Detecting Toxic Flow

This paper develops a framework to predict toxic trades that a broker receives from her clients. Toxic trades are predicted with a novel online Bayesian method which we call the projection-based unification of last-layer and subspace estimation (PULSE). PULSE is a fast and statistically-efficient online procedure to train a Bayesian neural network sequentially. We employ a proprietary dataset of foreign exchange transactions to test our methodology. PULSE outperforms 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, PULSE attains the highest PnL and the largest avoided loss for the horizons we consider.

Efficient Online Bayesian Inference for Neural Bandits

In this paper we present a new algorithm for online (sequential) inference in Bayesian neural networks, and show its suitability for tackling contextual bandit problems. The key idea is to combine the extended Kalman filter (which locally linearizes the likelihood function at each time step) with a (learned or random) low-dimensional affine subspace for the parameters; the use of a subspace enables us to scale our algorithm to models with $\sim 1M$ parameters. While most other neural bandit methods need to store the entire past dataset in order to avoid the problem of "catastrophic forgetting", our approach uses constant memory. This is possible because we represent uncertainty about all the parameters in the model, not just the final linear layer. We show good results on the "Deep Bayesian Bandit Showdown" benchmark, as well as MNIST and a recommender system.