DistPred

The repo is the official implementation for the paper: DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecasting.

1. Introduction

We employ proper scoring rules to train a probabilistic inference model end-to-end, enabling the model to infer numerous samples in a singular forward pass to estimate the latent distribution of the response variable.

2. Contributions

The key innovations are summarized as:

DistPred, a novel method for regression and forecasting tasks that can estimate the distribution of the response variable in a single forward pass.
DistPred transforms proper scoring rules into a differentiable form and uses them as a loss function to train the model end-to-end, allowing the model to sample multiple distributions efficiently in a single pass.
DistPred overcomes the limitations of existing methods like Bayesian inference, model ensembling, or MC Dropout, which either assume a Gaussian posterior distribution or require thousands of forward passes for sample generation.
DistPred achieves state-of-the-art performance on multiple datasets while significantly improving computational efficiency, with a 90x faster inference speed compared to existing state-of-the-art models.
DistPred can provide K predicted values of the response variable in a single forward pass, allowing for comprehensive statistical insights and uncertainty quantification.
DistPred is shown to be equivalent to Bayesian inference in distribution inference, addressing the challenge of capturing distribution information in regression and forecasting tasks efficiently and accurately.

3. Training and Testing on Toy Example or UCI Regression Dataset

1) UCI Regression Dataset

The datasets can be obtained from Google Drive.

2) Clone the code repository

git clone git@github.com:Anoise/DistPred.git

3) Training

Go to the directory "DistPred-UCI or DistPred-MCD-UCI", we'll find that the bash scripts are all in the 'training_scripts' folder, then run the bash script like this:

bash training_scripts/run_uci_boston.sh
bash training_scripts/run_uci_concrete.sh
bash training_scripts/run_uci_energy.sh
bash training_scripts/run_uci_kin8nm.sh
bash training_scripts/run_uci_power.sh
...

4. Training and Testing on Time Series Forecasting Dataset

1) Dataset

The datasets can be obtained from Google Drive or Tsinghua Cloud.

2) Clone the code repository

git clone git@github.com:Anoise/DistPred.git

3) Training on Time Series Dataset

Go to the directory "DistPred-Forecast", we'll find that the bash scripts are all in the 'scripts' folder, then run the bash script like this:

bash scripts/Electricity/Minusformer-96M.sh

Note that:

Model was trained with Python 3.7 with CUDA 11.2.
Model should work as expected with pytorch >= 1.12 support was recently included.

4. Performace on Toy Example

The generated samples seamlessly integrate with the authentic test instances, indicating the potential of DistPred to reconstruct the inherent data generation process.

5. Performace on UCI Regression Dataset

DistPred achieves the consistent SOTA performance across all datasets and prediction length configurations.

6. Training and Inference Speed

It is evident that DistPred is approximately 230 times faster in training and about 90 times faster in inference compared to the state-of-the-art model.

7. Training and Inference Speed

As shown in the following figure, with an increase in the number of output samples and ensembles, the model’s performance shows a gradual improvement, eventually reaching a point of saturation.

8. Performace on Time Series Forcasting

DistPred achieves the consistent SOTA performance across all datasets and prediction length configurations.

8. Citations

Daojun Liang, Haixia Zhang, Dongfeng Yuan, DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecasting. arXiv preprint arXiv:2406.11397 (2024).

@article{liang2024distpred,
  title={DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecasting},
  author={Liang, Daojun and Zhang, Haixia and Yuan, Dongfeng},
  journal={arXiv preprint arXiv:2406.11397},
  year={2024}
}