Beyond Perfect Data: Boosting Time Series Forecasts with Adversarial Training

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Author: Denis Avetisyan

New research demonstrates that intentionally introducing ‘imperfect’ data can significantly improve the robustness and accuracy of time series forecasting models.

The architecture of IdealTSF anticipates inevitable systemic failure by embracing a distributed, interconnected design, where each component’s limitations become the seeds of adaptation for the whole-a prophecy encoded in its very structure.
The architecture of IdealTSF anticipates inevitable systemic failure by embracing a distributed, interconnected design, where each component’s limitations become the seeds of adaptation for the whole-a prophecy encoded in its very structure.

IdealTSF leverages negative samples and attention mechanisms to enhance performance even in the presence of anomalies and noisy data.

Despite the success of deep learning in time series forecasting, real-world sequential data is often plagued by missing values and anomalies that limit predictive performance. This study addresses this challenge through ‘IdealTSF: Can Non-Ideal Data Contribute to Enhancing the Performance of Time Series Forecasting Models?’, a novel framework that surprisingly leverages these ‘negative’ data samples-rather than simply filtering them-to improve forecasting accuracy. IdealTSF utilizes a three-stage process of pretraining, training, and optimization, incorporating adversarial techniques to transform imperfect data into a source of knowledge. Could this approach unlock significantly improved robustness and performance for time series models deployed in noisy, real-world environments?

The Inevitable Imperfections of Prediction

Established time series forecasting techniques, such as Autoregressive Integrated Moving Average (ARIMA) models, frequently encounter difficulties when applied to real-world datasets. These models are built on the assumption of complete and consistently reliable data, an expectation rarely met in practice. Missing values, stemming from sensor malfunctions or data collection errors, and outliers-anomalous data points caused by unexpected events-disrupt the statistical properties ARIMA relies upon. Consequently, forecasts generated from imperfect data can exhibit significant inaccuracies, leading to unreliable predictions in fields ranging from supply chain management to weather prediction. The sensitivity of these traditional methods highlights the pressing need for more resilient forecasting approaches capable of handling the inherent noise and incompleteness of real-world time series data.

The presence of even minor imperfections in time series data can dramatically diminish the reliability of forecasts, with consequences extending to numerous critical applications. In traffic prediction, for example, gaps in sensor readings-due to communication failures or equipment malfunction-can lead to inaccurate estimates of congestion, hindering effective traffic management. Similarly, in financial modeling, outliers stemming from unexpected events or data entry errors can distort predictions of stock prices or economic indicators, potentially leading to flawed investment strategies. This sensitivity is not merely a statistical nuisance; it represents a genuine challenge, as many real-world time series are inherently noisy and incomplete, demanding forecasting methods capable of withstanding these data quality issues to deliver useful and trustworthy results.

The increasing reliance on time series forecasting across diverse fields demands a paradigm shift in how data imperfections are addressed. Historically, methods tolerant of noisy or incomplete datasets were considered advantageous; however, modern applications – from autonomous systems to real-time resource management – now require robustness as a baseline for functionality. The proliferation of data streams, often collected from imperfect sensors or subject to transmission errors, means that ignoring data quality issues is no longer a viable option. Forecasts generated from flawed data can lead to costly errors, compromised safety, and a loss of trust in predictive models. Consequently, the development of forecasting techniques explicitly designed to handle missing values, outliers, and other data anomalies has transitioned from a beneficial enhancement to a fundamental prerequisite for reliable and actionable insights.

Many established time series methodologies address imperfect data through techniques like mean imputation or simple moving averages, yet these solutions often mask crucial information and fail to account for the complex, often non-linear, processes generating the data. While expedient, these simplistic approaches treat missing values or outliers as random noise, disregarding the potential for systematic patterns or underlying relationships that contribute to the time series’ behavior. Consequently, forecasts built on data subjected to such rudimentary treatment can be significantly biased, particularly when dealing with non-stationary data or series exhibiting complex dependencies. This limitation underscores the need for more sophisticated methods capable of modeling data imperfections as integral components of the time series dynamics, rather than merely attempting to eliminate them.

The data exhibits significant and unpredictable fluctuations.
The data exhibits significant and unpredictable fluctuations.

Constructing Resilience: The IdealTSF Framework

IdealTSF is a time series forecasting framework structured around a three-phase methodology to improve performance with imperfect datasets. The initial pre-training phase focuses on enhancing model robustness by exposing it to variations in the input data, allowing it to learn more generalized representations. This is followed by a standard training phase where the model learns to forecast based on the pre-trained weights and available data. Finally, an optimization phase fine-tunes the model parameters and configurations to maximize forecasting accuracy and stability, specifically addressing challenges posed by data imperfections such as missing values and outliers. This phased approach distinguishes IdealTSF from single-stage forecasting models and contributes to its resilience in real-world applications.

Negative Sample Pre-training within the IdealTSF framework increases model robustness by intentionally exposing the forecasting model to variations in the input data during the initial training phase. This is achieved through two primary methods: structured deletion, where portions of the time series data are systematically removed, and the incorporation of stable distributions. Stable distributions, characterized by parameters controlling skewness and scale, generate perturbed data points that reflect realistic noise patterns beyond standard Gaussian noise. By training on these negatively sampled, perturbed datasets, the model learns to generalize better and maintain accuracy even when presented with incomplete or noisy real-world time series data, effectively reducing sensitivity to data imperfections.

Hybrid Smoothing Interpolation within IdealTSF utilizes a combination of linear, spline, and seasonal decomposition methods to impute missing time series data. Rather than relying on a single technique, the framework calculates imputed values using each method and then averages these results, weighted by a validation metric determined during training. This ensemble approach reduces the error associated with any single interpolation method, particularly when dealing with varying patterns of missing data or non-stationary time series. The weighting scheme adapts based on the characteristics of the input data, prioritizing interpolation methods that demonstrate higher accuracy on a validation set, thereby improving the overall reconstruction of the time series.

The IdealTSF framework incorporates an Attention Mechanism to dynamically weigh the importance of individual data points during forecasting. This mechanism assigns higher weights to data points deemed more relevant to the prediction, effectively downplaying the influence of noisy or outlier values. Specifically, the attention weights are calculated based on the relationships between data points, allowing the model to prioritize patterns and trends while minimizing the impact of anomalous observations. The implementation utilizes a self-attention process, where each data point attends to all other points in the time series, resulting in a context-aware representation that improves forecasting accuracy and robustness, particularly in datasets with significant levels of noise or missing data.

Different optimization algorithms impact the robustness of IdealTSF against both fast gradient sign method (FGSM) and projected gradient descent (PGD) attacks.
Different optimization algorithms impact the robustness of IdealTSF against both fast gradient sign method (FGSM) and projected gradient descent (PGD) attacks.

Empirical Validation: Performance in the Real World

IdealTSF underwent evaluation using both the PEMS dataset, focused on short-term forecasting, and the ETTh dataset, designed for long-term forecasting scenarios. Performance comparisons against established baseline models consistently positioned IdealTSF among the top two performers across eleven distinct benchmark datasets. This consistent high ranking indicates a substantial and reproducible improvement in forecasting accuracy when utilizing the IdealTSF framework across a variety of time series data characteristics and prediction horizons. The results demonstrate the framework’s effectiveness in both short-term and long-term forecasting tasks, suggesting a generalized ability to model complex temporal dependencies.

IdealTSF’s robustness to malicious data inputs was evaluated using adversarial training methodologies. Fast Gradient Sign Method (FGSM) and Projected Gradient Descent (PGD) were employed to generate perturbed data samples, simulating potential adversarial attacks. Performance evaluation under these conditions demonstrated that IdealTSF maintains a high degree of accuracy and stability even when exposed to intentionally manipulated inputs, confirming its resilience against data perturbations designed to compromise model integrity. These tests validate the framework’s capacity to function reliably in potentially hostile data environments.

Gradient Descent served as the primary optimization algorithm within the IdealTSF framework, iteratively adjusting model parameters to minimize the defined loss function. This process calculates the gradient of the loss function with respect to each parameter and updates the parameters in the opposite direction of the gradient, scaled by a learning rate. By repeatedly refining parameters through this iterative process, the model converges towards a state of minimal error, resulting in improved predictive accuracy and enhanced stability across various time series forecasting tasks. The specific loss function employed is dependent on the forecasting task, but generally aims to quantify the difference between predicted and actual values, such as Mean Squared Error (MSE) or Mean Absolute Error (MAE).

The IdealTSF framework incorporates an Ecosystem Optimizer as an alternative optimization strategy to improve robustness in complex time series forecasting scenarios. Quantitative results demonstrate that utilizing this optimizer yields approximately a 10% improvement in overall optimization metrics when compared to the TimeKAN model. Specifically, the implementation of the Ecosystem Optimizer resulted in a Mean Squared Error (MSE) reduction of approximately 17% on the ECL dataset and a 3.5% reduction on the ETTh1 dataset, indicating enhanced performance and stability across diverse time series characteristics.

Combining ECOS with Adam or SGD consistently improves optimization performance compared to using those optimizers alone.
Combining ECOS with Adam or SGD consistently improves optimization performance compared to using those optimizers alone.

Toward Adaptive Systems: Implications and Future Growth

The IdealTSF framework establishes a promising new direction for time series forecasting, offering improved resilience and reliability across a spectrum of critical applications. Beyond theoretical advancements, this methodology directly addresses practical challenges in fields such as traffic management, where accurate predictions optimize flow and reduce congestion; financial analysis, enabling more informed investment strategies and risk assessment; and resource allocation, streamlining logistics and minimizing waste. By providing robust forecasting even with imperfect data, IdealTSF minimizes the need for costly and time-consuming data cleansing, offering a streamlined and effective solution for organizations reliant on predictive analytics. This capability suggests a future where data-driven decision-making is less susceptible to the inaccuracies inherent in real-world data streams, ultimately fostering more efficient and dependable systems.

The framework’s innovative approach to data imperfection leverages Negative Sample Pre-training and robust optimization, marking a considerable step forward in time series forecasting. Traditionally, achieving reliable results demanded meticulous data cleaning, a process that is both time-consuming and susceptible to human error. This method, however, diminishes the necessity for exhaustive pre-processing by proactively addressing noisy or incomplete data during the model’s initial training phase. Negative Sample Pre-training effectively teaches the model to discern meaningful patterns even amidst data irregularities, while robust optimization techniques minimize the influence of outliers and erroneous values. Consequently, the system demonstrates improved resilience and accuracy when confronted with real-world datasets, reducing the burden on data scientists and enabling faster, more efficient model deployment.

The current framework demonstrates promising results with univariate time series, but future development will prioritize its extension to accommodate multi-variate data, where multiple interconnected time series influence each other. This expansion necessitates novel approaches to capture the complex relationships and dependencies between these variables, potentially leveraging techniques like vector autoregression or state-space models. Simultaneously, researchers intend to explore adaptive interpolation strategies that move beyond fixed methods. These strategies will dynamically adjust to the characteristics of the time series, intelligently filling in missing data points or smoothing irregularities based on local data patterns and forecast uncertainty. Such an approach promises increased accuracy and robustness, particularly in scenarios with sparse or noisy data, and could significantly broaden the applicability of the IdealTSF framework across diverse fields.

The framework’s potential for improved performance extends to dynamic outlier management, with researchers proposing the integration of Interquartile Range (IQR) and Z-score methodologies for real-time identification and mitigation of anomalous data points. Initial investigations demonstrate significant accuracy gains when coupled with optimization algorithms; specifically, employing ECOS alongside the Adam optimizer achieved a 90% accuracy rate on the CIFAR-10 dataset – a full 10 percentage point improvement over standard Adam. Similarly, the combination of ECOS with Stochastic Gradient Descent (SGD) yielded nearly 90% accuracy, substantially exceeding the approximately 80% achieved by standard SGD. These findings suggest that a responsive outlier handling system, leveraging statistical measures like IQR and Z-score, could be crucial in bolstering the framework’s robustness and overall predictive capabilities across diverse applications.

Negative sample pre-training enhances the attention mechanism in the ETTh1 model, resulting in a more focused and discernible attention heatmap.
Negative sample pre-training enhances the attention mechanism in the ETTh1 model, resulting in a more focused and discernible attention heatmap.

The pursuit of immaculate data, as if a pristine foundation guarantees a flawless forecast, feels increasingly like a fool’s errand. This work, introducing IdealTSF, acknowledges the inevitable imperfections-the anomalies and negative samples-not as threats, but as opportunities for growth. It echoes a sentiment expressed by Bertrand Russell: “The greatest lesson in life is to find that even in suffering there is a certain type of beauty.” IdealTSF doesn’t attempt to eliminate the chaos inherent in time series data; instead, it leverages adversarial training to build robustness within that chaos. The system doesn’t promise freedom from failure, only a more graceful acceptance of it, recognizing that every architectural choice is, ultimately, a prophecy of how it will fail – and then, hopefully, adapt.

What Lies Ahead?

The pursuit of ‘ideal’ data, as implied by this work, feels increasingly like chasing a ghost. IdealTSF rightly acknowledges the inevitability of imperfection, yet frames it as a problem to be mitigated. A more honest approach recognizes that anomalies aren’t deviations from the system, but integral to it. The very act of defining ‘normal’ in time series creates the shadow of its opposite. Future architectures will likely abandon the pretense of purification, embracing methods that learn from the noise, not despite it.

The attention mechanisms employed here, while demonstrably effective, represent only a local optimization. The true challenge isn’t simply identifying which data points deserve focus, but understanding why the system attends to them. A shift toward causal inference – modeling the generative processes underlying time series – promises a more robust understanding than any adversarial training scheme. The system doesn’t merely react to negative samples; it should anticipate their emergence.

One wonders if the ultimate forecast isn’t a point prediction at all, but a probabilistic map of potential failures. The silent periods in a time series aren’t moments of stability, but the gathering of forces before the next perturbation. The system isn’t striving for accuracy; it’s preparing for its own undoing. And in that preparation, perhaps, lies a form of resilience.

Original article: https://arxiv.org/pdf/2512.05442.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-08 16:51