  Many real world problems exhibit patterns that have periodic behavior. For
example, in astrophysics, periodic variable stars play a pivotal role in
understanding our universe. An important step when analyzing data from such
processes is the problem of identifying the period: estimating the period of a
periodic function based on noisy observations made at irregularly spaced time
points. This problem is still a difficult challenge despite extensive study in
different disciplines. The paper makes several contributions toward solving
this problem. First, we present a nonparametric Bayesian model for period
finding, based on Gaussian Processes (GP), that does not make strong
assumptions on the shape of the periodic function. As our experiments
demonstrate, the new model leads to significantly better results in period
estimation when the target function is non-sinusoidal. Second, we develop a new
algorithm for parameter optimization for GP which is useful when the likelihood
function is very sensitive to the setting of the hyper-parameters with numerous
local minima, as in the case of period estimation. The algorithm combines
gradient optimization with grid search and incorporates several mechanisms to
overcome the high complexity of inference with GP. Third, we develop a novel
approach for using domain knowledge, in the form of a probabilistic generative
model, and incorporate it into the period estimation algorithm. Experimental
results on astrophysics data validate our approach showing significant
improvement over the state of the art in this domain.
