Related papers: Spectral estimates for saddle point matrices arisi…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Data assimilation of atmospheric observations traditionally relies on variational and Kalman filter methods. Here, an alternative neural-network data assimilation (NNDA) with variational autoencoder (VAE) is proposed. The three-dimensional…
With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…
The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques combine physical models and observational data, often in a…
We present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
Singular Spectrum Analysis (SSA) occupies a prominent place in the real signal analysis toolkit alongside Fourier and Wavelet analysis. In addition to the two aforementioned analyses, SSA allows the separation of patterns directly from the…
A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…
Focusing on the well motivated aperture mass statistics $\Map$, we study the possibility of constraining cosmological parameters using future space based SNAP class weak lensing missions. Using completely analytical results we construct the…
Weak gravitational lensing on a cosmological scales can provide strong constraints both on the nature of dark matter and the dark energy equation of state. Most current weak lensing studies are restricted to (two-dimensional) projections,…
We study private matrix analysis in the sliding window model where only the last $W$ updates to matrices are considered useful for analysis. We give first efficient $o(W)$ space differentially private algorithms for spectral approximation,…
Here we present a multiscale method to calculate the saddle point associated with the effective dynamics arising from a stochastic system which couples slow deterministic drift and fast stochastic dynamics. This problem is motivated by the…
We perform a smoothed analysis of the componentwise condition numbers for determinant computation, matrix inversion, and linear equations solving for sparse n times n matrices. The bounds we obtain for the ex- pectations of the logarithm of…
We consider the problem of estimating common community structures in multi-layer stochastic block models, where each single layer may not have sufficient signal strength to recover the full community structure. In order to efficiently…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
Many observables in 4d $\mathcal N=4$ SYM with Gaiotto-Witten boundary conditions can be described exactly by matrix models via supersymmetric localization. The boundaries typically introduce new degrees of freedom, through a reduction of…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
For a general class of saddle point problems sharp estimates for Babu\v{s}ka's inf-sup stability constants are derived in terms of the constants in Brezzi's theory. In the finite-dimensional Hermitian case more detailed spectral properties…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
We study convex-concave saddle point problems with bilinear coupling, covering linearly constrained convex optimization and more general nonsmooth or constrained models via a proximable term in the dual objective. In linearly convergent…