Gradient Flows in Filtering and Fisher-Rao Geometry

@article{Halder2018GradientFI,
  title={Gradient Flows in Filtering and Fisher-Rao Geometry},
  author={Abhishek Halder and Tryphon T. Georgiou},
  journal={2018 Annual American Control Conference (ACC)},
  year={2018},
  pages={4281-4286}
}
  • Abhishek Halder, Tryphon T. Georgiou
  • Published 2018
  • Computer Science, Mathematics
  • 2018 Annual American Control Conference (ACC)
  • Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and a systematic way to formulate and solve the same for linear Gaussian systems has appeared in our previous work where the gradient flows were realized via proximal operators with respect to Wasserstein metric arising in optimal mass transport. In this paper… CONTINUE READING
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 29 REFERENCES

    Gradient flows in uncertainty propagation and filtering of linear Gaussian systems

    VIEW 6 EXCERPTS

    Poisson's equation in nonlinear filtering

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Likelihood Functions for Stochastic Signals in White Noise

    VIEW 6 EXCERPTS
    HIGHLY INFLUENTIAL

    Proximal Algorithms

    VIEW 2 EXCERPTS

    Convex Analysis and Monotone Operator Theory in Hilbert Spaces

    VIEW 1 EXCERPT