2,456 research outputs found
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
The Efficiency Loss of Capital Income Taxation under Imperfect Loss Offset Provisions
The importance of capital loss offset provisions in a world of risk is well documented in the tax literature. However, the potential deadweight losses owing to imperfect offset has not been fully explored. This paper develops a framework whereby that investigation can be carried out and utilizes numerical simulations to investigate the size of potential losses. Results show that when the government and private sector are equally efficient in handling market risk, welfare losses owing to the absence of offset provisions could be substantial. Under plausible assumptions about attitudes towards risk and time preference, and with a capital income tax rate of forty percent, over sixty cents per dollar of tax revenue raised would be dissipated. In contrast, full loss offset would reduce that loss to approximately fourteen cents.capital income taxation, uncertainty, deadweight loss, loss offset provisions
Super- and Anti-Principal Modes in Multi-Mode Waveguides
We introduce a new type of states for light in multimode waveguides featuring
strongly enhanced or reduced spectral correlations. Based on the experimentally
measured multi-spectral transmission matrix of a multimode fiber, we generate a
set of states that outperform the established "principal modes" in terms of the
spectral stability of their output spatial field profiles. Inverting this
concept also allows us to create states with a minimal spectral correlation
width, whose output profiles are considerably more sensitive to a frequency
change than typical input wavefronts. The resulting "super-" and
"anti-principal" modes are made orthogonal to each other even in the presence
of mode-dependent loss. By decomposing them in the principal mode basis, we
show that the super-principal modes are formed via interference of principal
modes with closeby delay times, whereas the anti-principal modes are a
superposition of principal modes with the most different delay times available
in the fiber. Such novel states are expected to have broad applications in
fiber communication, imaging, and spectroscopy.Comment: 8 pages, 5 figures, plus supplementary materia
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