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19 April 2024 |
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Article overview
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Marvels and Pitfalls of the Langevin Algorithm in Noisy High-dimensional Inference | | Stefano Sarao Mannelli
; Giulio Biroli
; Chiara Cammarota
; Florent Krzakala
; Pierfrancesco Urbani
; Lenka Zdeborová
; | | Date: |
21 Dec 2018 | | Abstract: | Gradient-descent-based algorithms and their stochastic versions have
widespread applications in machine learning and statistical inference. In this
work we perform an analytic study of the performances of one of them, the
Langevin algorithm, in the context of noisy high-dimensional inference. We
employ the Langevin algorithm to sample the posterior probability measure for
the spiked matrix-tensor model. The typical behaviour of this algorithm is
described by a system of integro-differential equations that we call the
Langevin state evolution, whose solution is compared with the one of the state
evolution of approximate message passing (AMP). Our results show that,
remarkably, the algorithmic threshold of the Langevin algorithm is sub-optimal
with respect to the one given by AMP. We conjecture this phenomenon to be due
to the residual glassiness present in that region of parameters. Finally we
show how a landscape-annealing protocol, that uses the Langevin algorithm but
violate the Bayes-optimality condition, can approach the performance of AMP. | | Source: | arXiv, 1812.9066 | | Services: | Forum | Review | PDF | Favorites | |
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