Introduces a new feature importance measure using Gram-Schmidt decorrelation.
problem Determining feature influence strength and nature in datasets.
method Gram-Schmidt decorrelation and random forest regression.
result Empirical comparison of new estimators with established methods.
A new training method improves stability and generalization of DeepONets.
problem Training deep operator networks (DeepONets) is challenging due to nonconvex and nonlinear nature.
method Two-step training method: first train trunk network, then branch network. Introduced Gram-Schmidt orthonormalization.
result Generalization error estimate and numerical examples demonstrating effectiveness.
EigenGame reinterprets PCA as a game to find eigenvectors.
problem Finding principal components efficiently and accurately.
method EigenGame treats PCA as a Nash equilibrium game, using gradient-based updates.
result EigenGame algorithm combines Oja's rule and Gram-Schmidt orthogonalization.
Improves interpretability of neural network intermediate layers by making concept activations more robust and effective.
problem Challenges in interpreting neural network decisions and learning in intermediate layers due to opacity and shared interactions.
method Proposes A-CAV to increase effectiveness and employs Gram-Schmidt process to improve robustness.
result Significant improvement in recall rate of concept images from 18.35% to 76.83% for VGG16, with reduced variance in recall across different random seeds.
As a type of pseudoinverse learning, extreme learning machine (ELM) is able to achieve high performances in a rapid pace on benchmark datasets. However, when it is applied to real life large data, decline related to low-convergence of singular value decomposition (SVD) method occurs. Our study aims to resolve this issu…
While progress has been made in crafting visually imperceptible adversarial examples, constructing semantically meaningful ones remains a challenge. In this paper, we propose a framework to generate semantics preserving adversarial examples. First, we present a manifold learning method to capture the semantics of the i…
In this technical report, we discuss several sampling algorithms for Determinantal Point Processes (DPP). DPPs have recently gained a broad interest in the machine learning and statistics literature as random point processes with negative correlation, i.e., ones that can generate a "diverse" sample from a set of items.…
A new method builds sparse polynomial chaos expansions for models with dependent inputs.
problem Quantifying uncertainty in models with dependent inputs.
method Data-driven approach to construct orthonormal polynomials recursively based on input correlations.
result Reduces the number of observations and improves numerical stability and computational efficiency.
The paper connects cut locus, Thom space, and Morse-Bott functions in Riemannian geometry.
problem Analyzing the square of the distance function to a submanifold in a Riemannian manifold.
method Investigates the Morse-Bott property of the square of the distance function on the complement of the cut locus.
result The Thom space of the normal bundle of a submanifold is homeomorphic to the quotient space of the complement of the cut locus.
Defines weak normals for irregular curves in high-dimensional spaces.
problem Dealing with irregular curves in high-dimensional Euclidean spaces.
method Using sequences of inscribed polygonals and Gram-Schmidt procedure, introduces a relaxed notion of weak normals.
result Weak normals for irregular curves are the strong limit of approximating polygonals and agree with relaxed energy.
This work proposes a new method to estimate joint probability from pairwise marginals, reducing sample complexity.
problem Direct nonparametric estimation of high-dimensional joint probability is infeasible due to the curse of dimensionality.
method Developed a coupled nonnegative matrix factorization (CNMF) framework using only pairwise marginals.
result The method provably recovers the joint probability mass function up to bounded error in finite iterations under reasonable conditions.
The paper studies the cut locus of submanifolds in Riemannian manifolds, providing geometric and topological insights.
problem Understanding the cut locus of submanifolds in Riemannian geometry.
method Analyzing the square of the distance function and using gradient flow lines to deform spaces.
result The cut locus of a submanifold is invariant under certain group actions and provides a deformation retraction.