Related papers: Logarithmic barriers for sparse matrix cones
Modern large scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
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…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
Convergence is a crucial issue in iterative algorithms. Damping is commonly employed to ensure the convergence of iterative algorithms. The conventional ways of damping are scalar-wise, and either heuristic or empirical. Recently, an…
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…
Many matrices appearing in numerical methods for partial differential equations and integral equations are rank-structured, i.e., they contain submatrices that can be approximated by matrices of low rank. A relatively general class of…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
Techniques based on $k$-th order Hodge Laplacian operators $L_k$ are widely used to describe the topology as well as the governing dynamics of high-order systems modeled as simplicial complexes. In all of them, it is required to solve a…
Fast matrix multiplication algorithms may be useful, provided that their running time is good in practice. Particularly, the leading coefficient of their arithmetic complexity needs to be small. Many sub-cubic algorithms have large leading…
We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
In polynomial optimization problems, nonnegativity constraints are typically handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and…
For each $n \geq 1$ and sign pattern $\epsilon \in \{ \pm 1 \}^n$, we introduce a cone of real symmetric matrices $LPM_n(\epsilon)$: those with leading principal $k \times k$ minors of signs $\epsilon_k$. These cones are pairwise disjoint…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…
The log Gaussian Cox process is a flexible class of point pattern models for capturing spatial and spatio-temporal dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented through…