Keywords: time series forecasting, time series prediction, neural stochastic differential equations, cooperative differential game
TL;DR: We proposed a novel framework on time series prediction as an application of cooperative differential games.
Abstract: Modeling time series dynamics with neural differential equations has become a major line of research that opened new ways to handle various real-world scenarios (e.g., missing observations, irregular times). Despite the progress, most existing methods still face challenges in providing an explainable rationale on temporal association, which tells how past observations affect future states. To tackle this challenge, we introduce novel multi-agent based neural stochastic differential equations and analyze the time series prediction through the lens of cooperative differential game. Our framework provides an explainable method that can reveal the underlying temporal relevance of the data and fully utilizes this information to systemically solve the prediction problem. We develop the gradient descent based deep neural fictitious play to approximate the Nash equilibrium and theoretical results assure the convergence. Throughout the experiments on various datasets, we demonstrate the superiority of our framework over all the benchmarks in modeling time series prediction by capitalizing on the underlying temporal dynamics without any inductive bias. An ablation study shows that neural agents of the proposed framework learn intrinsic temporal relevance to predict accurate time series.
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