# Beyond Output-Space Calibration: Spectral Evidence Bundling for Selective Reliability Estimation in Time-Series Classification

arXiv: https://arxiv.org/abs/2607.18279 · HTML: https://mlsanity.com/paper/2607.18279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [InceptionTime: Finding AlexNet for Time Series Classification](https://mlsanity.com/paper/1909.04939/) (2019)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline](https://mlsanity.com/paper/1611.06455/) (2016)
- [The UEA multivariate time series classification archive, 2018](https://mlsanity.com/paper/1811.00075/) (2018)
- [FilterNet: Harnessing Frequency Filters for Time Series Forecasting](https://mlsanity.com/paper/2411.01623/) (2024)
- [A Benchmark Study on Calibration](https://mlsanity.com/paper/2308.11838/) (2023)
- [Confidence Calibration of Classifiers with Many Classes](https://mlsanity.com/paper/2411.02988/) (2024)

## Abstract (arXiv)

Post-hoc calibration for time-series classification usually remaps output scores, but deployment decisions such as trust, abstention, and review depend on whether a confident prediction is supported by the current temporal signal. We address three time-series reliability gaps: identical confidence values can hide different temporal support, average calibration can miss false high-confidence errors, and output-space recalibration offers limited input-linked auditability. We introduce a validation-gated fixed-label reliability policy that keeps the backbone prediction unchanged while estimating whether it should be trusted. The method combines output-side cues with whole-sample spectral descriptors, including band energy, entropy, peak dominance, period support, and phase stability, to form a scalar reliability estimate and diagnostic band-level evidence. A validation gate enables spectral conditioning only when correctness ranking improves without breaching FalseConf@0.9 or AURC tolerances; otherwise it reverts to the safer output-space baseline. Across eight heterogeneous UCR/UEA datasets, eight time-series backbone families, and standard recalibrators, the unconstrained method improves fixed-label selective-reliability metrics on the matched evaluation subset, raising Corr-AURC from 0.693 to 0.779. The validation-gated policy further improves Corr-AURC to 0.786 and reduces FalseConf@0.9 to 0.094. These results suggest that reliability estimation for time-series classifiers benefits from bundling output confidence with spectral evidence, while validation gating prevents unsupported spectral conditioning.