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About this paper
Vladimir R. Kostic, Karim Lounici, Hélène Halconruy, Timothée Devergne, Pietro Novelli, Massimiliano Pontil
LaRRR estimates slow dynamical modes of continuous-time stochastic systems by approximating the generator’s bounded resolvent with a weighted sum of transfer operators at multiple time lags, then applying reduced-rank regression. In a simulated triple-well system, its relative error for the second generator eigenvalue stays broadly stable as sampling lag decreases, unlike transfer-operator RRR; this finding is specific to that experiment.
Key insights
- Leveraging the resolvent operator, which is bounded and spectrally independent of time-lag, overcomes the time-lag sensitivity of traditional TO methods for learning slow dynamics.
- The combination of multiple TOs through a Toeplitz matrix structure, coupled with low-rank iterative solvers, enables a crucial reduction to linear computational complexity with respect to the state-space dimension.
- Theoretical guarantees are established for learning the spectral decomposition of a broader class of 'sectorial' Infinitesimal Generators, significantly expanding the method's applicability beyond self-adjoint processes.
Summary by alphaXiv.
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