# Bayesian Bilinear Neural Network for Predicting the Mid-price Dynamics in Limit-Order Book Markets

arXiv: https://arxiv.org/abs/2203.03613 · HTML: https://mlsanity.com/paper/2203.03613/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 69 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [What do we need to build explainable AI systems for the medical domain?](https://mlsanity.com/paper/1712.09923/) (2017)
- [Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations](https://mlsanity.com/paper/1708.02691/) (2017)
- [Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models](https://mlsanity.com/paper/1703.04265/) (2017)
- [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)
- [Fast yet Simple Natural-Gradient Descent for Variational Inference in Complex Models](https://mlsanity.com/paper/1807.04489/) (2018)
- [Using Deep Learning for price prediction by exploiting stationary limit order book features](https://mlsanity.com/paper/1810.09965/) (2018)
- [A practical tutorial on Variational Bayes](https://mlsanity.com/paper/2103.01327/) (2021)
- [Tensor Representation in High-Frequency Financial Data for Price Change Prediction](https://mlsanity.com/paper/1709.01268/) (2017)
- [Multi-head Temporal Attention-Augmented Bilinear Network for Financial time series prediction](https://mlsanity.com/paper/2201.05459/) (2022)
- [Feature Engineering for Mid-Price Prediction with Deep Learning](https://mlsanity.com/paper/1904.05384/) (2019)
- [Automatic Relevance Determination Bayesian Neural Networks for Credit Card Default Modelling](https://mlsanity.com/paper/1906.06382/) (2019)

## Built on by (most cited first, 5 of 5)

- [Bayesian Learning for Neural Networks: an algorithmic survey](https://mlsanity.com/paper/2211.11865/) (2022)
- [Axial-LOB: High-Frequency Trading with Axial Attention](https://mlsanity.com/paper/2212.01807/) (2022)
- [Microstructure-Empowered Stock Factor Extraction and Utilization](https://mlsanity.com/paper/2308.08135/) (2023)
- [Manifold Gaussian Variational Bayes on the Precision Matrix](https://mlsanity.com/paper/2210.14598/) (2022)
- [UQ-LOB: Uncertainty-Aware Limit Order Book Mid-Price Forecasting](https://mlsanity.com/paper/2609.31491/) (2026)

## Abstract (arXiv)

The prediction of financial markets is a challenging yet important task. In modern electronically-driven markets, traditional time-series econometric methods often appear incapable of capturing the true complexity of the multi-level interactions driving the price dynamics. While recent research has established the effectiveness of traditional machine learning (ML) models in financial applications, their intrinsic inability to deal with uncertainties, which is a great concern in econometrics research and real business applications, constitutes a major drawback. Bayesian methods naturally appear as a suitable remedy conveying the predictive ability of ML methods with the probabilistically-oriented practice of econometric research. By adopting a state-of-the-art second-order optimization algorithm, we train a Bayesian bilinear neural network with temporal attention, suitable for the challenging time-series task of predicting mid-price movements in ultra-high-frequency limit-order book markets. We thoroughly compare our Bayesian model with traditional ML alternatives by addressing the use of predictive distributions to analyze errors and uncertainties associated with the estimated parameters and model forecasts. Our results underline the feasibility of the Bayesian deep-learning approach and its predictive and decisional advantages in complex econometric tasks, prompting future research in this direction.