Learn2Extend: Extending sequences by retaining their statistical
  properties with mixture models
Dimitris Vartziotis George Dasoulas Florian Pausinger
This paper addresses the challenge of extending general finite sequences of
real numbers within a subinterval of the real line, maintaining their inherent
statistical properties by employing machine learning. Our focus lies on
preserving the gap distribution and pair correlation function of these point
sets. Leveraging advancements in deep learning applied to point processes, this
paper explores the use of an auto-regressive \textit{Sequence Extension Mixture
Model} (SEMM) for extending finite sequences, by estimating directly the
conditional density, instead of the intensity function. We perform comparative
experiments on multiple types of point processes, including Poisson, locally
attractive, and locally repelling sequences, and we perform a case study on the
prediction of Riemann $\zeta$ function zeroes. The results indicate that the
proposed mixture model outperforms traditional neural network architectures in
sequence extension with the retention of statistical properties. Given this
motivation, we showcase the capabilities of a mixture model to extend
sequences, maintaining specific statistical properties, i.e. the gap
distribution, and pair correlation indicators.