Aleksandr Y. Aravkin

Robust and Trend-following Student’s t Kalman Smoothers

  • Aleksandr Y. Aravkin
  • James V. Burke
  • Gianluigi Pillonetto
    • Categories Finance and Economics, Robust Optimization, Statistics

    Two nonlinear Kalman smoothers are proposed using the Student’s t distribution. The first, which we call the T-Robust smoother, finds the maximum a posteriori (MAP) solution for Gaussian process noise and Student’s t observation noise. It is extremely robust against outliers, outperforming the recently proposed L1-Laplace smoother in extreme situations with data containing 20% or … Read more

    Robust inversion, dimensionality reduction, and randomized sampling

  • Aleksandr Y. Aravkin
  • Michael P. Friedlander
  • Felix Herrmann
  • Tristan van Leeuwen
    • Categories Basic Sciences Applications, Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only … Read more