Active Subspace

Active subspaces are low-dimensional representations of high-dimensional data that capture the most influential directions for a given function or model. Research focuses on identifying these subspaces efficiently, often employing techniques like gradient-based methods, principal component analysis extensions, and Riemannian geometry for specific data types (e.g., covariance matrices). This methodology improves efficiency in various applications, including deep learning training, uncertainty quantification in generative models, and robust subspace recovery in computer vision, by reducing computational complexity and enhancing interpretability. The impact spans diverse fields, from materials science and drug discovery to reinforcement learning and image processing.

Papers

August 20, 2024

Subspace Prototype Guidance for Mitigating Class Imbalance in Point Cloud Semantic Segmentation
Jiawei Han, Kaiqi Liu, Wei Li, Guangzhi Chen
Semantic Segmentation Class Imbalance Segmentation Network Deep Subspace Point Cloud Semantic Segmentation Subspace Prototype Active Subspace

June 23, 2024

Mamba-based Light Field Super-Resolution with Efficient Subspace Scanning
Ruisheng Gao, Zeyu Xiao, Zhiwei Xiong
Super Resolution 4 Dimensional Active Subspace 4 Dimensional Light Field Light Field Super Resolution Spatial Angular Correlation

May 25, 2024

Does SGD really happen in tiny subspaces?
Minhak Song, Kwangjun Ahn, Chulhee Yun
Deep Neural Network Stochastic Gradient Descent Hessian Matrix Large Learning Rate Active Subspace

April 30, 2024

Leveraging Active Subspaces to Capture Epistemic Model Uncertainty in Deep Generative Models for Molecular Design
A N M Nafiz Abeer, Sanket Jantre, Nathan M Urban, Byung-Jun Yoon
Epistemic Uncertainty Molecular Design Molecular Optimization Active Subspace Generative Molecular Design Tree Variational

April 17, 2024

A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion
Feng Yu, Teng Zhang, Gilad Lerman
Financial Application Motion Information Inner Structure Robust Estimation Linear Estimator Active Subspace

January 5, 2024

Shared active subspace for multivariate vector-valued functions
Khadija Musayeva, Mickael Binois
Vector Valued Sharing Matter Multivariate Approach Active Subspace Symmetric Positive Definite

December 6, 2023

Accelerated Gradient Algorithms with Adaptive Subspace Search for Instance-Faster Optimization
Yuanshi Liu, Hanzhen Zhao, Yang Xu, Pengyun Yue, Cong Fang
Optimization Purpose Worst Case Accelerated Gradient Method Gradient Complexity Gradient Based Algorithm Active Subspace

October 17, 2023

Surrogate Active Subspaces for Jump-Discontinuous Functions
Nathan Wycoff
Gaussian Process Surrogate Modeling Computational Model Surrogate Assisted Version Active Subspace Discontinuous Function

September 6, 2023

Learning Active Subspaces for Effective and Scalable Uncertainty Quantification in Deep Neural Networks
Sanket Jantre, Nathan M. Urban, Xiaoning Qian, Byung-Jun Yoon
Deep Neural Network Uncertainty Quantification Variational Inference Bayesian Deep Learning Active Subspace Scalable Bayesian

July 11, 2023

Learning Active Subspaces and Discovering Important Features with Gaussian Radial Basis Functions Neural Networks
Danny D'Agostino, Ilija Ilievski, Christine Annette Shoemaker
Model Interpretability Predictive Performance Radial Basis Function Gaussian Kernel Active Subspace Precision Matrix Important Feature

December 30, 2022

Disentangled Explanations of Neural Network Predictions by Finding Relevant Subspaces
Pattarawat Chormai, Jan Herrmann, Klaus-Robert Müller, Grégoire Montavon
Explainable AI Disentanglement Capability Disentangle Content Activation Pattern Neural Network Prediction Active Subspace

November 18, 2022

Provable Defense against Backdoor Policies in Reinforcement Learning
Shubham Kumar Bharti, Xuezhou Zhang, Adish Singla, Xiaojin Zhu
Reinforcement Learning Active Subspace Provable Defense Backdoor Policy

September 15, 2022

The Controllability and Structural Controllability of Laplacian Dynamics
Jijun Qu, Zhijian Ji, Yungang Liu, Chong Lin
Controllability Condition Active Subspace Structural Controllability

July 29, 2022

Learning idempotent representation for subspace clustering
Lai Wei, Shiteng Liu, Rigui Zhou, Changming Zhu
LeArning Abstract Low Rank Subspace Prototype Active Subspace

April 11, 2022

Multi-view graph structure learning using subspace merging on Grassmann manifold
Razieh Ghiasi, Hossein Amirkhani, Alireza Bosaghzadeh
Graph Neural Network Multi View Graph Classification Graph Structure Learning Grassmann Manifold Active Subspace

January 2, 2022

Riemannian Nearest-Regularized Subspace Classification for Polarimetric SAR images
Junfei Shi, Haiyan Jin
Riemannian Counterpart Riemannian Geometry Approach Active Subspace Polarimetric Synthetic Aperture Radar Symmetric Positive Definite Matrix Polarimetric Cue PolSAR Image Classification

December 2, 2021

Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximation
Yuankai Teng, Zhu Wang, Lili Ju, Anthony Gruber, Guannan Zhang
Neural Network High Dimensional Dimensionality Reduction Function Approximation Different Level Dimensional Input Active Subspace

Active Subspace

Papers

Subspace Prototype Guidance for Mitigating Class Imbalance in Point Cloud Semantic Segmentation

Mamba-based Light Field Super-Resolution with Efficient Subspace Scanning

Does SGD really happen in tiny subspaces?

Leveraging Active Subspaces to Capture Epistemic Model Uncertainty in Deep Generative Models for Molecular Design

A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion

Shared active subspace for multivariate vector-valued functions

Accelerated Gradient Algorithms with Adaptive Subspace Search for Instance-Faster Optimization

Surrogate Active Subspaces for Jump-Discontinuous Functions

Learning Active Subspaces for Effective and Scalable Uncertainty Quantification in Deep Neural Networks

Learning Active Subspaces and Discovering Important Features with Gaussian Radial Basis Functions Neural Networks

Disentangled Explanations of Neural Network Predictions by Finding Relevant Subspaces

Provable Defense against Backdoor Policies in Reinforcement Learning

The Controllability and Structural Controllability of Laplacian Dynamics

Learning idempotent representation for subspace clustering

Multi-view graph structure learning using subspace merging on Grassmann manifold

Riemannian Nearest-Regularized Subspace Classification for Polarimetric SAR images

Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximation