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Extracting meaningful information from high-dimensional data poses a formidable modeling challenge, particularly when the data is obscured by noise or represented through different modalities. This research proposes a novel non-parametric…

Bayesian optimization is a powerful method for optimizing black-box functions with limited function evaluations. Recent works have shown that optimization in a latent space through deep generative models such as variational autoencoders…

Exploratory Landscape Analysis (ELA) provides numerical features for characterizing black-box optimization problems. In high-dimensional settings, however, ELA suffers from sparsity effects, high estimator variance, and the prohibitive cost…

The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy…

The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…

The efficient estimation of an approximate model order is very important for real applications with multi-dimensional data if the observed low-rank data is corrupted by additive noise. In this paper, we present a novel robust method for…

Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a nonconvex generalization of a \emph{Trust-Region Subproblem}…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain…

Non-Gaussian component analysis (NGCA) is aimed at identifying a linear subspace such that the projected data follows a non-Gaussian distribution. In this paper, we propose a novel NGCA algorithm based on log-density gradient estimation.…

Modeling response surfaces with abrupt jumps and discontinuities remains a major challenge across scientific and engineering domains. Although Gaussian process models excel at capturing smooth nonlinear relationships, their stationarity…

While many phenomena in physics and engineering are formally high-dimensional, their long-time dynamics often live on a lower-dimensional manifold. The present work introduces an autoencoder framework that combines implicit regularization…

Black-box algorithms are designed to optimize functions without relying on their underlying analytical structure or gradient information, making them essential when gradients are inaccessible or difficult to compute. Traditional methods for…

Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…

In this paper, a hybrid Lagrangian-Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian…

A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…

Novelty detection using deep generative models such as autoencoder, generative adversarial networks mostly takes image reconstruction error as novelty score function. However, image data, high dimensional as it is, contains a lot of…

Deep learning methods, including Convolutional Neural Networks, Transformers and Mamba, have achieved remarkable success in hyperspectral image (HSI) classification. Nevertheless, existing methods exhibit inflexible integration of…

We consider the problem of optimizing combinatorial spaces (e.g., sequences, trees, and graphs) using expensive black-box function evaluations. For example, optimizing molecules for drug design using physical lab experiments. Bayesian…