Related papers: Matrix-free construction of HSS representation usi…
We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…
This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise…
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…
The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often…
Let o be a 4k-length column vector whose all entries are 1s, with k a positive integer. Let V={v_i} be a set of semi-normalized Hadamard (SH)-vectors, which are 4k-length vectors whose 2k entries are -1s and the remaining 2k are 1s. We…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…
An algorithm for sampling from non-log-concave multivariate distributions is proposed, which improves the adaptive rejection Metropolis sampling (ARMS) algorithm by incorporating the hit and run sampling. It is not rare that the ARMS is…
The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections between fixed rank matrices and Hankel matrices to obtain such an approximation. Convergence,…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…
We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…
Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…
Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (2016; JMLR) based on randomized sketching matrices. However, it is computationally…
Classification in the dissimilarity space has become a very active research area since it provides a possibility to learn from data given in the form of pairwise non-metric dissimilarities, which otherwise would be difficult to cope with.…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
We describe an algorithm for sampling a low-rank random matrix $Q$ that best approximates a fixed target matrix $P\in\mathbb{C}^{n\times m}$ in the following sense: $Q$ is unbiased, i.e., $\mathbb{E}[Q] = P$; $\mathsf{rank}(Q)\leq r$; and…
We consider low-rank reconstruction of a matrix using its columns and we present asymptotically optimal algorithms for both spectral norm and Frobenius norm reconstruction. The main tools we introduce to obtain our r esults are: (i) the use…
Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an…
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…