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Nonlinear Estimators and Tail Bounds for Dimension Reduction in l1 Using Cauchy Random Projections
dimension reduction l1 norm Johnson-Lindenstrauss (JL) lemma Cauchy random projections
2015/8/21
For1 dimension reduction in the l1 norm, the method of Cauchy random projections multiplies the original data matrix A ∈ Rn×D with a random matrix R ∈ RD×k (k D) whose entries are i.i.d. samples of ...
Adaptive Sensing Performance Lower Bounds for Sparse Signal Estimation and Testing
adaptive sensing minimax lower bounds sequential experimental design sparsity-based models
2012/6/19
This paper gives a precise characterization of the fundamental limits of adaptive sensing for diverse estimation and testing problems concerning sparse signals. We consider in particular the setting i...
New bounds on the maximum ionization of atoms
maximum ionization Pauli operator magnetic field relativistic atoms
2010/12/6
We prove that the maximum number Nc of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z1/3. This improves Lieb’s upper bound Nc < 2Z + 1 [Phys. Rev. A 29, 3018-30...
Pac-bayesian bounds for sparse regression estimation with exponential weights
Sparsity Oracle Inequality High-dimensional Regression
2010/12/6
We consider the sparse regression model where the number of parameters p is larger than the sample size n. The difficulty when considering high-dimensional problems is to propose estimators achieving ...
Performance Bounds and Design Criteria for Estimating Finite Rate of Innovation Signals
Terms—Finite rate of innovation Sampling
2010/12/3
In this paper, we consider the problem of estimating finite rate of innovation (FRI) signals from noisy measurements,and specifically analyze the interaction between FRI techniques
and the underlying...