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Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions
- ANNALS OF STATISTICS,40(2):1171
, 2013
"... We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an (approximately) low rank matrix � ⋆ with a second matrix Ɣ ⋆ endowed with a complementary for ..."
Abstract
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Cited by 61 (8 self)
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We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an (approximately) low rank matrix � ⋆ with a second matrix Ɣ ⋆ endowed with a complementary
A stochastic modeling methodology based on weighted Wiener chaos and Malliavin calculus,
- Proc. Natl. Acad. Sci. USA
, 2009
"... In many stochastic partial differential equations (SPDEs) involving random coefficients, modeling the randomness by spatial white noise may lead to ill-posed problems. Here we consider an elliptic problem with spatial Gaussian coefficients and present a methodology that resolves this issue. It is b ..."
Abstract
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Cited by 6 (2 self)
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. It is based on stochastic convolution implemented via generalized Malliavin operators in conjunction with weighted Wiener spaces that ensure the ellipticity condition. We present theoretical and numerical results that demonstrate the fast convergence of the method in the proper norm. Our approach is general
1Backing off from Infinity: Performance Bounds via Concentration of Spectral Measure for Random MIMO Channels
"... Abstract—The performance analysis of random vector chan-nels, particularly multiple-input-multiple-output (MIMO) chan-nels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of characterizing the exact distribution of the objectiv ..."
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outputs. Our results lead to simple, informative, and reasonably accurate control of various performance metrics in the finite-dimensional regime, as corroborated by the numerical simulations. Our analysis frame-work is established via the concentration of spectral measure phenomenon for random matrices
DOI: 10.1140/epjst/e2012-01529-y THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS Review Active Brownian Particles From Individual to Collective Stochastic Dynamics
, 2012
"... Abstract. We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of sta ..."
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Abstract. We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework
RICE UNIVERSITY Regime Change: Sampling Rate vs. Bit-Depth in Compressive Sensing
, 2011
"... The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated that structured signals can be acquired with just a small number of linear measurements, on the order of t ..."
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that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement
POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR
"... 2010 to my wife, Joyce, and my family...- Résumé- ..."
Active Mask Framework for Segmentation of Fluorescence Microscope Images
"... m]]l]]s¶D]]¿÷mB]iv]b]oD]m¶¨]iv]§]iv]r]j]t¿rv]]irj]]t]]m] / | ap]]r¿]ÎNy]s¶D]]mb¶r]ix} Û]Ix]]rd]mb]} p—N]t]o%ism] in]ty]m] / || Û]Is]¡uÎc]rN]]riv]nd]p]*N]m]st¶ I always bow to Śri ̄ Śāradāmbā, the limitless ocean of the nectar of compassion, who bears a rosary, a vessel of nectar, the symbol of ..."
Abstract
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facilitated the task of understanding complex sys-tems at cellular and molecular levels in recent years. Segmentation, an important yet dif-ficult problem, is often the first processing step following acquisition. Our team previously demonstrated that a stochastic active contour based algorithm together
Scenario Generation and Reduction for Long-term and Short-term Power System Generation Planning under Uncertainties
"... ii ..."
port Vector Machines, Kernel Fisher Discriminant analysis
"... Abstract | This review provides an introduction to Sup- ..."
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