When autonomous robots interact with humans, such as during autonomous driving, explicit safety guarantees are crucial in order to avoid potentially life-threatening accidents. Many data-driven methods have explored learning probabilistic bounds over human agents trajectories (i.e. confidence tubes that contain trajectories with probability $delta$), which can then be used to guarantee safety with probability $1-delta$. However, almost all existing works consider $delta geq 0.001$. The purpose of this paper is to argue that (1) in safety-critical applications, it is necessary to provide safety guarantees with $delta < 10^{-8}$, and (2) current learning-based methods are ill-equipped to compute accurate confidence bounds at such low $delta$. Using human driving data (from the highD dataset), as well as synthetically generated data, we show that current uncertainty models use inaccurate distributional assumptions to describe human behavior and/or require infeasible amounts of data to accurately learn confidence bounds for $delta leq 10^{-8}$. These two issues result in unreliable confidence bounds, which can have dangerous implications if deployed on safety-critical systems.
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