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The forest matrix plays a crucial role in network science, opinion dynamics, and machine learning, offering deep insights into the structure of and dynamics on networks. In this paper, we study the problem of querying entries of the forest…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) for minimizing the…
The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…
Black-box variational inference (BBVI) scales poorly to high-dimensional problems when it is used to estimate a multivariate Gaussian approximation with a full covariance matrix. In this paper, we extend the batch-and-match (BaM) framework…
This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…
The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…
We prove that the permanent of nonnegative matrices can be deterministically approximated within a factor of $\sqrt{2}^n$ in polynomial time, improving upon the previous deterministic approximations. We show this by proving that the Bethe…
A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…
Consider a unit-intensity point process $\Pi$ on the vertex set $V$ of a transitive non-amenable unimodular graph. We study invariant matchings between $\Pi$ and $V$ having small typical matching distances. When $\Pi$ is either a Poisson…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between…