  Perception of time from sequentially acquired sensory inputs is rooted in
everyday behaviors of individual organisms. Yet, most algorithms for
time-series modeling fail to learn dynamics of random event timings directly
from visual or audio inputs, requiring timing annotations during training that
are usually unavailable for real-world applications. For instance, neuroscience
perspectives on postdiction imply that there exist variable temporal ranges
within which the incoming sensory inputs can affect the earlier perception, but
such temporal ranges are mostly unannotated for real applications such as
automatic speech recognition (ASR). In this paper, we present a probabilistic
ordinary differential equation (ODE), called STochastic boundaRy ODE (STRODE),
that learns both the timings and the dynamics of time series data without
requiring any timing annotations during training. STRODE allows the usage of
differential equations to sample from the posterior point processes,
efficiently and analytically. We further provide theoretical guarantees on the
learning of STRODE. Our empirical results show that our approach successfully
infers event timings of time series data. Our method achieves competitive or
superior performances compared to existing state-of-the-art methods for both
synthetic and real-world datasets.
