Related papers: On randomness reduction in the Johnson-Lindenstrau…

This work constructs Jonson-Lindenstrauss embeddings with best accuracy, as measured by variance, mean-squared error and exponential concentration of the length distortion. Lower bounds for any data and embedding dimensions are determined,…

The Johnson-Lindenstrauss Lemma allows for the projection of $n$ points in $p-$dimensional Euclidean space onto a $k-$dimensional Euclidean space, with $k \ge \frac{24\ln \emph{n}}{3\epsilon^2-2\epsilon^3}$, so that the pairwise distances…

The famous Johnson-Lindenstrauss lemma states that for any set of n vectors, there is a linear transformation into a space of dimension O(log n) that approximately preserves all their lengths. In fact, a Haar random unitary transformation…

Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…

We prove a variant of a Johnson-Lindenstrauss lemma for matrices with circulant structure. This approach allows to minimise the randomness used, is easy to implement and provides good running times. The price to be paid is the higher…

The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…

We use Stein's method to obtain explicit bounds on the rate of convergence for the Laplace approximation of two different sums of independent random variables; one being a random sum of mean zero random variables and the other being a…

Johnson--Lindenstrauss Transforms are powerful tools for reducing the dimensionality of data while preserving key characteristics of that data, and they have found use in many fields from machine learning to differential privacy and more.…

We present a simplified and unified analysis of the Johnson-Lindenstrauss (JL) lemma, a cornerstone of dimensionality reduction for managing high-dimensional data. Our approach simplifies understanding and unifies various constructions…

Johnson-Lindenstrauss embeddings are widely used to reduce the dimension and thus the processing time of data. To reduce the total complexity, also fast algorithms for applying these embeddings are necessary. To date, such fast algorithms…

Dimension reduction is a key algorithmic tool with many applications including nearest-neighbor search, compressed sensing and linear algebra in the streaming model. In this work we obtain a {\em sparse} version of the fundamental tool in…

This note gives a simple analysis of a randomized approximation scheme for matrix multiplication proposed by Sarlos (2006) based on a random rotation followed by uniform column sampling. The result follows from a matrix version of…

Many finance, physics, and engineering phenomena are modeled by continuous-time dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform time series analysis in this context is rooted in rough path theory…

Let $\mathcal{M}$ be a smooth $d$-dimensional submanifold of $\mathbb{R}^N$ with boundary that's equipped with the Euclidean (chordal) metric, and choose $m \leq N$. In this paper we consider the probability that a random matrix $A \in…

We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method:…

For a set $X$ of $N$ points in $\mathbb{R}^D$, the Johnson-Lindenstrauss lemma provides random linear maps that approximately preserve all pairwise distances in $X$ -- up to multiplicative error $(1\pm \epsilon)$ with high probability --…

In this paper we obtain a Bernstein type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix…

We introduce the first probabilistic framework tailored for sequential random projection, an approach rooted in the challenges of sequential decision-making under uncertainty. The analysis is complicated by the sequential dependence and…

Random projection techniques based on Johnson-Lindenstrauss lemma are used for randomly aggregating the constraints or variables of optimization problems while approximately preserving their optimal values, that leads to smaller-scale…

Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L)…