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Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes…

Embedding techniques have become essential components of large databases in the deep learning era. By encoding discrete entities, such as words, items, or graph nodes, into continuous vector spaces, embeddings facilitate more efficient…

The ability to detect Out-of-Distribution (OOD) data is important in safety-critical applications of deep learning. The aim is to separate In-Distribution (ID) data drawn from the training distribution from OOD data using a measure of…

Real-world data is often assumed to lie within a low-dimensional structure embedded in high-dimensional space. In practical settings, we observe only a finite set of samples, forming what we refer to as the sample data subspace. It serves…

Feature embeddings are one of the most essential steps when training deep learning based Click-Through Rate prediction models, which map high-dimensional sparse features to dense embedding vectors. Classic human-crafted embedding size…

The infinite-depth paradigm pioneered by Neural ODEs has launched a renaissance in the search for novel dynamical system-inspired deep learning primitives; however, their utilization in problems of non-trivial size has often proved…

With the development of feature extraction technique, one sample always can be represented by multiple features which locate in high-dimensional space. Multiple features can re ect various perspectives of one same sample, so there must be…

This paper introduces Memory-limited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of streaming data and reducing its dimension. More specifically, in various applications such as sensor networks,…

Oversampled adaptive sensing (OAS) is a recently proposed Bayesian framework which sequentially adapts the sensing basis. In OAS, estimation quality is, in each step, measured by conditional mean squared errors (MSEs), and the basis for the…

Sliced inverse regression (SIR, Li 1991) is a pioneering work and the most recognized method in sufficient dimension reduction. While promising progress has been made in theory and methods of high-dimensional SIR, two remaining challenges…

Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of traditional mesh-based methods. Since 2017, the Deep BSDE…

Cybersecurity has emerged as a critical global concern. Intrusion Detection Systems (IDS) play a critical role in protecting interconnected networks by detecting malicious actors and activities. Machine Learning (ML)-based behavior analysis…

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

Quality diversity (QD) optimization searches for a collection of solutions that optimize an objective while attaining diverse outputs of a user-specified, vector-valued measure function. Contemporary QD algorithms are typically limited to…

Recent work reported that simple Bayesian optimization (BO) methods perform well for high-dimensional real-world tasks, seemingly contradicting prior work and tribal knowledge. This paper investigates why. We identify underlying challenges…

In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding…

Out-of-distribution (OOD) detection is essential for building reliable AI systems, as models that produce outputs for invalid inputs cannot be trusted. Although deep learning (DL) is often assumed to outperform traditional machine learning…

Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…