Minusformer: A Progressive Approach to Enhance Time Series Forecasting by Learning Residuals

Core Concepts

The core message of this article is that the proposed Minusformer architecture can effectively mitigate the overfitting problem in time series forecasting by progressively learning the residuals of the supervision signal through a subtraction-based information aggregation mechanism.

Abstract

The article presents a novel deep learning model called Minusformer for time series forecasting. The key insights are: Prevalent deep learning models, such as Transformer-based approaches, are prone to severe overfitting on time series data. This is due to the complex and non-stationary nature of real-world time series. To address this issue, the authors propose a de-redundancy approach that implicitly decomposes the supervision signals to progressively steer the learning process. Specifically, Minusformer renovates the vanilla Transformer architecture by replacing the addition-based information aggregation with subtraction. Minusformer incorporates an auxiliary output branch into each block, constructing a highway that guides the model to learn the residuals of the supervision signal layer by layer. This learning-driven implicit progressive decomposition of both the inputs and labels empowers the model with enhanced versatility, interpretability, and resilience against overfitting. The authors provide a theoretical analysis demonstrating that the subtraction-based design in Minusformer can effectively reduce the variance of the model, thereby mitigating the overfitting problem. Extensive experiments on diverse real-world time series datasets show that Minusformer outperforms existing state-of-the-art methods, yielding an average performance improvement of 11.9%.

Stats

The sculpture is already complete within the marble block, before I start my work. It is already there. I just have to chisel away the superfluous material. Ubiquitous time series (TS) forecasting models are prone to severe overfitting. The latest studies suggest that the improvements in predictive performance using Attention-based methods, compared to Multi-Layer Perceptrons (MLP), have not been significant. GNN-based methods have not shown substantial improvement in predictive performance compared to MLP.

Quotes

"The sculpture is already complete within the marble block, before I start my work. It is already there. I just have to chisel away the superfluous material." - Michelangelo "The latest studies suggest that the improvements in predictive performance using Attention-based methods, compared to Multi-Layer Perceptrons (MLP), have not been significant." "GNN-based methods have not shown substantial improvement in predictive performance compared to MLP."

Key Insights Distilled From

Minusformer

by Daojun Liang... at arxiv.org 04-12-2024

https://arxiv.org/pdf/2402.02332.pdf

Deeper Inquiries

How can the progressive learning approach in Minusformer be extended to other time series analysis tasks beyond forecasting, such as anomaly detection or classification

The progressive learning approach in Minusformer can be extended to other time series analysis tasks beyond forecasting by adapting the concept of progressively learning residuals to tasks such as anomaly detection or classification. For anomaly detection, the model can be trained to identify deviations or outliers in the time series data by learning the residuals between the actual data and the predicted values. By progressively refining the model's understanding of normal patterns in the data, it can effectively detect anomalies that deviate significantly from the learned patterns. This approach leverages the model's ability to capture subtle changes and deviations in the data over time, making it well-suited for anomaly detection tasks. Similarly, for classification tasks, the model can be trained to classify different patterns or categories within the time series data by learning the residuals between different classes or categories. By progressively decomposing the input data and learning the residuals at each stage, the model can gain a deeper understanding of the underlying patterns that distinguish one class from another. This approach enables the model to capture the intricate relationships and nuances in the data, leading to more accurate and interpretable classification results.

What are the potential limitations of the subtraction-based information aggregation mechanism, and how could it be further improved or combined with other techniques to enhance the model's performance

One potential limitation of the subtraction-based information aggregation mechanism in Minusformer is the risk of information loss or distortion during the subtraction process. If the model relies too heavily on subtracting the learned results from the input data, it may overlook important patterns or relationships in the data that could contribute to the overall forecasting performance. To address this limitation, the subtraction-based mechanism could be further improved by incorporating adaptive weighting or gating mechanisms that dynamically adjust the importance of the subtracted information based on its relevance to the task at hand. Additionally, the subtraction-based mechanism could be combined with other techniques, such as attention mechanisms or residual connections, to enhance the model's performance. By integrating attention mechanisms, the model can focus on specific parts of the input data that are most relevant for the forecasting task, while residual connections can help propagate gradients more effectively through the network, improving the model's ability to learn complex patterns in the data. By combining these techniques with the subtraction-based mechanism, the model can achieve a more robust and effective learning process.

Given the interpretability of the Minusformer architecture, how could the insights gained from the progressive decomposition of the time series be leveraged to gain a deeper understanding of the underlying patterns and dynamics in the data

The interpretability of the Minusformer architecture provides valuable insights into the underlying patterns and dynamics in the data, which can be leveraged to gain a deeper understanding of the time series data. By analyzing the residuals learned at each stage of the model, researchers can identify the components of the data that contribute most significantly to the forecasting performance. This analysis can reveal the key features or attributes that drive the predictions, shedding light on the important factors influencing the time series data. Furthermore, the progressive decomposition of the time series data in Minusformer allows researchers to track the evolution of patterns and relationships over time, providing a comprehensive view of how the data changes and adapts. By studying the residual components and their impact on the final predictions, researchers can uncover hidden trends, anomalies, or correlations in the data that may not be apparent from the raw input. This deeper understanding can inform future modeling decisions, data preprocessing steps, or domain-specific insights, enhancing the overall analysis of the time series data.