  Investigating the relationship, particularly the lead-lag effect, between
time series is a common question across various disciplines, especially when
uncovering biological process. However, analyzing time series presents several
challenges. Firstly, due to technical reasons, the time points at which
observations are made are not at uniform inintervals. Secondly, some lead-lag
effects are transient, necessitating time-lag estimation based on a limited
number of time points. Thirdly, external factors also impact these time series,
requiring a similarity metric to assess the lead-lag relationship. To counter
these issues, we introduce a model grounded in the Gaussian process, affording
the flexibility to estimate lead-lag effects for irregular time series. In
addition, our method outputs dissimilarity scores, thereby broadening its
applications to include tasks such as ranking or clustering multiple pair-wise
time series when considering their strength of lead-lag effects with external
factors. Crucially, we offer a series of theoretical proofs to substantiate the
validity of our proposed kernels and the identifiability of kernel parameters.
Our model demonstrates advances in various simulations and real-world
applications, particularly in the study of dynamic chromatin interactions,
compared to other leading methods.
