Differentiable Adversarial Attacks for Marked Temporal Point Processes

Marked temporal point processes (MTPPs) have been shown to be extremely effective in modeling continuous time event sequences (CTESs). In this work, we present adversarial attacks designed specifically for MTPP models. A key criterion for a good adversarial attack is its imperceptibility. For objects such as images or text, this is often achieved by bounding perturbation in some fixed Lp norm-ball. However, similarly minimizing distance norms between two CTESs in the context of MTPPs is challenging due to their sequential nature and varying time-scales and lengths. We address this challenge by first permuting the events and then incorporating the additive noise to the arrival timestamps. However, the worst case optimization of such adversarial attacks is a hard combinatorial problem, requiring exploration across a permutation space that is factorially large in the length of the input sequence. As a result, we propose a novel differentiable scheme PERMTPP using which we can perform adversarial attacks by learning to minimize the likelihood, while minimizing the distance between two CTESs. Our experiments on four real-world datasets demonstrate the offensive and defensive capabilities, and lower inference times of PERMTPP.