Accurate and Reliable Uncertainty Estimates for Deterministic Predictions Extensions to Under and Overpredictions
| Authors | Rileigh Bandy et al. |
| Year | 2026 |
| Field | AI / ML |
| arXiv | 2604.08755 |
| Download | |
| Categories | cs.CE, cs.LG, stat.ML |
Abstract
Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by sampling input parameter distributions or by augmenting deterministic outputs with uncertainty representations, including distribution-free and distributional methods. However, sampling-based methods are often computationally prohibitive for real-time applications, and many existing uncertainty representations either ignore input dependence or rely on restrictive Gaussian assumptions that fail to capture asymmetry and heavy-tailed behavior. Therefore, we extend the ACCurate and Reliable Uncertainty Estimate (ACCRUE) framework to learn input-dependent, non-Gaussian uncertainty distributions, specifically two-piece Gaussian and asymmetric Laplace forms, using a neural network trained with a loss function that balances predictive accuracy and reliability. Through synthetic and real-world experiments, we show that the proposed approach captures an input-dependent uncertainty structure and improves probabilistic forecasts relative to existing methods, while maintaining flexibility to model skewed and non-Gaussian errors.
Engineering Breakdown
Plain English
This paper extends the ACCRUE framework to generate probabilistic predictions that quantify uncertainty in computational models used for high-stakes engineering and scientific decisions. The key problem is that existing approaches either require computationally expensive sampling of input distributions or produce uncertainty estimates that ignore how inputs affect the predictions or rely on restrictive Gaussian assumptions that fail for asymmetric and heavy-tailed distributions. The authors' solution learns input-dependent, non-Gaussian uncertainty representations that capture the true conditional distribution of model outputs given inputs, enabling fast, accurate uncertainty quantification suitable for real-time applications without sacrificing fidelity.
Core Technical Contribution
The core novelty is extending ACCRUE to learn input-dependent, non-Gaussian conditional distributions rather than assuming fixed or Gaussian uncertainty. Prior work either samples input distributions (slow) or augments deterministic predictions with generic uncertainty that doesn't adapt to the input context. This paper's key insight is that uncertainty itself varies systematically with the input parameters — a prediction might be more uncertain for certain input regimes and less uncertain for others — and capturing this dependence with flexible distributional families (beyond Gaussian) provides dramatically better uncertainty quantification. The technical contribution is making this feasible at inference time by learning a parameterized distribution conditioned on inputs, avoiding the need for computationally prohibitive Monte Carlo sampling.
How It Works
The framework takes a deterministic computational model and an input parameter distribution as starting inputs. Rather than sampling many inputs and running the model repeatedly (which is slow), ACCRUE learns a neural network that maps from input parameters directly to the parameters of a flexible probability distribution. For a given input, this network outputs distribution parameters (not just a mean and variance) — for example, shape and scale parameters for a Weibull or log-normal distribution, enabling non-Gaussian behavior. During inference, you pass an input through the network once to get the distribution parameters, then immediately have a full conditional probability distribution for the model output. The framework is trained on pairs of (input, model output) data, learning to predict how uncertainty changes across the input space. The output is a fast, input-dependent uncertainty estimate that captures asymmetry and heavy tails without Monte Carlo sampling.
Production Impact
For engineers building real-time systems that make high-stakes decisions (structural engineering, drug efficacy prediction, financial forecasting), this replaces slow Monte Carlo uncertainty quantification with single-pass neural network inference — orders of magnitude faster. You'd integrate this by training ACCRUE once on your model and dataset, then deploying it as a lightweight secondary model that runs alongside or within your primary system. A key practical benefit: decisions can now be made with calibrated, input-dependent confidence intervals rather than generic uncertainty bounds, enabling smarter threshold-setting and risk-adjusted decisions. The trade-offs are: you need representative training data covering your input distribution, the approach requires training infrastructure upfront, and you must validate that learned distributions match empirical uncertainty on held-out test sets. Integration complexity is moderate — typically adding a learned distribution layer to your inference pipeline.
Limitations and When Not to Use This
This paper assumes the underlying computational model is deterministic (not inherently stochastic), so it cannot capture aleatoric uncertainty within the model itself — only epistemic uncertainty from input variation. The learned distributions must be chosen a priori; if the true conditional distribution doesn't fit standard families (Weibull, log-normal, etc.), representational mismatch will degrade performance. The approach requires sufficient training data to learn input-dependent distributions; in very high-dimensional input spaces or with sparse data, generalization may suffer. The paper does not address model misspecification — if the computational model itself is wrong, correct input-dependent uncertainty quantification won't rescue poor predictions. Follow-up work is needed on how to select appropriate distributional families automatically, handle multimodal outputs, and scale to extremely high-dimensional inputs.
Research Context
This work builds on the ACCRUE framework (prior work on uncertainty quantification) and the broader literature on distribution-free and distributional uncertainty methods for neural networks and surrogate models. It directly addresses limitations of sampling-based approaches like Monte Carlo and parametric methods that assume Gaussian output distributions. The paper contributes to the active research area of uncertainty quantification (UQ) for scientific computing, where practitioners need both fast inference and reliable confidence bounds — increasingly important as neural surrogates replace expensive physics simulators. This opens research directions on scalable non-parametric uncertainty methods, automated distributional family selection, and extensions to settings with multiple correlated outputs.
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