Related papers: Exponentially Improved Dimensionality Reduction fo…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…
We study the problem of reconstructing an unknown point in $\mathbb{R}^d$ from approximate linear queries. This setting arises naturally in applications ranging from low-dimensional remote sensing and signal recovery to high-dimensional…
This work focuses on dimension-reduction techniques for modelling conditional extreme values. Specifically, we investigate the idea that extreme values of a response variable can be explained by nonlinear functions derived from linear…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
We introduce estimation and test procedures through divergence minimiza- tion for models satisfying linear constraints with unknown parameter. These procedures extend the empirical likelihood (EL) method and share common features with…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
In this paper, we made an extension to the convergence analysis of the dynamics of two-layered bias-free networks with one $ReLU$ output. We took into consideration two popular regularization terms: the $\ell_1$ and $\ell_2$ norm of the…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
An oblivious subspace embedding (OSE), characterized by parameters $m,n,d,\epsilon,\delta$, is a random matrix $\Pi\in \mathbb{R}^{m\times n}$ such that for any $d$-dimensional subspace $T\subseteq \mathbb{R}^n$, $\Pr_\Pi[\forall x\in T,…
In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as…
We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer neural network with random iid inputs. We study the generalization performances of standard classifiers in the…
We consider a generalization of the classic linear regression problem to the case when the loss is an Orlicz norm. An Orlicz norm is parameterized by a non-negative convex function $G:\mathbb{R}_+\rightarrow\mathbb{R}_+$ with $G(0)=0$: the…
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…
The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…
In this paper we investigate the generalization error of gradient descent (GD) applied to an $\ell_2$-regularized OLS objective function in the linear model. Based on our analysis we develop new methodology for computationally tractable and…
Why does the low dimensionality of representations, typically $d\approx 1000$, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin…
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…
Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…
Consider the communication-constrained estimation of discrete distributions under $\ell^p$ losses, where each distributed terminal holds multiple independent samples and uses limited number of bits to describe the samples. We obtain the…