Related papers: Stable Sparse Subspace Embedding for Dimensionalit…

Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…

In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases…

We study beyond worst-case dimensionality reduction for $s$-sparse vectors. Our work is divided into two parts, each focusing on a different facet of beyond worst-case analysis: We first consider average-case guarantees. A folklore upper…

We propose a flexible ensemble classification framework, Random Subspace Ensemble (RaSE), for sparse classification. In the RaSE algorithm, we aggregate many weak learners, where each weak learner is a base classifier trained in a subspace…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

An "oblivious subspace embedding (OSE)" given some parameters eps,d is a distribution D over matrices B in R^{m x n} such that for any linear subspace W in R^n with dim(W) = d it holds that Pr_{B ~ D}(forall x in W ||B x||_2 in (1 +/-…

Dimension reduction, widely used in science, maps high-dimensional data into low-dimensional space. We investigate a basic mathematical model underlying the techniques of stochastic neighborhood embedding (SNE) and its popular variant…

In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be…

As a basic component of SE(3)-equivariant deep feature learning, steerable convolution has recently demonstrated its advantages for 3D semantic analysis. The advantages are, however, brought by expensive computations on dense, volumetric…

Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…

We describe MPSE: a Multi-Perspective Simultaneous Embedding method for visualizing high-dimensional data, based on multiple pairwise distances between the data points. Specifically, MPSE computes positions for the points in 3D and provides…

We introduce and analyse a new nonparametric estimator of a multi-dimensional density. Our smooth projection estimator (SPE) is defined by a least squares projection of the sample onto an infinite dimensional mixture class via an…

In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse…

Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…

We introduce a nonlinear method for directly embedding large, sparse, stochastic graphs into low-dimensional spaces, without requiring vertex features to reside in, or be transformed into, a metric space. Graph data and models are prevalent…

Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex…

For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if $\rho=\lim\frac{p}{n}=0$, where $p$ is the dimension…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

Sufficient dimension reduction (SDR) is a popular tool in regression analysis, which replaces the original predictors with a minimal set of their linear combinations. However, the estimated linear combinations generally contain all original…

We prove, using the subspace embedding guarantee in a black box way, that one can achieve the spectral norm guarantee for approximate matrix multiplication with a dimensionality-reducing map having $m = O(\tilde{r}/\varepsilon^2)$ rows.…