This paper develops a framework to predict toxic trades that a broker receives from her clients. Toxic trades are predicted with a novel online learning Bayesian method which we call the projection-based unification of last-layer and subspace estimation (PULSE). PULSE is a fast and statistically-efficient Bayesian procedure for online training of neural networks. We employ a proprietary dataset of foreign exchange transactions to test our methodology. Neural networks trained with PULSE outperform standard machine learning and statistical methods when predicting if a trade will be toxic; the benchmark methods are logistic regression, random forests, and a recursively-updated maximum-likelihood estimator. We devise a strategy for the broker who uses toxicity predictions to internalise or to externalise each trade received from her clients. Our methodology can be implemented in real-time because it takes less than one millisecond to update parameters and make a prediction. Compared with the benchmarks, online learning of a neural network with PULSE attains the highest PnL and avoids the most losses by externalising toxic trades.

翻译：本文开发了一个框架，用于预测经纪商从其客户处接收的毒性交易。毒性交易通过一种新颖的在线学习贝叶斯方法进行预测，我们称之为基于投影的末层与子空间估计统一方法（PULSE）。PULSE是一种快速且统计高效的贝叶斯过程，用于神经网络的在线训练。我们采用一个专有的外汇交易数据集来测试我们的方法。在预测交易是否具有毒性时，使用PULSE训练的神经网络优于标准的机器学习和统计方法；基准方法包括逻辑回归、随机森林和递归更新的最大似然估计器。我们为经纪商设计了一种策略，该策略利用毒性预测来决定将接收到的每笔客户交易进行内部消化或外部转移。我们的方法可以实现实时操作，因为更新参数并做出预测所需时间不到一毫秒。与基准方法相比，使用PULSE进行神经网络的在线学习获得了最高的损益（PnL），并通过外部转移毒性交易避免了最多的损失。