5,090 research outputs found
Feature detection using spikes: the greedy approach
A goal of low-level neural processes is to build an efficient code extracting
the relevant information from the sensory input. It is believed that this is
implemented in cortical areas by elementary inferential computations
dynamically extracting the most likely parameters corresponding to the sensory
signal. We explore here a neuro-mimetic feed-forward model of the primary
visual area (VI) solving this problem in the case where the signal may be
described by a robust linear generative model. This model uses an over-complete
dictionary of primitives which provides a distributed probabilistic
representation of input features. Relying on an efficiency criterion, we derive
an algorithm as an approximate solution which uses incremental greedy inference
processes. This algorithm is similar to 'Matching Pursuit' and mimics the
parallel architecture of neural computations. We propose here a simple
implementation using a network of spiking integrate-and-fire neurons which
communicate using lateral interactions. Numerical simulations show that this
Sparse Spike Coding strategy provides an efficient model for representing
visual data from a set of natural images. Even though it is simplistic, this
transformation of spatial data into a spatio-temporal pattern of binary events
provides an accurate description of some complex neural patterns observed in
the spiking activity of biological neural networks.Comment: This work links Matching Pursuit with bayesian inference by providing
the underlying hypotheses (linear model, uniform prior, gaussian noise
model). A parallel with the parallel and event-based nature of neural
computations is explored and we show application to modelling Primary Visual
Cortex / image processsing.
http://incm.cnrs-mrs.fr/perrinet/dynn/LaurentPerrinet/Publications/Perrinet04tau
Support Recovery of Sparse Signals
We consider the problem of exact support recovery of sparse signals via noisy
measurements. The main focus is the sufficient and necessary conditions on the
number of measurements for support recovery to be reliable. By drawing an
analogy between the problem of support recovery and the problem of channel
coding over the Gaussian multiple access channel, and exploiting mathematical
tools developed for the latter problem, we obtain an information theoretic
framework for analyzing the performance limits of support recovery. Sharp
sufficient and necessary conditions on the number of measurements in terms of
the signal sparsity level and the measurement noise level are derived.
Specifically, when the number of nonzero entries is held fixed, the exact
asymptotics on the number of measurements for support recovery is developed.
When the number of nonzero entries increases in certain manners, we obtain
sufficient conditions tighter than existing results. In addition, we show that
the proposed methodology can deal with a variety of models of sparse signal
recovery, hence demonstrating its potential as an effective analytical tool.Comment: 33 page
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
Orthogonal Matching Pursuit: A Brownian Motion Analysis
A well-known analysis of Tropp and Gilbert shows that orthogonal matching
pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n)
noise-free linear measurements obtained through a random Gaussian measurement
matrix with a probability that approaches one as n approaches infinity. This
work strengthens this result by showing that a lower number of measurements, 2
k log(n - k), is in fact sufficient for asymptotic recovery. More generally,
when the sparsity level satisfies kmin <= k <= kmax but is unknown, 2 kmax
log(n - kmin) measurements is sufficient. Furthermore, this number of
measurements is also sufficient for detection of the sparsity pattern (support)
of the vector with measurement errors provided the signal-to-noise ratio (SNR)
scales to infinity. The scaling 2 k log(n - k) exactly matches the number of
measurements required by the more complex lasso method for signal recovery with
a similar SNR scaling.Comment: 11 pages, 2 figure
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