scholarly journals Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions

2021 ◽  
Vol 31 (4) ◽  
pp. 2638-2664
Author(s):  
Jeffrey Larson ◽  
Matt Menickelly ◽  
Baoyu Zhou
Keyword(s):  
Manifold Sampling

Manifold Sampling for $\ell_1$ Nonconvex Optimization

2016 ◽  
Vol 26 (4) ◽  
pp. 2540-2563 ◽  
Author(s):  
Jeffrey Larson ◽  
Matt Menickelly ◽  
Stefan M. Wild
Keyword(s):  
Nonconvex Optimization ◽  
Manifold Sampling

scholarly journals Data Augmentation with Variational Autoencoders and Manifold Sampling

2021 ◽  
pp. 184-192
Author(s):  
Clément Chadebec ◽  
Stéphanie Allassonnière
Keyword(s):  
Data Augmentation ◽  
Manifold Sampling

scholarly journals Function-guided protein design by deep manifold sampling

2021 ◽  
Author(s):  
Vladimir Gligorijevic ◽  
Daniel Berenberg ◽  
Stephen Ra ◽  
Andrew Watkins ◽  
Simon Kelow ◽  
...  
Keyword(s):  
Protein Design ◽  
Metal Binding ◽  
Protein Sequences ◽  
Test Time ◽  
Learning Approaches ◽  
Denoising Autoencoder ◽  
Global Fold ◽  
Manifold Sampling ◽  
Combinatorial Space ◽  
Function Predictor

Protein design is challenging because it requires searching through a vast combinatorial space that is only sparsely functional. Self-supervised learning approaches offer the potential to navigate through this space more effectively and thereby accelerate protein engineering. We introduce a sequence denoising autoencoder (DAE) that learns the manifold of protein sequences from a large amount of potentially unlabelled proteins. This DAE is combined with a function predictor that guides sampling towards sequences with higher levels of desired functions. We train the sequence DAE on more than 20M unlabeled protein sequences spanning many evolutionarily diverse protein families and train the function predictor on approximately 0.5M sequences with known function labels. At test time, we sample from the model by iteratively denoising a sequence while exploiting the gradients from the function predictor. We present a few preliminary case studies of protein design that demonstrate the effectiveness of this proposed approach, which we refer to as "deep manifold sampling", including metal binding site addition, function-preserving diversification, and global fold change.

scholarly journals Environmental Economics and Uncertainty: Review and a Machine Learning Outlook

2020 ◽  
Author(s):  
Ruda Zhang ◽  
Patrick Wingo ◽  
Rodrigo Duran ◽  
Kelly Rose ◽  
Jennifer Bauer ◽  
...  
Keyword(s):  
Machine Learning ◽  
Environmental Economics ◽  
Latent Variables ◽  
Integrated Assessment ◽  
Probability Model ◽  
Joint Probability ◽  
Estimation Methods ◽  
Environmental Models ◽  
Manifold Sampling ◽  
Joint Probability Model

Economic assessment in environmental science means measuring and evaluating environmental impacts, adaptation, and vulnerability. Integrated assessment modeling (IAM) is a unifying framework of environmental economics, which attempts to combine key elements of physical, ecological, and socioeconomic systems. The first part of this article reviews the literature on the IAM framework: its components, relations between the components, and examples. For such models to inform environmental decision-making, they must quantify the uncertainties associated with their estimates. Uncertainty characterization in integrated assessment varies by component models: uncertainties associated with mechanistic physical models are often assessed with an ensemble of simulations or Monte Carlo sampling, while uncertainties associated with impact models are evaluated by conjecture or econometric analysis. The second part of this article reviews the literature on uncertainty in integrated assessment, by type and by component. Probabilistic learning on manifolds (PLoM) is a machine learning technique that constructs a joint probability model of all relevant variables, which may be concentrated on a low-dimensional geometric structure. Compared to traditional density estimation methods, PLoM is more efficient especially when the data are generated by a few latent variables. With the manifold-constrained joint probability model learned by PLoM from a small, initial sample, manifold sampling creates new samples for evaluating converged statistics, which helps answer policy-making questions from prediction, to response, and prevention. As a concrete example, this article reviews IAMs of offshore oil spills—which integrate environmental models, transport models, spill scenarios, and exposure metrics—and demonstrates the use of manifold sampling in assessing the risk of drilling in the Gulf of Mexico.

Specular manifold sampling for rendering high-frequency caustics and glints

2020 ◽  
Vol 39 (4) ◽  
Author(s):  
Tizian Zeltner ◽  
Iliyan Georgiev ◽  
Wenzel Jakob
Keyword(s):  
High Frequency ◽  
Manifold Sampling
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