Related papers: Small Width, Low Distortions: Quantized Random Emb…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…
This article introduces a novel structured random matrix composed blockwise from subsampled randomized Hadamard transforms (SRHTs). The block SRHT is expected to outperform well-known dimension reduction maps, including SRHT and Gaussian…
We establish quantitative stability results for classical distortion minimization problems in the theory of quasiconformal mappings. We consider the mean distortion functional and prove sharp stability estimates for the minimization…
We study the average distortion introduced by scalar, vector, and entropy coded quantization of compressive sensing (CS) measurements. The asymptotic behavior of the underlying quantization schemes is either quantified exactly or…
The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this…
Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with…
Embeddings provide compact representations of signals in order to perform efficient inference in a wide variety of tasks. In particular, random projections are common tools to construct Euclidean distance-preserving embeddings, while…
Motivated by Tverberg-type problems in topological combinatorics and by classical results about embeddings (maps without double points), we study the question whether a finite simplicial complex K can be mapped into R^d without…
We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to…
Visualization is a crucial step in exploratory data analysis. One possible approach is to train an autoencoder with low-dimensional latent space. Large network depth and width can help unfolding the data. However, such expressive networks…
Oblivious low-distortion subspace embeddings are a crucial building block for numerical linear algebra problems. We show for any real $p, 1 \leq p < \infty$, given a matrix $M \in \mathbb{R}^{n \times d}$ with $n \gg d$, with constant…
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…
Johnson-Lindenstrauss guarantees certain topological structure is preserved under random projections when project high dimensional deterministic vectors to low dimensional vectors. In this work, we try to understand how random matrix affect…
The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…
For a family of interpolation norms $\| \cdot \|_{1,2,s}$ on $\mathbb{R}^n$, we provide a distribution over random matrices $\Phi_s \in \mathbb{R}^{m \times n}$ parametrized by sparsity level $s$ such that for a fixed set $X$ of $K$ points…
In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the ill-posed nature of such problems, we use a low-dimension…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…
Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing…