# UQ-LOB: Uncertainty-Aware Limit Order Book Mid-Price Forecasting

arXiv: https://arxiv.org/abs/2609.31491 · HTML: https://mlsanity.com/paper/2609.31491/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Deeper Depth Prediction with Fully Convolutional Residual Networks](https://mlsanity.com/paper/1606.00373/) (2016)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Universal features of price formation in financial markets: perspectives from Deep Learning](https://mlsanity.com/paper/1803.06917/) (2018)
- [Benchmark Dataset for Mid-Price Forecasting of Limit Order Book Data with Machine Learning Methods](https://mlsanity.com/paper/1705.03233/) (2017)
- [Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysis](https://mlsanity.com/paper/1712.00975/) (2017)
- [Faithful Heteroscedastic Regression with Neural Networks](https://mlsanity.com/paper/2212.09184/) (2022)
- [Using Deep Learning for price prediction by exploiting stationary limit order book features](https://mlsanity.com/paper/1810.09965/) (2018)
- [Generative AI for End-to-End Limit Order Book Modelling: A Token-Level Autoregressive Generative Model of Message Flow Using a Deep State Space Network](https://mlsanity.com/paper/2309.00638/) (2023)
- [Deep Limit Order Book Forecasting](https://mlsanity.com/paper/2403.09267/) (2024)
- [Bayesian Bilinear Neural Network for Predicting the Mid-price Dynamics in Limit-Order Book Markets](https://mlsanity.com/paper/2203.03613/) (2022)
- [DeepFolio: Convolutional Neural Networks for Portfolios with Limit Order Book Data](https://mlsanity.com/paper/2008.12152/) (2020)
- [LOBERT: Generative AI Foundation Model for Limit Order Book Messages](https://mlsanity.com/paper/2511.12563/) (2025)

## Abstract (arXiv)

Forecasting short-horizon mid-price movements from limit order book (LOB) data is central to algorithmic trading, yet most deep LOB forecasters are point predictors: they output a direction or a displacement, but never indicate which of their forecasts can be trusted. We introduce UQ-LOB, a lightweight, encoder-agnostic uncertainty quantification module that attaches to any pretrained LOB encoder and, in the spirit of attentive neural processes, conditions each forecast on a context set of recently completed windows whose outcomes are already realised. The UQ-regression variant outputs a calibrated Gaussian over the future tick displacement, while the UQ-classification variant outputs a categorical distribution over down/up/stationary. Both expose a scalar confidence (predicted signal-to-noise ratio or class probability) that supports selective prediction. On 5.2 billion LOB events across seven cryptocurrency assets and horizons of 5, 10 and 15 seconds, UQ-regression attains near-nominal 68% interval coverage, and restricting to the most confident 10% of predictions raises directional macro F1 by 0.11-0.15 for UQ-regression and 0.05-0.11 for UQ-classification, at every horizon. On large, economically meaningful moves, the tightest confidence tier reaches a directional F1 of 0.88 (down) and 0.83 (up) at the 5-second horizon.