This repository contains the implementation of PSW-I, a novel framework for robust and effective imputation of missing values in time-series data. The approach is built upon the Proximal Spectrum Wasserstein (PSW) discrepancy, tailored to address key challenges in time-series imputation.

Abstract

Missing data imputation through distribution alignment has demonstrated advantages for non-temporal datasets but exhibits suboptimal performance in time-series applications. The primary obstacle is crafting a discrepancy measure that simultaneously:

1. Captures temporal patterns—accounting for periodicities and temporal dependencies inherent in time-series.
2. Accommodates non-stationarity, ensuring robustness amidst multiple coexisting temporal patterns.

In response to these challenges, we introduce the Proximal Spectrum Wasserstein (PSW) discrepancy based on the stochastic optimal transport framework. PSW integrates:

• Pairwise spectral distance to encapsulate temporal patterns.
• Selective matching regularization to accommodate non-stationarity.

Building on PSW, we propose the PSW-I framework, which iteratively refines imputation results by minimizing the PSW discrepancy. Extensive experiments demonstrate that PSW-I effectively addresses these challenges and significantly outperforms prevailing time-series imputation methods.

Key Features

• Temporal Pattern Capturing: Utilizes spectral distances to understand time-series periodicities and dependencies.
• Non-Stationarity Adaptation: Incorporates selective matching for robustness across varied temporal patterns.
• Iterative Refinement: Refines imputed values progressively for enhanced accuracy.
• Comprehensive Evaluation: Outperforms state-of-the-art methods on multiple benchmark datasets.

Usage

Data Preparation

Prepare your time-series dataset with missing values following the format in out_data/.
then use

python process_data.py --dataset dataset_name

Running the Model

To run PSW-I for imputation:

sh scripts/etth1.sh