arXiv research

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

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

Unified framework for high-dimensional bandit problems with low-dimensional structures.

A new BO method tackles high-dimensional optimization without reconstruction.

Shallow diffusion models learn hidden low-dimensional structures effectively.

LASE improves local network structure visualization by targeting locally low-dimensional regions.

Study symplectic structures on low dimensional 2-step nilmanifolds.

High-dimensional representations often have a lower dimensional underlying structure. This is particularly the case in many decision making settings. For example, when the representation of actions is generated from a deep neural network, it is reasonable to expect a low-rank structure whereas conventional structures l…

Generative models learn complex data from low-dimensional manifolds.

The paper shows diffusion models can converge faster to a target distribution with low-dimensional structure.

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…

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

Paper adapts DDPM to low-dimensional structures in image distributions.

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

New embeddings capture local structure in complex networks.

We propose a framework for solving high-dimensional Bayesian inference problems using \emph{structure-exploiting} low-dimensional transport maps or flows. These maps are confined to a low-dimensional subspace (hence, lazy), and the subspace is identified by minimizing an upper bound on the Kullback--Leibler divergence …

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

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

Language models exhibit low-rank structure, which can be used for generation.

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

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…

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

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

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

Mercat preserves angles to create accurate low-dimensional embeddings.

Proposes a neural density estimator that adapts to low-dimensional structures and integrates into generative models.

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured by solving a non-linear, low-rank representation problem. We show that this low-…

A new framework detects anomalies in structured data.

Improved likelihood estimation for singular distributions using deep models.

Diffusion models adapt to low-dimensional structures for nonparametric density estimation.

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…

Develops TOFU for tensor bandits with low-rank structure.

The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. W…

Generates low-dimensional node vectors for graphs with privacy while preserving structural preferences.

Proposes a method to compare noisy high-dimensional datasets with low-dimensional manifolds.

Localized diffusion models reduce training complexity by exploiting low-dimensional structure.

MoEs can efficiently model complex tasks with low-dimensionality and sparsity.

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern high-dimensional data and interactions thereof can be modeled as lying approximat…

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy becau…

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space that spans the conditional means, it is possible to consistently recover the struc…

SCBMs model causal effects using low-dimensional bottlenecks.

A new method for Bayesian inference tackles high-dimensional problems.

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

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

LIT-LVM improves linear predictors by estimating interaction terms with latent vectors.

Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters in some low-dimensional model subspace. In such settings, it is desirable for est…

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

Ray-based framework classifies high-dimensional structures with reduced data.