An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

Fung, Samy Wu; Ruthotto, Lars

doi:10.1137/18m119166x

Cited by 11 publications

(14 citation statements)

References 43 publications

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“…4) A key k ← k + 1 19: end while 20: return v (k) . difference between our work and [8] is that our weights adaptively change at each iteration, and thus convergence is more delicate.…”

Section: Constructing the Uq-based Weightsmentioning

confidence: 96%

“…Thus, when W (k) j = diag(H (k) j ), higher weights are assigned to elements in the local model with higher certainty and vice-versa. The idea for this UQ-framework was first used in the context of estimating parameters of PDEs [8]. In this work, the diagonal entries of the Hessian were estimated using a low-rank approximation to alleviate computational costs.…”

Section: Constructing the Uq-based Weightsmentioning

confidence: 99%

“…We call this approach AUQ-ADMM. Similarly to [8], the weights are constructed in a systematic way based on an uncertainty quantification (UQ) framework. However, the AUQ-ADMM scheme presented in this paper is adaptive and extends the theory presented in [32] from scalar-weighted local models to diagonal matrix-weighted local models.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Uncertainty-Weighted ADMM for Distributed Optimization

Ye¹,

Wan²,

Fung³

2021

Preprint

Self Cite

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We present AUQ-ADMM, an adaptive uncertainty-weighted consensus ADMM method for solving large-scale convex optimization problems in a distributed manner. Our key contribution is a novel adaptive weighting scheme that empirically increases the progress made by consensus ADMM scheme and is attractive when using a large number of subproblems. The weights are related to the uncertainty associated with the solutions of each subproblem, and are efficiently computed using lowrank approximations. We show AUQ-ADMM provably converges and demonstrate its effectiveness on a series of machine learning applications, including elastic net regression, multinomial logistic regression, and support vector machines. We provide an implementation based on the PyTorch package 1 .

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“…4) A key k ← k + 1 19: end while 20: return v (k) . difference between our work and [8] is that our weights adaptively change at each iteration, and thus convergence is more delicate.…”

Section: Constructing the Uq-based Weightsmentioning

confidence: 96%

Section: Constructing the Uq-based Weightsmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive Uncertainty-Weighted ADMM for Distributed Optimization

Ye¹,

Wan²,

Fung³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Instead, to derive local optimal solution, a number of optimization methods have been proposed. Because Alternating Direction Multiplier (ADM) [24] is suitable to handle the large-scale data, we adopt the ADM approach to optimize each variable separately.…”

Section: Optimizationmentioning

confidence: 99%

Multi-Metric Induced Robust Graph

Zhang

Sun

et al. 2021

IEEE Access

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Graph-based learning model has a wide range of applications in machine learning and computer vision. The key issue of the graph-based applications is to construct an informative graph to effectively represent data correlations. In practice, real-world data is usually contaminated by complex noise beyond Gaussian noise and sparse noise, which degrades learning performance dramatically. To construct a robust graph that represents real-world data distribution well, we propose a novel graph construction method. The proposed method is designed to be robust to complex noise beyond sparse or Gaussian noise by combining different previously given metrics of measuring data errors, which robustly and correctly generates a set of edges. To demonstrate the superiority of the proposed method, we employed the clustering and classification tasks on the real-world datasets. The experimental results demonstrate that the proposed method is superior to the existing methods in both accuracy and robustness to complex noise.

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“…This joint reconstruction is easily set up by using the jInv inversion package [38], which we use for our computations. Joint multi modal inversions using this package were also recently applied in a geophysical context [44,19].…”

Section: Joint Reconstruction Usingmentioning

confidence: 99%

Multimodal 3D Shape Reconstruction under Calibration Uncertainty Using Parametric Level Set Methods

Eliasof¹,

Sharf²,

Treister³

2020

SIAM J. Imaging Sci.

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We consider the problem of 3D shape reconstruction from multi-modal data, given uncertain calibration parameters. Typically, 3D data modalities can come in diverse forms such as sparse point sets, volumetric slices, 2D photos and so on. To jointly process these data modalities, we exploit a parametric level set method that utilizes ellipsoidal radial basis functions. This method not only allows us to analytically and compactly represent the object, it also confers on us the ability to overcome calibration-related noise that originates from inaccurate acquisition parameters. This essentially implicit regularization leads to a highly robust and scalable reconstruction, surpassing other traditional methods. In our results we first demonstrate the ability of the method to compactly represent complex objects. We then show that our reconstruction method is robust both to a small number of measurements and to noise in the acquisition parameters. Finally, we demonstrate our reconstruction abilities from diverse modalities such as volume slices obtained from liquid displacement (similar to CT scans and XRays), and visual measurements obtained from shape silhouettes as well as point-clouds.

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An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

Cited by 11 publications

References 43 publications

Adaptive Uncertainty-Weighted ADMM for Distributed Optimization

Adaptive Uncertainty-Weighted ADMM for Distributed Optimization

Multi-Metric Induced Robust Graph

Multimodal 3D Shape Reconstruction under Calibration Uncertainty Using Parametric Level Set Methods

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