相关论文: Another view of the Gaussian algorithm

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…

For quantum spin models defined on a two-dimensional lattice, we look for the best numbering of the lattice sites (a layout) that, at fixed bond dimension and other parameters of the density matrix renormalization group (DMRG) algorithm,…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…

We consider gradient-related methods for low-rank matrix optimization with a smooth cost function. The methods operate on single factors of the low-rank factorization and share aspects of both alternating and Riemannian optimization. Two…

Efficiently solving sparse linear systems $Ax=b$, where $A$ is a large, sparse, symmetric positive semi-definite matrix, is a core challenge in scientific computing, machine learning, and optimization. A major bottleneck in Gaussian…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…

We give a novel algorithm for enumerating lattice points in any convex body, and give applications to several classic lattice problems, including the Shortest and Closest Vector Problems (SVP and CVP, respectively) and Integer Programming…

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…

Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…

With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. In this paper, we focus on quasi-submodularity, a universal generalization, which…

We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…

The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially…

The Shortest Lattice Vector (SLV) problem is in general hard to solve, except for special cases (such as root lattices and lattices for which an obtuse superbase is known). In this paper, we present a new class of SLV problems that can be…

We give a randomized $2^{n+o(n)}$-time and space algorithm for solving the Shortest Vector Problem (SVP) on n-dimensional Euclidean lattices. This improves on the previous fastest algorithm: the deterministic $\widetilde{O}(4^n)$-time and…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…