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Sparse Bayesian Learning and the Relevance Vector Machine

by Michael E. Tipping , 2001
"... This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classification tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance vect ..."
Abstract - Cited by 966 (5 self) - Add to MetaCart
This paper introduces a general Bayesian framework for obtaining sparse solutions to regression and classification tasks utilising models linear in the parameters. Although this framework is fully general, we illustrate our approach with a particular specialisation that we denote the `relevance

Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging

by Michael Lustig, David Donoho, John M. Pauly - MAGNETIC RESONANCE IN MEDICINE 58:1182–1195 , 2007
"... The sparsity which is implicit in MR images is exploited to significantly undersample k-space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finit ..."
Abstract - Cited by 538 (11 self) - Add to MetaCart
finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressedsensing, images with a sparse representation can be recovered from randomly undersampled k-space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts

Optimally sparse representation in general (non-orthogonal) dictionaries via ℓ¹ minimization

by David L. Donoho, Michael Elad - PROC. NATL ACAD. SCI. USA 100 2197–202 , 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
Abstract - Cited by 633 (38 self) - Add to MetaCart
Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work

Estimation of probabilities from sparse data for the language model component of a speech recognizer

by Slava M. Katz - IEEE Transactions on Acoustics, Speech and Signal Processing , 1987
"... Abstract-The description of a novel type of rn-gram language model is given. The model offers, via a nonlinear recursive procedure, a com-putation and space efficient solution to the problem of estimating prob-abilities from sparse data. This solution compares favorably to other proposed methods. Wh ..."
Abstract - Cited by 799 (2 self) - Add to MetaCart
Abstract-The description of a novel type of rn-gram language model is given. The model offers, via a nonlinear recursive procedure, a com-putation and space efficient solution to the problem of estimating prob-abilities from sparse data. This solution compares favorably to other proposed methods

Efficient sparse coding algorithms

by Honglak Lee, Alexis Battle, Rajat Raina, Andrew Y. Ng - In NIPS , 2007
"... Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higher-level features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we ..."
Abstract - Cited by 445 (14 self) - Add to MetaCart
significant speedup for sparse coding, allowing us to learn larger sparse codes than possible with previously described algorithms. We apply these algorithms to natural images and demonstrate that the inferred sparse codes exhibit end-stopping and non-classical receptive field surround suppression and

Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise

by Joel A. Tropp , 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
Abstract - Cited by 483 (2 self) - Add to MetaCart
that has been contaminated with additive noise, the goal is to identify which elementary signals participated and to approximate their coefficients. Although many algorithms have been proposed, there is little theory which guarantees that these algorithms can accurately and efficiently solve the problem

Generalization in Reinforcement Learning: Successful Examples Using Sparse Coarse Coding

by Richard S. Sutton - Advances in Neural Information Processing Systems 8 , 1996
"... On large problems, reinforcement learning systems must use parameterized function approximators such as neural networks in order to generalize between similar situations and actions. In these cases there are no strong theoretical results on the accuracy of convergence, and computational results have ..."
Abstract - Cited by 433 (20 self) - Add to MetaCart
the control tasks they attempted, and for one that is significantly larger. The most important differences are that we used sparse-coarse-coded function approximators (CMACs) whereas they used mostly global function approximators, and that we learned online whereas they learned offline. Boyan and Moore

The "Independent Components" of Natural Scenes are Edge Filters

by Anthony J. Bell, Terrence J. Sejnowski , 1997
"... It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm that attem ..."
Abstract - Cited by 617 (29 self) - Add to MetaCart
It has previously been suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representation of natural scenes, and it has been reasoned that such responses should emerge from an unsupervised learning algorithm

Hierarchical mixtures of experts and the EM algorithm

by Michael I. Jordan, Robert A. Jacobs , 1993
"... We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM’s). Learning is treated as a max-imum likelihood ..."
Abstract - Cited by 885 (21 self) - Add to MetaCart
We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM’s). Learning is treated as a max-imum likelihood

Compressed sensing

by Yaakov Tsaig, David L. Donoho , 2004
"... We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal numbe ..."
Abstract - Cited by 3625 (22 self) - Add to MetaCart
norm. We perform a series of numerical experiments which validate in general terms the basic idea proposed in [14, 3, 5], in the favorable case where the transform coefficients are sparse in the strong sense that the vast majority are zero. We then consider a range of less-favorable cases, in which
Results 1 - 10 of 7,701