3,280 research outputs found
Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices
We study minimax rates for denoising simultaneously sparse and low rank
matrices in high dimensions. We show that an iterative thresholding algorithm
achieves (near) optimal rates adaptively under mild conditions for a large
class of loss functions. Numerical experiments on synthetic datasets also
demonstrate the competitive performance of the proposed method
An MDL framework for sparse coding and dictionary learning
The power of sparse signal modeling with learned over-complete dictionaries
has been demonstrated in a variety of applications and fields, from signal
processing to statistical inference and machine learning. However, the
statistical properties of these models, such as under-fitting or over-fitting
given sets of data, are still not well characterized in the literature. As a
result, the success of sparse modeling depends on hand-tuning critical
parameters for each data and application. This work aims at addressing this by
providing a practical and objective characterization of sparse models by means
of the Minimum Description Length (MDL) principle -- a well established
information-theoretic approach to model selection in statistical inference. The
resulting framework derives a family of efficient sparse coding and dictionary
learning algorithms which, by virtue of the MDL principle, are completely
parameter free. Furthermore, such framework allows to incorporate additional
prior information to existing models, such as Markovian dependencies, or to
define completely new problem formulations, including in the matrix analysis
area, in a natural way. These virtues will be demonstrated with parameter-free
algorithms for the classic image denoising and classification problems, and for
low-rank matrix recovery in video applications
- …