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- Emmanuel J. Candès, Benjamin Recht
- Commun. ACM
- 2009

Suppose that one observes an incomplete subset of entries selected from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We demonstrate that in very general settings, one can perfectly recover all of the missing entries from most sufficiently large subsets by solving a convex programming problem… (More)

- Ali Rahimi, Benjamin Recht
- NIPS
- 2007

To accelerate the training of kernel machines, we propose to map the input data to a randomized low-dimensional feature space and then apply existing fast linear methods. The features are designed so that the inner products of the transformed data are approximately equal to those in the feature space of a user specified shift-invariant kernel. We explore… (More)

- Benjamin Recht, Maryam Fazel, Pablo A. Parrilo
- SIAM Review
- 2010

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved… (More)

- Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo, Alan S. Willsky
- Foundations of Computational Mathematics
- 2012

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees of… (More)

- Benjamin Recht, Christopher Ré, Stephen J. Wright, Feng Niu
- NIPS
- 2011

Stochastic Gradient Descent (SGD) is a popular algorithm that can achieve state-of-the-art performance on a variety of machine learning tasks. Several researchers have recently proposed schemes to parallelize SGD, but all require performance-destroying memory locking and synchronization. This work aims to show using novel theoretical analysis, algorithms,… (More)

- Gongguo Tang, Badri Narayan Bhaskar, Parikshit Shah, Benjamin Recht
- IEEE Transactions on Information Theory
- 2013

This paper investigates the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a grid, but can assume any values in the normalized frequency domain [0, 1]. An atomic norm minimization… (More)

- Benjamin Recht
- Journal of Machine Learning Research
- 2011

This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candès and Recht [3], Candès and Tao [6], and Keshavan, Montanari, and Oh [13]. The reconstruction is accomplished by minimizing the nuclear norm, or sum of the singular values, of… (More)

- Ali Ahmed, Benjamin Recht, Justin K. Romberg
- IEEE Transactions on Information Theory
- 2014

We consider the problem of recovering two unknown vectors, w and x, of length L from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with dimension N and the other with dimension K. Although the observed convolution is nonlinear in both w and x, it is linear in the rank-1 matrix formed… (More)

In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In the important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the… (More)

- Badri Narayan Bhaskar, Benjamin Recht
- IEEE Transactions on Signal Processing
- 2011

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to… (More)