Talk by Adeline Fermanian (Sorbonne Université, Paris)

Speaker: Adeline Fermanian (Sorbonne Université, Paris)

Title: Learning from time-dependent data: signatures, RNN, and neural ODE

Abstract: Time-dependent data arise in many fields of research, such as quantitative finance, medicine, or computer vision. We will be concerned with a novel approach for learning with such data, called the signature transform, and rooted in rough path theory. Its basic principle is to represent multidimensional paths by a graded feature set of their iterated integrals, called the signature. After a general overview of signatures in machine learning, we show its application on one specific problem. Building on the interpretation of a recurrent neural network (RNN) as a continuous- time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function on the signature. This connection allows us to frame a RNN as a kernel method in a suitable reproducing kernel Hilbert space. As a consequence, we obtain theoretical guarantees on generalization and stability for a large class of recurrent networks.