Corpus ID: 218763479

Infinite-dimensional gradient-based descent for alpha-divergence minimisation

@article{Daudel2020InfinitedimensionalGD,
  title={Infinite-dimensional gradient-based descent for alpha-divergence minimisation},
  author={Kam'elia Daudel and Randal Douc and Franccois Portier},
  journal={arXiv: Statistics Theory},
  year={2020}
}
  • Kam'elia Daudel, Randal Douc, Franccois Portier
  • Published 2020
  • Mathematics
  • arXiv: Statistics Theory
  • This paper introduces the $(\alpha, \Gamma)$-descent, an iterative algorithm which operates on measures and performs $\alpha$-divergence minimisation in a Bayesian framework. This gradient-based procedure extends the commonly-used variational approximation by adding a prior on the variational parameters in the form of a measure. We prove that for a rich family of functions $\Gamma$, this algorithm leads at each step to a systematic decrease in the $\alpha$-divergence. Our framework recovers the… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 50 REFERENCES

    Black-Box Alpha Divergence Minimization

    VIEW 2 EXCERPTS

    Variational Inference with Tail-adaptive f-Divergence

    VIEW 2 EXCERPTS

    Rényi Divergence Variational Inference

    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    Advances in Variational Inference

    VIEW 2 EXCERPTS