Beyond Accuracy: Forecasting with Confidence in Critical Time Series

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Author: Denis Avetisyan

A new approach to time series forecasting prioritizes managing risk and uncertainty, crucial for applications like clinical decision support where errors can have serious consequences.

SoTra bypasses typical probabilistic modeling by directly translating predicted probability distributions-$p_t$-into continuous embeddings, facilitating fully differentiable trajectory generation and ultimately enabling point forecasts decoded through application-specific risk minimization rather than conventional distance metrics.
SoTra bypasses typical probabilistic modeling by directly translating predicted probability distributions-$p_t$-into continuous embeddings, facilitating fully differentiable trajectory generation and ultimately enabling point forecasts decoded through application-specific risk minimization rather than conventional distance metrics.

This paper introduces Soft-Token Trajectory Forecasting (SoTra), a risk-aware autoregressive framework designed to mitigate exposure bias and improve probabilistic forecasting in time series data.

While autoregressive time series forecasting excels in predictive control applications like diabetes and hemodynamic management, standard models often suffer from exposure bias, leading to unstable multi-step predictions crucial for closed-loop systems. This paper, ‘Mitigating Exposure Bias in Risk-Aware Time Series Forecasting with Soft Tokens’, introduces Soft-Token Trajectory Forecasting (SoTra), a novel framework that propagates probabilistic distributions to reduce forecasting errors and learn calibrated uncertainty. Demonstrating an 18% reduction in glucose-related risk and a 15% decrease in blood-pressure clinical risk, SoTra offers a pathway to more robust and safer predictive control-but can this approach be generalized across diverse, high-stakes clinical domains?

Decoding the Temporal Labyrinth: The Challenge of Prediction

The ability to accurately predict future events within a time series is paramount across a diverse range of fields, influencing decisions in areas like optimizing supply chains, managing energy grids, and even forecasting patient outcomes. However, many established forecasting techniques falter when confronted with the intricacies of real-world temporal data, which rarely follows linear patterns. These traditional methods often struggle to capture the nuanced, long-range dependencies and non-linear relationships inherent in complex systems; a past event can have a delayed, disproportionate impact on future values, or multiple factors can interact in unpredictable ways. Consequently, there’s a growing need for advanced modeling approaches-such as recurrent neural networks and state-space models-capable of discerning these subtle temporal dynamics and delivering more reliable predictions than conventional statistical techniques.

The efficacy of forecasting models extends beyond generalized error measurements, particularly when applied to high-stakes domains like clinical risk assessment. Traditional metrics, such as mean squared error, offer a broad overview of predictive performance but fail to account for the asymmetrical costs of misprediction; falsely predicting a low-risk patient as high-risk carries different consequences than the reverse. Consequently, evaluating these models necessitates the implementation of nuanced metrics that prioritize the minimization of dangerous mispredictions – focusing on sensitivity and specificity rather than overall accuracy. This shift in evaluation criteria demands a careful consideration of the relative costs associated with false positives and false negatives, ensuring that forecasts are not only precise but also aligned with the critical needs of patient safety and effective healthcare resource allocation.

Although Forecast B achieves a lower mean squared error, its failure to detect a hypoglycemic event renders it clinically unsafe, unlike Forecast A which consistently provides safe predictions within acceptable error zones.
Although Forecast B achieves a lower mean squared error, its failure to detect a hypoglycemic event renders it clinically unsafe, unlike Forecast A which consistently provides safe predictions within acceptable error zones.

The Ghost in the Machine: Autoregressive Models and Exposure Bias

Autoregressive (AR) models are a class of time series forecasting techniques where future values are predicted as a linear function of past values. Formally, an AR model of order $p$ is denoted as $AR(p)$ and can be expressed as $y_t = c + \phi_1 y_{t-1} + \phi_2 y_{t-2} + … + \phi_p y_{t-p} + \epsilon_t$, where $y_t$ is the value at time $t$, $\phi_i$ represents the coefficients to be estimated, and $\epsilon_t$ is white noise. This recursive nature allows the model to capture temporal dependencies within the data, making it suitable for applications like predicting stock prices, weather patterns, or signal processing. The ‘autoregressive’ designation stems from the regression of the variable on its own lagged values; increasing the order $p$ allows the model to consider a longer history of past observations in its predictions.

Autoregressive models, while effective for time series forecasting, exhibit performance degradation due to exposure bias. This bias arises from the differing conditions between training and inference phases. During training, models are typically fed ground truth values from the training data – a process known as teacher forcing – to predict the subsequent value. However, during inference, the model relies on its own previous predictions as inputs for future predictions – a process called self-prediction. This creates a discrepancy, as the model never learns to recover from its own errors during training, leading to accumulated errors and decreased accuracy when operating in a self-predictive manner. The magnitude of exposure bias is often correlated with the length of the forecast horizon and the inherent difficulty of the prediction task.

Scheduled Sampling addresses exposure bias by incrementally replacing ground truth values with the model’s own predictions during training. Initially, training relies heavily on the true preceding values, but as training progresses, the proportion of model-generated inputs increases according to a defined schedule. This process forces the model to learn to handle its own errors and become more robust to compounding prediction inaccuracies. The schedule is typically governed by a probability parameter, $p_t$, which determines the likelihood of using the model’s prediction at time step $t$ instead of the true value. By gradually exposing the model to its own predictions, Scheduled Sampling aims to reduce the discrepancy between training and inference conditions, thereby improving generalization performance on unseen data.

Risk-aware decoding substantially decreases prediction errors in clinically critical zones, as demonstrated by a reduced density of points in high-risk areas like Zone D (DCLP3) and Zone C (SBP) over a 48-step prediction horizon.
Risk-aware decoding substantially decreases prediction errors in clinically critical zones, as demonstrated by a reduced density of points in high-risk areas like Zone D (DCLP3) and Zone C (SBP) over a 48-step prediction horizon.

Establishing the Baseline: Benchmarking Forecasting Performance

Established time series forecasting models are crucial benchmarks against which the performance of novel methodologies is measured. These benchmarks provide a standardized basis for comparison, allowing researchers and practitioners to objectively assess improvements in forecasting accuracy, computational efficiency, and scalability. Common benchmark models include statistical approaches like ARIMA and exponential smoothing, as well as machine learning models adapted for time series data. Utilizing these established models ensures that any reported gains from new approaches are meaningful and represent genuine advancements in the field, rather than simply differing implementations or data preprocessing techniques. The consistent evaluation against these baselines facilitates progress and reproducibility within the time series forecasting community.

DLinear serves as a computationally inexpensive baseline for time series forecasting, utilizing a simple linear regression approach applied to time series decomposition. In contrast, iTransformer applies the transformer architecture – originally developed for natural language processing – to time series data by treating each time step as a token and leveraging self-attention mechanisms to capture temporal dependencies. This allows iTransformer to model long-range dependencies more effectively than traditional recurrent neural networks, though at a higher computational cost than DLinear. Both models provide valuable points of comparison; DLinear for its speed and simplicity, and iTransformer for demonstrating the potential of transformer-based methods in the time series domain.

PatchTST improves long-term time series forecasting by dividing the input sequence into smaller, non-overlapping “patches” and processing these patches as individual tokens, reducing computational complexity and enabling the model to capture dependencies across extended time horizons. This patching approach facilitates parallel processing and allows the model to scale to longer sequences more effectively than traditional recurrent or convolutional methods. Complementing this, Chronos is a foundational model specifically designed for long-range forecasting, utilizing a multi-horizon attention mechanism and a hierarchical structure to efficiently model temporal relationships and dependencies. Chronos’ architecture allows for both univariate and multivariate forecasting and provides a strong baseline for evaluating the performance of more complex models on long-term prediction tasks.

Robust evaluation of time series forecasting models requires analysis beyond aggregate error metrics. The Clarke Error Grid is a specific tool used to visually assess forecast accuracy by categorizing errors based on their magnitude and direction relative to clinical risk. This grid plots individual forecast errors against corresponding reference values, dividing the space into zones representing clinically acceptable, marginal, or unacceptable error levels. Analysis using the Clarke Error Grid identifies systematic biases and allows determination of whether model errors are concentrated in regions where they could potentially lead to adverse clinical outcomes, providing a more nuanced understanding of model performance than traditional metrics like Mean Absolute Error (MAE) or Root Mean Squared Error (RMSE).

Beyond the Numbers: Towards Clinically Relevant Forecasting

While commonly used in forecasting, metrics like Mean Squared Error (MSE) present a limited view of predictive performance in critical applications. MSE treats all errors equally, failing to distinguish between minor inaccuracies and those with potentially severe consequences; a 2mg/dL error in glucose prediction carries vastly different implications than a 200mg/dL deviation. This can lead to models that excel in minimizing average error but still produce a disproportionate number of high-impact, clinically significant mispredictions. Consequently, relying solely on such metrics can mask crucial vulnerabilities and hinder the development of truly reliable forecasting systems, particularly in healthcare contexts where the cost of error extends beyond statistical measures.

Traditional forecasting evaluation often prioritizes minimizing overall error, overlooking the critical distinction between harmless and harmful inaccuracies. Zone-Based Risk Assessment addresses this limitation by shifting the focus from aggregate metrics to the clinical consequences of predictions. This framework categorizes forecast errors not simply by their magnitude, but by the specific ‘zone’ of predicted values and the associated risks within each zone – for instance, a slight error in glucose prediction for a patient with stable blood sugar is far less concerning than the same magnitude of error for someone at risk of hypoglycemia. By quantifying the probability of forecasts falling into high-risk zones, this approach provides a more clinically meaningful assessment of model performance, allowing for the selection of models that minimize the potential for adverse events rather than simply achieving the lowest average error. This granular evaluation is crucial for applications where even seemingly small errors can have significant consequences for patient health and safety.

The Soft-Token Trajectory Forecasting (SoTra) framework represents a significant advancement in predictive modeling for critical health metrics. By focusing on clinically relevant outcomes, SoTra achieves substantial reductions in zone-based risk – up to 18% improvement in glucose prediction accuracy and 15% in blood pressure forecasting. This improvement isn’t at the expense of overall accuracy; SoTra maintains competitive Root Mean Squared Error (RMSE) scores when compared to existing models. The framework’s efficacy stems from its ability to not only predict values but to accurately categorize the potential impact of forecasting errors, thereby enabling more proactive and safer clinical interventions. This focus on minimizing high-risk predictions differentiates SoTra and highlights its potential to improve patient care through more reliable forecasting.

Analysis reveals the Soft-Token Trajectory Forecasting (SoTra) framework significantly minimizes potentially harmful forecasting errors in critical health applications. Specifically, SoTra achieves a 32% reduction in forecasts identified as ‘risky’ for glucose prediction and a substantial 24% reduction in risky blood pressure forecasts, when contrasted with the performance of both iTransformer and PatchTST models. This improvement isn’t simply about overall accuracy; it directly addresses the frequency with which predictions could lead to adverse clinical outcomes, suggesting a tangible benefit for patient care through more reliable predictive analytics.

Evaluations reveal that the Soft-Token Trajectory Forecasting (SoTra) framework surpasses Chronos in its ability to accurately predict the probability of future values, a crucial aspect of reliable forecasting. This enhanced probabilistic accuracy is quantified through improvements in Continuous Ranked Probability Score (CRPS), a metric that assesses the calibration of probabilistic predictions; lower CRPS scores indicate better alignment between predicted probabilities and observed outcomes. The observed gains in CRPS demonstrate SoTra’s capacity to not only predict a range of possible future values, but also to assign appropriate confidence levels to those predictions, ultimately providing clinicians with more trustworthy and actionable insights for patient care.

Effective forecasting extends beyond simply minimizing traditional error metrics; the selection of both a forecasting model and its evaluation criteria must be intrinsically linked to the specific application and the potential risks associated with inaccurate predictions. A model that performs well according to metrics like Mean Squared Error may still yield clinically unacceptable outcomes if its errors manifest in high-risk zones – for example, predicting dangerously low blood glucose levels. Therefore, a careful consideration of the consequences of forecasting errors is crucial; metrics should reflect the practical impact of those errors, and models should be chosen not just for overall accuracy, but for their ability to mitigate the most critical risks within a given domain. This alignment ensures that forecasting efforts translate into meaningful improvements in real-world applications, rather than simply achieving statistical optimization.

The pursuit of SoTra, as detailed in the paper, embodies a spirit of calculated disruption. It doesn’t simply accept the limitations of existing autoregressive models and the inherent exposure bias within time series forecasting; instead, it actively dismantles them through probabilistic propagation and risk-based optimization. This echoes Ada Lovelace’s observation: “The Analytical Engine has no pretensions whatever to originate anything.” SoTra, much like Lovelace’s envisioned engine, doesn’t conjure forecasting accuracy from nothing. Rather, it meticulously refines the process, manipulating existing probabilities to minimize risk and produce more reliable, safety-critical outcomes in clinical decision support. It’s a testament to the power of understanding a system well enough to intelligently reshape its parameters.

Beyond the Horizon

The pursuit of accurate forecasting, particularly in high-stakes domains like clinical decision support, often fixates on minimizing point estimates of error. This work, by shifting focus toward propagating full probability distributions and explicitly optimizing for risk, reveals the inadequacy of that approach. It’s a subtle, yet crucial, dismantling of a long-held assumption: that knowing what will happen is sufficient, when understanding how likely each outcome is proves far more valuable. The framework, though promising, inherently relies on the fidelity of the initial probability estimates-a known weakness in real-world data. Future iterations must address this vulnerability, perhaps through adversarial training to robustify against noisy or incomplete inputs.

The ‘soft token’ mechanism, while effective in transmitting distributional information, presents an intriguing bottleneck. It essentially distills complex probabilistic states into a fixed-length vector. One wonders if the information loss, though currently acceptable, will become limiting as models scale and datasets grow more nuanced. Exploring alternative encoding schemes-perhaps leveraging attention mechanisms or variational autoencoders-could unlock greater representational capacity. Moreover, the autoregressive nature of the model invites investigation into non-autoregressive alternatives, potentially bypassing sequential dependencies and accelerating inference times.

Ultimately, this work isn’t simply about improving forecast accuracy; it’s about a philosophical shift in how one approaches prediction. It’s a tacit acknowledgement that certainty is an illusion, and that intelligent systems must operate effectively in a world defined by inherent uncertainty. The real challenge lies not in eliminating risk, but in intelligently managing it – a task that demands continuous refinement and a willingness to deconstruct established paradigms.

Original article: https://arxiv.org/pdf/2512.10056.pdf

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

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2025-12-14 04:45