Condition numbers of random matrices
Journal of Complexity
On Model Selection Consistency of Lasso
The Journal of Machine Learning Research
On the Consistency of Feature Selection using Greedy Least Squares Regression
The Journal of Machine Learning Research
IEEE Transactions on Information Theory
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Efficient agnostic learning of neural networks with bounded fan-in
IEEE Transactions on Information Theory - Part 2
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise
IEEE Transactions on Information Theory
Orthogonal Matching Pursuit: A Brownian Motion Analysis
IEEE Transactions on Signal Processing
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The performance of orthogonal matching pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the design matrix, one can have far less stringent sparsity constraints on the coefficient vector. We demonstrate that for exact sparse vectors, the performance of the OMP is similar to known results on the Lasso algorithm (Wainwright, 2009). Moreover, variable selection under a more relaxed sparsity assumption on the coefficient vector, whereby one has only control on the l1 norm of the smaller coefficients, is also analyzed. As consequence of these results, we also show that the coefficient estimate satisfies strong oracle type inequalities.