Discussion: Latent variable graphical model selection via convex optimization

Nov 05, 2012

Martin J. Wainwright

Discussion of "Latent variable graphical model selection via convex optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
Nov 05, 2012

Martin J. Wainwright

* Annals of Statistics 2012, Vol. 40, No. 4, 1978-1983

* Published in at http://dx.doi.org/10.1214/12-AOS981 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Inconsistent parameter estimation in Markov random fields: Benefits in the computation-limited setting

Feb 27, 2006

Martin J. Wainwright

Feb 27, 2006

Martin J. Wainwright

* UC Berkeley, Department of Statistics; Technical Report 690

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Convergence guarantees for a class of non-convex and non-smooth optimization problems

Apr 25, 2018

Koulik Khamaru, Martin J. Wainwright

Apr 25, 2018

Koulik Khamaru, Martin J. Wainwright

* 50 pages, 2 figures

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Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees

Sep 10, 2015

Yudong Chen, Martin J. Wainwright

Sep 10, 2015

Yudong Chen, Martin J. Wainwright

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Newton Sketch: A Linear-time Optimization Algorithm with Linear-Quadratic Convergence

May 09, 2015

Mert Pilanci, Martin J. Wainwright

May 09, 2015

Mert Pilanci, Martin J. Wainwright

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Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squares

Nov 03, 2014

Mert Pilanci, Martin J. Wainwright

Nov 03, 2014

Mert Pilanci, Martin J. Wainwright

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Randomized Sketches of Convex Programs with Sharp Guarantees

Apr 29, 2014

Mert Pilanci, Martin J. Wainwright

Apr 29, 2014

Mert Pilanci, Martin J. Wainwright

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Sampled forms of functional PCA in reproducing kernel Hilbert spaces

Feb 13, 2013

Arash A. Amini, Martin J. Wainwright

We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map from $\mathcal{H}$ to $\mathbb{R}^m$, where the functional components to lie in some Hilbert subspace $\mathcal{H}$ of $L^2$, such as a reproducing kernel Hilbert space of smooth functions. This model includes time and frequency sampling as special cases. In contrast to classical approach in fPCA in which access to entire functions is assumed, having a limited number m of functional samples places limitations on the performance of statistical procedures. We study these effects by analyzing the rate of convergence of an M-estimator for the subspace spanned by the leading components in a multi-spiked covariance model. The estimator takes the form of regularized PCA, and hence is computationally attractive. We analyze the behavior of this estimator within a nonasymptotic framework, and provide bounds that hold with high probability as a function of the number of statistical samples n and the number of functional samples m. We also derive lower bounds showing that the rates obtained are minimax optimal.
Feb 13, 2013

Arash A. Amini, Martin J. Wainwright

* Annals of Statistics 2012, Vol. 40, No. 5, 2483-2510

* Published in at http://dx.doi.org/10.1214/12-AOS1033 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Belief Propagation for Continuous State Spaces: Stochastic Message-Passing with Quantitative Guarantees

Dec 16, 2012

Nima Noorshams, Martin J. Wainwright

Dec 16, 2012

Nima Noorshams, Martin J. Wainwright

* Portions of the results were presented at the International Symposium on Information Theory 2012. The results were also submitted to the Journal of Machine Learning Research on December 16th 2012

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Stochastic Belief Propagation: A Low-Complexity Alternative to the Sum-Product Algorithm

May 25, 2012

Nima Noorshams, Martin J. Wainwright

May 25, 2012

Nima Noorshams, Martin J. Wainwright

* Portions of the results were initially reported at the Allerton Conference on Communications, Control, and Computing (September 2011). The work was also submitted to IEEE Transaction on Information Theory in November 2011

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Approximation properties of certain operator-induced norms on Hilbert spaces

May 31, 2011

Arash A. Amini, Martin J. Wainwright

We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproducing kernel Hilbert spaces (RKHS). Our results have implications to the analysis of M-estimators in models based on finite-dimensional linear approximation of functions, and also to some related packing problems.
May 31, 2011

Arash A. Amini, Martin J. Wainwright

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Information-theoretic limits of selecting binary graphical models in high dimensions

May 16, 2009

Narayana Santhanam, Martin J. Wainwright

May 16, 2009

Narayana Santhanam, Martin J. Wainwright

* 27 pages

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High-dimensional subset recovery in noise: Sparsified measurements without loss of statistical efficiency

May 20, 2008

Dapo Omidiran, Martin J. Wainwright

May 20, 2008

Dapo Omidiran, Martin J. Wainwright

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Lossy source encoding via message-passing and decimation over generalized codewords of LDGM codes

Aug 15, 2005

Martin J. Wainwright, Elitza Maneva

Aug 15, 2005

Martin J. Wainwright, Elitza Maneva

* To appear in the Proceedings of the International Symposium on Information Theory, Adelaide, Australia; September, 2005

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Simple, Robust and Optimal Ranking from Pairwise Comparisons

Apr 27, 2016

Nihar B. Shah, Martin J. Wainwright

Apr 27, 2016

Nihar B. Shah, Martin J. Wainwright

* Changes in version 2: In addition to recovery in the exact and Hamming metrics, v2 analyzes a general, abstract recovery criterion based on a notion of "allowed sets"

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Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima

Jan 01, 2015

Po-Ling Loh, Martin J. Wainwright

Jan 01, 2015

Po-Ling Loh, Martin J. Wainwright

* 58 pages, 13 figures. To appear in JMLR

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Support recovery without incoherence: A case for nonconvex regularization

Dec 17, 2014

Po-Ling Loh, Martin J. Wainwright

Dec 17, 2014

Po-Ling Loh, Martin J. Wainwright

* 51 pages, 13 figures

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Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses

Jan 06, 2014

Po-Ling Loh, Martin J. Wainwright

We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an open question about the significance of the inverse covariance matrix of a non-Gaussian distribution. The proof exploits a combination of ideas from the geometry of exponential families, junction tree theory and convex analysis. These population-level results have various consequences for graph selection methods, both known and novel, including a novel method for structure estimation for missing or corrupted observations. We provide nonasymptotic guarantees for such methods and illustrate the sharpness of these predictions via simulations.
Jan 06, 2014

Po-Ling Loh, Martin J. Wainwright

* Annals of Statistics 2013, Vol. 41, No. 6, 3022-3049

* Published in at http://dx.doi.org/10.1214/13-AOS1162 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity

Sep 25, 2012

Po-Ling Loh, Martin J. Wainwright

Sep 25, 2012

Po-Ling Loh, Martin J. Wainwright

* Annals of Statistics 2012, Vol. 40, No. 3, 1637-1664

* Published in at http://dx.doi.org/10.1214/12-AOS1018 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Towards Optimal Estimation of Bivariate Isotonic Matrices with Unknown Permutations

Jun 25, 2018

Cheng Mao, Ashwin Pananjady, Martin J. Wainwright

Jun 25, 2018

Cheng Mao, Ashwin Pananjady, Martin J. Wainwright

* 46 pages, 1 figure. This paper is a longer version of the paper arXiv:1802.09963, v3 of which appeared in part as a 4-page extended abstract at Conference on Learning Theory (COLT) 2018. This paper studies the problem in another metric, and makes the appropriate corrections to Theorem 2 in v1 and v2 of arXiv:1802.09963, which was incorrect as stated and removed in v3

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