arXiv research

Given a hyperbolic knot $K$ and any $n\geq 2$ the abelian representations and the holonomy representation each give rise to an $(n-1)$-dimensional component in the $\operatorname{SL}(n,\Bbb{C})$-character variety. A component of the $\operatorname{SL}(n,\Bbb{C})$-character variety of dimension $\geq n$ is called high-d…

A fast method estimates Gaussian mixture components without iterative fitting.

Character varieties of prime knots have high-dimensional components.

We develop a mean-field theory for multi-component ICA in high dimensions.

The paper introduces a method for interpretable principal component analysis of high-dimensional time series.

SPPCSO addresses multicollinearity in high-dimensional data, improving model stability and predictive accuracy.

New method improves PCA for high-dimensional data with n < p.

The paper develops methods to accurately locate change points in high-dimensional mean shift models.

The paper analyzes PLS-SVD in high-dimensional data integration, revealing its strengths and limitations.

SP-SPCA improves sparse PCA by adaptively adjusting variable penalties, enhancing interpretability and stability.

PCCs combine PCA and copulas for high-dimensional tail dependence modeling.

Novel method converts time series data into functional data for high dimensional classification.

Develops methods for estimating and providing confidence bands in sparse high-dimensional additive models.

This paper proposes a probabilistic neural network developed on the basis of time-series discriminant component analysis (TSDCA) that can be used to classify high-dimensional time-series patterns. TSDCA involves the compression of high-dimensional time series into a lower-dimensional space using a set of orthogonal tra…

We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension $d$ to scale with the series length $T$. We treat the transition matrix of time series as a nuisance parameter and directly apply sparse principal component…

AP-CDE uses NF to estimate high-dimensional conditional densities, improving interpretability.

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA in three as…

High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models …

Non-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian "signals" from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of projection pursuit (PP) and independent component analysis (ICA) to mu…

Modern techniques simplify complex high-dimensional data.

This paper studies clustering and embedding in high-dimensional Gaussian mixture block models.

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables of each observation, and the data set contains some (arbitrarily) corrupted obse…

For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important problem of estimating high dimensional covariance matrix. Then we explore some …

Study on autoencoder denoising in high dimensions.

EigenBayes: A fast, adaptive Bayesian shrinkage approach for high-dimensional matrix factorization

A new PCA-based imputation method for high-dimensional data.

Optimal tensor PCA for estimating factors and loadings in high-dimensional panel data.

Paper examines LASSO for high-dimensional predictive regression, improving its performance in forecasting unemployment.

In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in interest rate markets, we investigate correlation in high-dimensional high-frequency …

We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature selection components. Our feature selection component naturally simplifies to wei…

Combines OT and PCA for DR, preserving clusters.

Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even a few tens of full-order model runs are impracticable. While dimensionality redu…

Survey of SDR methods for high-dimensional regression and embedding.

Learning rate needs to decrease with higher data moments for effective ICA in high dimensions.

Meta-learning improves support recovery in high-dimensional PCA.

One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to the PCA of a high dimensional random walk. We compute the eigenvalues and eigenvec…

FCPCA fuzzy clusters high-dimensional time series data efficiently.

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on the global convergence. Sparse PCA algorithms based on a convex formulation, for…

We identify and validate a model for PCR in high dimensions, improving prediction guarantees.

The paper develops a method for optimal projection selection in high-dimensional classification.

Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new approach to direct estimation of the projector on the target space based on semidefinit…

A new method for high-dimensional functional regression reduces multicollinearity and improves interpretability.

Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.

Paper detects and estimates breaks in high-dimensional functional time series.

We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high dimensional problems. In the {\it sparse regime} when the components are sufficientl…

New algorithms improve tensor CP decomposition under mild conditions.

New method recovers latent confounders from high-dimensional proxy variables.

A new debiasing method for high-dimensional regression with applications to PCR.