arXiv research

Let $Φ\in\mathbb{R}^{m\times n}$ be a sparse Johnson-Lindenstrauss transform [KN14] with $s$ non-zeroes per column. For a subset $T$ of the unit sphere, $\varepsilon\in(0,1/2)$ given, we study settings for $m,s$ required to ensure $\mathop{\mathbb{E}}_Φ\sup_{x\in T} \left|\|Φx\|_2^2 - 1 \right| < \varepsilon ,$ i.e…

Fast method solves large-scale sparse regression problems using JL transforms.

A new method for private query release using Johnson-Lindenstrauss projection.

Novel privatization framework for high-dimensional variable selection with differential privacy.

This paper compares and analyzes random projections and column sub-sampling for dimension reduction in regression.

New method improves accuracy of compressed least-squares solutions.

Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.

New algorithm reduces dictionary learning complexity.

The paper studies how norms of random vectors are preserved by random projections.

Unified analysis simplifies Johnson-Lindenstrauss lemma for data reduction.

Sparse JL with higher sparsity improves feature hashing accuracy.

This paper improves binary embeddings and quantized compressed sensing methods.

A fast binary embedding method preserves Euclidean distances in high-dimensional data.

We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we recover and, in several cases, improve results for sets of sparse and structured spars…

This paper surveys various methods for dimensionality reduction and nearest neighbor search.

Optimization can learn Johnson-Lindenstrauss embeddings without randomization.

Improved Johnson-Lindenstrauss lemma for preserving distances in Euclidean space.

Improved machine learning performance through structured random orthogonal embeddings.

Efficiently reduces data dimensionality with guaranteed geometry preservation.

We develop a probabilistic framework for sequential random projection.

Sparse random projections simplify complex choice models.

Random projections help in representing sparse graphs efficiently.

New algorithm speeds up regression tasks for large datasets.

New algorithms cluster high-dimensional polygonal curves efficiently.

Paper uses random projection to preserve subspace structure for efficient data analysis.

The Johnson-Lindenstrauss Lemma allows for the projection of $n$ points in $p-$dimensional Euclidean space onto a $k-$dimensional Euclidean space, with $k \ge \frac{24\ln \emph{n}}{3ε^2-2ε^3}$, so that the pairwise distances are preserved within a factor of $1\pmε$. Here, working directly with the distributions of the …

New method speeds up machine learning computations using structured matrices.

This work proposes a method to learn nonlinear feature relations using non-convex regularized binned regression.

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

The paper examines how well node similarities are preserved by random projections in graph embeddings.

Tensorized random projections reduce high-dimensional tensor size efficiently.

Combines distance measures and dimension reduction for comparing distributions.

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

This work improves tensor decomposition methods, especially for large datasets.

A new method uses matrix sketches for efficient graph clustering in dynamic environments.

Optimizes embedding accuracy for data variance and error.

We provide fast algorithms for overconstrained $\ell_p$ regression and related problems: for an $n\times d$ input matrix $A$ and vector $b\in\mathbb{R}^n$, in $O(nd\log n)$ time we reduce the problem $\min_{x\in\mathbb{R}^d} \|Ax-b\|_p$ to the same problem with input matrix $\tilde A$ of dimension $s \times d$ and corr…

Unified bounds for sketched bilinear forms in machine learning and statistics.

Corrects bias in random sampling matrices for improved ML methods.

Derandomization reveals structure in neural networks, reducing sample complexity.

Gaussian sketching preserves kernel inner products in low dimensions.

New faster, space-saving methods for subspace embeddings in tensors.

Sparse butterfly network replaces dense layers in neural networks, improving expressibility and performance.

Market microstructure studies aim to reduce frictions in financial markets by analyzing price, volume, and volatility.

Neural networks approximate high-dimensional functions better than theory predicts.

Optimally sketches tensors with minimal rows for preserving norms.

New bounds on random quadratic forms hold under dependence, useful for adaptive modeling.

From a fresh data science perspective, this thesis discusses the prediction of coronary artery disease based on genetic variations at the DNA base pair level, called Single-Nucleotide Polymorphisms (SNPs), collected from the Ontario Heart Genomics Study (OHGS). First, the thesis explains two commonly used supervised le…