scholarly journals Deep Active Subspaces: A Scalable Method for High-Dimensional Uncertainty Propagation

2019 ◽  
Author(s):  
Rohit Tripathy ◽  
Ilias Bilionis
Keyword(s):  
Dimensionality Reduction ◽  
Stochastic Systems ◽  
Uncertainty Propagation ◽  
Gaussian Process Regression ◽  
Surrogate Modeling ◽  
Forward Model ◽  
High Dimensional ◽  
Great Promise ◽  
Gradient Information ◽  
Active Subspaces

Abstract A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accurate surrogate modeling in such systems, is further compounded by data scarcity brought about by the large cost of forward model evaluations. Traditional response surface techniques, such as Gaussian process regression (or Kriging) and polynomial chaos are difficult to scale to high dimensions. To make surrogate modeling tractable in expensive high-dimensional systems, one must resort to dimensionality reduction of the stochastic parameter space. A recent dimensionality reduction technique that has shown great promise is the method of ‘active subspaces’. The classical formulation of active subspaces, unfortunately, requires gradient information from the forward model — often impossible to obtain. In this work, we present a simple, scalable method for recovering active subspaces in high-dimensional stochastic systems, without gradient-information that relies on a reparameterization of the orthogonal active subspace projection matrix, and couple this formulation with deep neural networks. We demonstrate our approach on challenging synthetic datasets and show favorable predictive comparison to classical active subspaces.

On the usefulness of gradient information in surrogate modeling: Application to uncertainty propagation in composite material models

2020 ◽  
Vol 60 ◽  
pp. 103024
Author(s):  
Anindya Bhaduri ◽  
David Brandyberry ◽  
Michael D. Shields ◽  
Philippe Geubelle ◽  
Lori Graham-Brady
Keyword(s):  
Composite Material ◽  
Uncertainty Propagation ◽  
Surrogate Modeling ◽  
Material Models ◽  
Gradient Information

scholarly journals A generalization of t-SNE and UMAP to single-cell multimodal omics

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Van Hoan Do ◽  
Stefan Canzar
Keyword(s):  
Dimensionality Reduction ◽  
Single Cell ◽  
Cell Types ◽  
High Dimensional ◽  
Omics Data ◽  
Relative Contribution ◽  
Reduction Techniques ◽  
Dimensionality Reduction Techniques ◽  
Concise Representation ◽  
Cellular Identity

AbstractEmerging single-cell technologies profile multiple types of molecules within individual cells. A fundamental step in the analysis of the produced high-dimensional data is their visualization using dimensionality reduction techniques such as t-SNE and UMAP. We introduce j-SNE and j-UMAP as their natural generalizations to the joint visualization of multimodal omics data. Our approach automatically learns the relative contribution of each modality to a concise representation of cellular identity that promotes discriminative features but suppresses noise. On eight datasets, j-SNE and j-UMAP produce unified embeddings that better agree with known cell types and that harmonize RNA and protein velocity landscapes.

scholarly journals Parallel Framework for Dimensionality Reduction of Large-Scale Datasets

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Sai Kiranmayee Samudrala ◽  
Jaroslaw Zola ◽  
Srinivas Aluru ◽  
Baskar Ganapathysubramanian
Keyword(s):  
Dimensionality Reduction ◽  
Organic Solar Cells ◽  
Large Scale ◽  
Parallel Implementation ◽  
High Dimensional Data ◽  
Real Life ◽  
Processing Parameters ◽  
High Dimensional ◽  
Morphology Evolution ◽  
Reduction Techniques

Dimensionality reduction refers to a set of mathematical techniques used to reduce complexity of the original high-dimensional data, while preserving its selected properties. Improvements in simulation strategies and experimental data collection methods are resulting in a deluge of heterogeneous and high-dimensional data, which often makes dimensionality reduction the only viable way to gain qualitative and quantitative understanding of the data. However, existing dimensionality reduction software often does not scale to datasets arising in real-life applications, which may consist of thousands of points with millions of dimensions. In this paper, we propose a parallel framework for dimensionality reduction of large-scale data. We identify key components underlying the spectral dimensionality reduction techniques, and propose their efficient parallel implementation. We show that the resulting framework can be used to process datasets consisting of millions of points when executed on a 16,000-core cluster, which is beyond the reach of currently available methods. To further demonstrate applicability of our framework we perform dimensionality reduction of 75,000 images representing morphology evolution during manufacturing of organic solar cells in order to identify how processing parameters affect morphology evolution.

scholarly journals High dimensional Kriging metamodelling utilising gradient information

2016 ◽  
Vol 40 (9-10) ◽  
pp. 5256-5270 ◽  
Author(s):  
S. Ulaganathan ◽  
I. Couckuyt ◽  
T. Dhaene ◽  
J. Degroote ◽  
E. Laermans
Keyword(s):  
High Dimensional ◽  
Gradient Information

scholarly journals Generalization-Based Acquisition of Training Data for Motor Primitive Learning by Neural Networks

2021 ◽  
Vol 11 (3) ◽  
pp. 1013
Author(s):  
Zvezdan Lončarević ◽  
Rok Pahič ◽  
Aleš Ude ◽  
Andrej Gams
Keyword(s):  
Neural Networks ◽  
Dimensionality Reduction ◽  
Gaussian Process Regression ◽  
Search Space ◽  
Robot Learning ◽  
Training Data ◽  
Practical Applications ◽  
Latent Space ◽  
Real Robot ◽  
Low Dimensional

Autonomous robot learning in unstructured environments often faces the problem that the dimensionality of the search space is too large for practical applications. Dimensionality reduction techniques have been developed to address this problem and describe motor skills in low-dimensional latent spaces. Most of these techniques require the availability of a sufficiently large database of example task executions to compute the latent space. However, the generation of many example task executions on a real robot is tedious, and prone to errors and equipment failures. The main result of this paper is a new approach for efficient database gathering by performing a small number of task executions with a real robot and applying statistical generalization, e.g., Gaussian process regression, to generate more data. We have shown in our experiments that the data generated this way can be used for dimensionality reduction with autoencoder neural networks. The resulting latent spaces can be exploited to implement robot learning more efficiently. The proposed approach has been evaluated on the problem of robotic throwing at a target. Simulation and real-world results with a humanoid robot TALOS are provided. They confirm the effectiveness of generalization-based database acquisition and the efficiency of learning in a low-dimensional latent space.

Multi-Instance Dimensionality Reduction via Sparsity and Orthogonality

2018 ◽  
Vol 30 (12) ◽  
pp. 3281-3308
Author(s):  
Hong Zhu ◽  
Li-Zhi Liao ◽  
Michael K. Ng
Keyword(s):  
Dimensionality Reduction ◽  
Optimization Problem ◽  
Augmented Lagrangian ◽  
Main Idea ◽  
Real Data ◽  
Learning Performance ◽  
High Dimensional ◽  
Data Sets ◽  
Outer Loop ◽  
Orthogonality Constraints

We study a multi-instance (MI) learning dimensionality-reduction algorithm through sparsity and orthogonality, which is especially useful for high-dimensional MI data sets. We develop a novel algorithm to handle both sparsity and orthogonality constraints that existing methods do not handle well simultaneously. Our main idea is to formulate an optimization problem where the sparse term appears in the objective function and the orthogonality term is formed as a constraint. The resulting optimization problem can be solved by using approximate augmented Lagrangian iterations as the outer loop and inertial proximal alternating linearized minimization (iPALM) iterations as the inner loop. The main advantage of this method is that both sparsity and orthogonality can be satisfied in the proposed algorithm. We show the global convergence of the proposed iterative algorithm. We also demonstrate that the proposed algorithm can achieve high sparsity and orthogonality requirements, which are very important for dimensionality reduction. Experimental results on both synthetic and real data sets show that the proposed algorithm can obtain learning performance comparable to that of other tested MI learning algorithms.

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