.6879	3.7922
	21	2.6500	4.3192	4.2347	3.5501	3.0014	3.3616	4.4739
	28	2.7228	4.9964	4.8125	4.1188	3.1983	3.4132	5.0347
ILI-US2	7	0.4122	0.7097	0.6507	0.5284	0.4400	0.4632	0.7355
	14	0.4752	0.8635	0.7896	0.6556	0.5852	0.5827	0.8435
	21	0.5425	1.0286	0.8042	0.6794	0.6245	0.6683	0.9124
	28	0.5538	1.1525	0.9619	0.8853	0.6512	0.7175	0.9805
ILI-US9	7	0.2622	0.4116	0.4057	0.3239	0.3149	0.3185	0.4675
	14	0.3084	0.5020	0.4702	0.4060	0.3571	0.3791	0.5467
	21	0.3179	0.5935	0.5106	0.4576	0.3418	0.4754	0.6001
	28	0.3532	0.6665	0.6498	0.5124	0.3747	0.4769	0.6564

Acknowledgements

• Our implementation of attention deformation was inspired by DAT.
• We also acknowledge Informer and Autoformer for their valuable code and data for time series forecasting.