相关论文: Sparse Fourier Transforms on Rank-1 Lattices for t…

Consider the model where we can access a parity function through random uniform labeled examples in the presence of random classification noise. In this paper, we show that approximating the number of relevant variables in the parity…

We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…

In metric of spaces $L_{s}, \ 1< s\leq\infty$, we obtain exact order estimates of best approximations and approximations by Fourier sums of classes of convolutions the periodic functions that belong to unit ball of space $L_{1}$, with…

This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…

Accurate reconstruction of piecewise-smooth functions from a finite number of Fourier coefficients is an important problem in various applications. The inherent inaccuracy, in particular the Gibbs phenomenon, is being intensively…

Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…

Given $n$ samples of a function $f\colon D\to\mathbb C$ in random points drawn with respect to a measure $\varrho_S$ we develop theoretical analysis of the $L_2(D, \varrho_T)$-approximation error. For a parituclar choice of $\varrho_S$…

Noisy $k$-XOR is a basic average-case inference problem in which one observes random noisy $k$-ary parity constraints and seeks to recover, or more weakly, detect, a hidden Boolean assignment. A central question is to characterize the…

We study distributed low rank approximation in which the matrix to be approximated is only implicitly represented across the different servers. For example, each of $s$ servers may have an $n \times d$ matrix $A^t$, and we may be interested…

Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…

We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…

We propose faster methods for unconstrained optimization of \emph{structured convex quartics}, which are convex functions of the form \begin{equation*} f(x) = c^\top x + x^\top \mathbf{G} x + \mathbf{T}[x,x,x] + \frac{1}{24} \mathopen\|…

We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice $\mathbb Z^d$ and on the torus $(\mathbb Z/n…

In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements. Crucially, the proposed random measurement ensembles are both designed to be…

Optimization problems with set submodular objective functions have many real-world applications. In discrete scenarios, where the same item can be selected more than once, the domain is generalized from a 2-element set to a bounded integer…

A variety of techniques have been developed for the approximation of non-periodic functions. In particular, there are approximation techniques based on rank-$1$ lattices and transformed rank-$1$ lattices, including methods that use sampling…

We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…

The FFT algorithm that implements the discrete Fourier transform is considered one of the top ten algorithms of the $20$th century. Its main strengths are the low computational cost of $\mathcal{O}(n \log n$) and its stability. It is one of…

Randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization,…

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…