1,535 research outputs found
A Tight Bound on the Performance of a Minimal-Delay Joint Source-Channel Coding Scheme
An analog source is to be transmitted across a Gaussian channel in more than
one channel use per source symbol. This paper derives a lower bound on the
asymptotic mean squared error for a strategy that consists of repeatedly
quantizing the source, transmitting the quantizer outputs in the first channel
uses, and sending the remaining quantization error uncoded in the last channel
use. The bound coincides with the performance achieved by a suboptimal decoder
studied by the authors in a previous paper, thereby establishing that the bound
is tight.Comment: 5 pages, submitted to IEEE International Symposium on Information
Theory (ISIT) 201
How long does it take to generate a group?
The diameter of a finite group with respect to a generating set is
the smallest non-negative integer such that every element of can be
written as a product of at most elements of . We denote this
invariant by \diam_A(G). It can be interpreted as the diameter of the Cayley
graph induced by on and arises, for instance, in the context of
efficient communication networks.
In this paper we study the diameters of a finite abelian group with
respect to its various generating sets . We determine the maximum possible
value of \diam_A(G) and classify all generating sets for which this maximum
value is attained. Also, we determine the maximum possible cardinality of
subject to the condition that \diam_A(G) is "not too small". Connections with
caps, sum-free sets, and quasi-perfect codes are discussed
Local stability and robustness of sparse dictionary learning in the presence of noise
A popular approach within the signal processing and machine learning
communities consists in modelling signals as sparse linear combinations of
atoms selected from a learned dictionary. While this paradigm has led to
numerous empirical successes in various fields ranging from image to audio
processing, there have only been a few theoretical arguments supporting these
evidences. In particular, sparse coding, or sparse dictionary learning, relies
on a non-convex procedure whose local minima have not been fully analyzed yet.
In this paper, we consider a probabilistic model of sparse signals, and show
that, with high probability, sparse coding admits a local minimum around the
reference dictionary generating the signals. Our study takes into account the
case of over-complete dictionaries and noisy signals, thus extending previous
work limited to noiseless settings and/or under-complete dictionaries. The
analysis we conduct is non-asymptotic and makes it possible to understand how
the key quantities of the problem, such as the coherence or the level of noise,
can scale with respect to the dimension of the signals, the number of atoms,
the sparsity and the number of observations
Cognitive scale-free networks as a model for intermittency in human natural language
We model certain features of human language complexity by means of advanced
concepts borrowed from statistical mechanics. Using a time series approach, the
diffusion entropy method (DE), we compute the complexity of an Italian corpus
of newspapers and magazines. We find that the anomalous scaling index is
compatible with a simple dynamical model, a random walk on a complex scale-free
network, which is linguistically related to Saussurre's paradigms. The model
yields the famous Zipf's law in terms of the generalized central limit theorem.Comment: Conference FRACTAL 200
Sample Complexity of Dictionary Learning and other Matrix Factorizations
Many modern tools in machine learning and signal processing, such as sparse
dictionary learning, principal component analysis (PCA), non-negative matrix
factorization (NMF), -means clustering, etc., rely on the factorization of a
matrix obtained by concatenating high-dimensional vectors from a training
collection. While the idealized task would be to optimize the expected quality
of the factors over the underlying distribution of training vectors, it is
achieved in practice by minimizing an empirical average over the considered
collection. The focus of this paper is to provide sample complexity estimates
to uniformly control how much the empirical average deviates from the expected
cost function. Standard arguments imply that the performance of the empirical
predictor also exhibit such guarantees. The level of genericity of the approach
encompasses several possible constraints on the factors (tensor product
structure, shift-invariance, sparsity \ldots), thus providing a unified
perspective on the sample complexity of several widely used matrix
factorization schemes. The derived generalization bounds behave proportional to
w.r.t.\ the number of samples for the considered matrix
factorization techniques.Comment: to appea
- âŠ