Imanol Perez Arribas

Patric Bonnier, Patrick Kidger, Imanol Perez Arribas et al.

The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a model may be built. We propose a novel approach which combines the advantages of the signature transform with modern deep learning frameworks. By learning an augmentation of the stream prior to the signature transform, the terms of the signature may be selected in a data-dependent way. More generally, we describe how the signature transform may be used as a layer anywhere within a neural network. In this context it may be interpreted as a pooling operation. We present the results of empirical experiments to back up the theoretical justification. Code available at https://github.com/patrick-kidger/Deep-Signature-Transforms.

Hans Bühler, Blanka Horvath, Terry Lyons et al.

Neural network based data-driven market simulation unveils a new and flexible way of modelling financial time series without imposing assumptions on the underlying stochastic dynamics. Though in this sense generative market simulation is model-free, the concrete modelling choices are nevertheless decisive for the features of the simulated paths. We give a brief overview of currently used generative modelling approaches and performance evaluation metrics for financial time series, and address some of the challenges to achieve good results in the latter. We also contrast some classical approaches of market simulation with simulation based on generative modelling and highlight some advantages and pitfalls of the new approach. While most generative models tend to rely on large amounts of training data, we present here a generative model that works reliably in environments where the amount of available training data is notoriously small. Furthermore, we show how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series in such environments where available training data is scarce. Finally, we also propose a suitable performance evaluation metric for financial time series and discuss some connections of our Market Generator to deep hedging.

Terry Lyons, Imanol Perez Arribas

Unravelling hidden patterns in datasets is a classical problem with many potential applications. In this paper, we present a challenge whose objective is to discover nonlinear relationships in noisy cloud of points. If a set of point satisfies a nonlinear relationship that is unlikely to be due to randomness, we will label the set with this relationship. Since points can satisfy one, many or no such nonlinear relationships, cloud of points will typically have one, multiple or no labels at all. This introduces the labelling problem that will be studied in this paper. The objective of this paper is to develop a framework for the labelling problem. We introduce a precise notion of a label, and we propose an algorithm to discover such labels in a given dataset, which is then tested in synthetic datasets. We also analyse, using tools from random matrix theory, the problem of discovering false labels in the dataset.

Imanol Perez Arribas, Kate Saunders, Guy Goodwin et al.

Mobile technologies offer opportunities for higher resolution monitoring of health conditions. This opportunity seems of particular promise in psychiatry where diagnoses often rely on retrospective and subjective recall of mood states. However, getting actionable information from these rather complex time series is challenging, and at present the implications for clinical care are largely hypothetical. This research demonstrates that, with well chosen cohorts (of bipolar disorder, borderline personality disorder, and control) and modern methods, it is possible to objectively learn to identify distinctive behaviour over short periods (20 reports) that effectively separate the cohorts. Participants with bipolar disorder or borderline personality disorder and healthy volunteers completed daily mood ratings using a bespoke smartphone app for up to a year. A signature-based machine learning model was used to classify participants on the basis of the interrelationship between the different mood items assessed and to predict subsequent mood. The signature methodology was significantly superior to earlier statistical approaches applied to this data in distinguishing the participant three groups, clearly placing 75% into their original groups on the basis of their reports. Subsequent mood ratings were correctly predicted with greater than 70% accuracy in all groups. Prediction of mood was most accurate in healthy volunteers (89-98%) compared to bipolar disorder (82-90%) and borderline personality disorder (70-78%).