Ensemble Kalman methods for training neural networks

Data assimilation for network weights

2022-09-20 — 2024-11-29

Bayes
dynamical systems
likelihood free
linear algebra
machine learning
Monte Carlo
neural nets
nonparametric
particle
probability
sciml
signal processing
sparser than thou
statistics
statmech
stochastic processes
time series
uncertainty

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Figure 1

Training neural networks by ensemble Kalman updates instead of SGD. Arises naturally from the dynamical perspective on neural networks. TBD.

Claudia Schilling’s filter (Schillings and Stuart 2017) is an elegant variant of the ensemble Kalman Filter which looks somehow more general than the original but also simpler and may be applicable. Haber, Lucka, and Ruthotto (2018) use it to train neural nets (!) and show a rather beautiful connection to stochastic gradient descent in section 3.2.

1 References

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Chen, Chong, Dou, Chen, et al. 2022. “A Novel Neural Network Training Framework with Data Assimilation.” The Journal of Supercomputing.
Chen, Yuming, Sanz-Alonso, and Willett. 2022. “Autodifferentiable Ensemble Kalman Filters.” SIAM Journal on Mathematics of Data Science.
———. 2023. “Reduced-Order Autodifferentiable Ensemble Kalman Filters.” Inverse Problems.
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