379 research outputs found
ReBoot: Distributed statistical learning via refitting Bootstrap samples
In this paper, we study a one-shot distributed learning algorithm via
refitting Bootstrap samples, which we refer to as ReBoot. Given the local
models that are fit on multiple independent subsamples, ReBoot refits a new
model on the union of the Bootstrap samples drawn from these local models. The
whole procedure requires only one round of communication of model parameters.
Theoretically, we analyze the statistical rate of ReBoot for generalized linear
models (GLM) and noisy phase retrieval, which represent convex and non-convex
problems respectively. In both cases, ReBoot provably achieves the full-sample
statistical rate whenever the subsample size is not too small. In particular,
we show that the systematic bias of ReBoot, the error that is independent of
the number of subsamples, is in GLM, where n is the subsample
size. This rate is sharper than that of model parameter averaging and its
variants, implying the higher tolerance of ReBoot with respect to data splits
to maintain the full-sample rate. Simulation study exhibits the statistical
advantage of ReBoot over competing methods including averaging and CSL
(Communication-efficient Surrogate Likelihood) with up to two rounds of
gradient communication. Finally, we propose FedReBoot, an iterative version of
ReBoot, to aggregate convolutional neural networks for image classification,
which exhibits substantial superiority over FedAve within early rounds of
communication
VarRCWA: An Adaptive High-Order Rigorous Coupled Wave Analysis Method
Semi-analytical methods, such as rigorous coupled wave analysis, have been
pivotal for numerical analysis of photonic structures. In comparison to other
methods, they offer much faster computation, especially for structures with
constant cross-sectional shapes (such as metasurface units). However, when the
cross-sectional shape varies even mildly (such as a taper), existing
semi-analytical methods suffer from high computational cost. We show that the
existing methods can be viewed as a zeroth-order approximation with respect to
the structure's cross-sectional variation. We instead derive a high-order
perturbative expansion with respect to the cross-sectional variation. Based on
this expansion, we propose a new semi-analytical method that is fast to compute
even in presence of large cross-sectional shape variation. Furthermore, we
design an algorithm that automatically discretizes the structure in a way that
achieves a user specified accuracy level while at the same time reducing the
computational cost
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