arXiv research

Study shows double descent curve in high-dimensional linear regression with random projections.

Aggregates predictions from multiple regression models using random projections and kernel methods.

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

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

Tensorized random projections reduce high-dimensional tensor size efficiently.

The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.

Rare data in a large-scale database are called outliers that reveal significant information in the real world. The subspace-based outlier detection is regarded as a feasible approach in very high dimensional space. However, the outliers found in subspaces are only part of the true outliers in high dimensional space, in…

New Cantor sets with high-dimensional projections discovered.

TTRP method preserves distances in high-dimensional data with reduced storage and speed.

New method clusters high-dimensional data with anisotropic noise.

Deep Jump Gaussian Processes model high-dimensional piecewise functions.

This paper tackles high-dimensional Bayesian optimization by projecting a manifold into a lower space.

A new geometric metric identifies true data changes from parametrization artifacts in high-dimensional representations.

The paper provides bounds for high-dimensional U-statistics with novel order-explicit inequalities.

Develops a two-sample test using projected Wasserstein distance to handle high-dimensional data.

Have you ever looked at a machine learning classification model and thought, I could have made that? Well, that is what we test in this project, comparing XGBoost trained on human engineered features to training directly on data. The human engineered features do not outperform XGBoost trained di- rectly on the data, bu…

HD-BWDM improves clustering validation in high-dimensional data.

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation …

CP-factorization for high-dimensional tensor time series and double projection iterations

Develops optimal low-dimensional approximations to high-dimensional SDEs.

Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to $\mathbb{CP}^2$. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plan…

We present function preserving projections (FPP), a scalable linear projection technique for discovering interpretable relationships in high-dimensional data. Conventional dimension reduction methods aim to maximally preserve the global and/or local geometric structure of a dataset. However, in practice one is often mo…

This work improves understanding of projection robust optimal transport distances.

We propose fast approximations for the generalized sliced-Wasserstein distance.

The paper analyzes an ensemble of randomly projected linear discriminants for high-dimensional data.

This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use few literal expressions, equations, functions, etc. We barely suppose that the re…

A new framework for dimension reduction using ensemble of random projections.

SLMC improves sampling efficiency for high-dimensional distributions.

In this paper, we consider the problem of learning high-dimensional tensor regression problems with low-rank structure. One of the core challenges associated with learning high-dimensional models is computation since the underlying optimization problems are often non-convex. While convex relaxations could lead to polyn…

Paper proposes a new clustering model that preserves cluster recovery with fewer dimensions.

This article develops a framework for testing general hypothesis in high-dimensional models where the number of variables may far exceed the number of observations. Existing literature has considered less than a handful of hypotheses, such as testing individual coordinates of the model parameter. However, the problem o…

Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to biva…

The package High-dimensional Metrics (\Rpackage{hdm}) is an evolving collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence intervals and significance testing for (possibly many) low-dimensional subcomponents…

KOD detects outliers in high-dimensional data.

SILBO optimizes high-dimensional Bayesian optimization using semi-supervised embedding learning.

Paper proposes a novel approach to density ratio estimation using projection pursuit.

New method for estimating and testing impulse responses in high-dimensional VAR systems.

When applying principal component analysis (PCA) for dimension reduction, the most varying projections are usually used in order to retain most of the information. For the purpose of anomaly and change detection, however, the least varying projections are often the most important ones. In this article, we present a nov…

A method for clustering small datasets in high dimensions using random projections.

Sharp-SSL uses random projections to identify important variables for semi-supervised learning.

For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4n+1, these groups are related to computations in stable cohomotopy. Using stable homotopy theory, we make explicit computations to show that the inertia group is non-trivi…

Paper optimizes approximating high-dimensional diffusions by independent coordinates.

Bayesian optimization is an effective method for finding extrema of a black-box function. We propose a new type of Bayesian optimization for learning user preferences in high-dimensional spaces. The central assumption is that the underlying objective function cannot be evaluated directly, but instead a minimizer along …

Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution …

Adapts causal inference for high-dimensional treatments like text strings.

Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In classification problems there are two general techniques using random projections. T…

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…

MaxSketch improves distinct counting in high-dimensional, noisy data streams.