11,866 research outputs found
Reed-solomon forward error correction (FEC) schemes, RFC 5510
This document describes a Fully-Specified Forward Error Correction (FEC) Scheme for the Reed-Solomon FEC codes over GF(2^^m), where m is in {2..16}, and its application to the reliable delivery of data objects on the packet erasure channel (i.e., a communication path where packets are either received without any corruption or discarded during transmission). This document also describes a Fully-Specified FEC Scheme for the special case of Reed-Solomon codes over GF(2^^8) when there is no encoding symbol group. Finally, in the context of the Under-Specified Small Block Systematic FEC Scheme (FEC Encoding ID 129), this document assigns an FEC Instance ID to the special case of Reed-Solomon codes over GF(2^^8).
Reed-Solomon codes belong to the class of Maximum Distance Separable (MDS) codes, i.e., they enable a receiver to recover the k source symbols from any set of k received symbols. The schemes described here are compatible with the implementation from Luigi Rizzo
Bayesian Dropout
Dropout has recently emerged as a powerful and simple method for training
neural networks preventing co-adaptation by stochastically omitting neurons.
Dropout is currently not grounded in explicit modelling assumptions which so
far has precluded its adoption in Bayesian modelling. Using Bayesian entropic
reasoning we show that dropout can be interpreted as optimal inference under
constraints. We demonstrate this on an analytically tractable regression model
providing a Bayesian interpretation of its mechanism for regularizing and
preventing co-adaptation as well as its connection to other Bayesian
techniques. We also discuss two general approximate techniques for applying
Bayesian dropout for general models, one based on an analytical approximation
and the other on stochastic variational techniques. These techniques are then
applied to a Baysian logistic regression problem and are shown to improve
performance as the model become more misspecified. Our framework roots dropout
as a theoretically justified and practical tool for statistical modelling
allowing Bayesians to tap into the benefits of dropout training.Comment: 21 pages, 3 figures. Manuscript prepared 2014 and awaiting submissio
Sparse Subspace Clustering: Algorithm, Theory, and Applications
In many real-world problems, we are dealing with collections of
high-dimensional data, such as images, videos, text and web documents, DNA
microarray data, and more. Often, high-dimensional data lie close to
low-dimensional structures corresponding to several classes or categories the
data belongs to. In this paper, we propose and study an algorithm, called
Sparse Subspace Clustering (SSC), to cluster data points that lie in a union of
low-dimensional subspaces. The key idea is that, among infinitely many possible
representations of a data point in terms of other points, a sparse
representation corresponds to selecting a few points from the same subspace.
This motivates solving a sparse optimization program whose solution is used in
a spectral clustering framework to infer the clustering of data into subspaces.
Since solving the sparse optimization program is in general NP-hard, we
consider a convex relaxation and show that, under appropriate conditions on the
arrangement of subspaces and the distribution of data, the proposed
minimization program succeeds in recovering the desired sparse representations.
The proposed algorithm can be solved efficiently and can handle data points
near the intersections of subspaces. Another key advantage of the proposed
algorithm with respect to the state of the art is that it can deal with data
nuisances, such as noise, sparse outlying entries, and missing entries,
directly by incorporating the model of the data into the sparse optimization
program. We demonstrate the effectiveness of the proposed algorithm through
experiments on synthetic data as well as the two real-world problems of motion
segmentation and face clustering
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