arXiv research

This work refines Cover's theory for binary classification on low-dimensional data.

Generative models learn complex data from low-dimensional manifolds.

Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold. This paper studies nonparametric regression of Hölder functions on low-dimensional manifolds using deep ReLU networks. Suppose $n$ training data are sampled from a Hölder function in $\mathc…

Diffusion models adapt to low-dimensional data regardless of coefficient choices.

The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden parameters by utilizing distance metrics that consider the set of attributes as…

This paper improves diffusion models for low-dimensional data.

The paper analyzes side effects of learning from low-dimensional data embedded in a Euclidean space.

ConvResNets approximate Besov functions and classify on low-dimensional manifolds.

New algorithms extract low-dimensional representations from sequential data, revealing insights into complex processes.

Proposes GPLFR for predicting high-dimensional outputs with few data.

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such data. We first show that the first two layers of a deep network can exactly embed…

Unified approach tackles high-dimensional tensor bandits with convex optimization and weakly decomposable regularizers.

Paper solves globally optimal k-means for low dimensional data.

UAPCA projects uncertain data to low dimensions using GMMs.

Scattering networks maximize separation on low-dimensional data.

Extracting an understanding of the underlying system from high dimensional data is a growing problem in science. Discovering informative and meaningful features is crucial for clustering, classification, and low dimensional data embedding. Here we propose to construct features based on their ability to discriminate bet…

Mercat preserves angles to create accurate low-dimensional embeddings.

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates better understanding of the underlying processes, and enables their optimization. I…

Optimizes optimal transport distances using low-dimensional embeddings.

SRCA reduces high-dimensional data to lower dimensions while preserving geometric structures.

Finding rare information hidden in a huge amount of data from the Internet is a necessary but complex issue. Many researchers have studied this issue and have found effective methods to detect anomaly data in low dimensional space. However, as the dimension increases, most of these existing methods perform poorly in de…

Cryo-em images are found to be low-dimensional.

Kernel-spectral embedding learns low-dim. structures from noisy data.

For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric according to angular changes along a geodesic line, thereby reflecting the underlying …

New research shows DDPM can adapt to data's intrinsic low dimensionality efficiently.

Low-dimensional structure in images helps deep learning models generalize better.

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical syst…

PCENet reduces uncertainty in high-dimensional data efficiently.

Two-layer networks trained on low-dimensional subspaces are vulnerable to adversarial examples.

Study shows how diffusion models learn on low-dimensional manifolds.

We develop a method to summarize causal models with cycles in cubic time.

In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs). DNNs generally provide outstanding empirical performance. Hence, numerous studies have actively investigated the theoretical properties of DNNs to understand thei…

Isometry regularizer improves autoencoder performance on manifold learning.

Improved likelihood estimation for singular distributions using deep models.

Extends dimension reduction to data-driven settings without gradients.

The paper explores how regularization can improve multi-objective learning with high-dimensional data.

Two methods factor out prior knowledge from low-dimensional embeddings.

Method learns low-dim. state vars from noisy high-dim. data.

New methods combine low and high-fidelity data for accurate surrogate modeling.

New method identifies differences between groups in low-dimensional data representations.

Enhances Gaussian process regression with multi-fidelity models and active subspaces for high-dimensional problems.

p-SNE embeds Poisson count data into low dimensions preserving structure.

A low-rank tensor model simplifies multi-dimensional Markov chains.

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the lit…

Method determines latent dimensionality in international trade flows.

We propose a low-rank approach to learning a Mahalanobis metric from data. Inspired by the recent geometric mean metric learning (GMML) algorithm, we propose a low-rank variant of the algorithm. This allows to jointly learn a low-dimensional subspace where the data reside and the Mahalanobis metric that appropriately f…

Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides approximation and statistical guarantees of GANs for the estimation of data distri…

Paper explores how Rectified Flow adapts to low-dimensional data.