Provable local learning rule by expert aggregation for a Hawkes network

Sophie Jaffard, Samuel Vaiter, Alexandre Muzy, Patricia Reynaud-Bouret

Abstract: We propose a simple network of Hawkes processes as a cognitive model capable of learning to classify objects. Our learning algorithm, named HAN for Hawkes Aggregation of Neurons, is based on a local synaptic learning rule based on spiking probabilities at each output node. We were able to use local regret bounds to prove mathematically that the network is able to learn on average and even asymptotically under more restrictive assumptions.