Approximate Bayesian Computation with Path Signatures
- URL: http://arxiv.org/abs/2106.12555v1
- Date: Wed, 23 Jun 2021 17:25:43 GMT
- Title: Approximate Bayesian Computation with Path Signatures
- Authors: Joel Dyer, Patrick Cannon, Sebastian M Schmon
- Abstract summary: We introduce the use of path signatures as a natural candidate feature set for constructing distances between time series data.
Our experiments show that such an approach can generate more accurate approximate Bayesian posteriors than existing techniques for time series models.
- Score: 0.5156484100374059
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Simulation models of scientific interest often lack a tractable likelihood
function, precluding standard likelihood-based statistical inference. A popular
likelihood-free method for inferring simulator parameters is approximate
Bayesian computation, where an approximate posterior is sampled by comparing
simulator output and observed data. However, effective measures of closeness
between simulated and observed data are generally difficult to construct,
particularly for time series data which are often high-dimensional and
structurally complex. Existing approaches typically involve manually
constructing summary statistics, requiring substantial domain expertise and
experimentation, or rely on unrealistic assumptions such as iid data. Others
are inappropriate in more complex settings like multivariate or irregularly
sampled time series data. In this paper, we introduce the use of path
signatures as a natural candidate feature set for constructing distances
between time series data for use in approximate Bayesian computation
algorithms. Our experiments show that such an approach can generate more
accurate approximate Bayesian posteriors than existing techniques for time
series models.
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