51,491 research outputs found
Model Consistency of Partly Smooth Regularizers
This paper studies least-square regression penalized with partly smooth
convex regularizers. This class of functions is very large and versatile
allowing to promote solutions conforming to some notion of low-complexity.
Indeed, they force solutions of variational problems to belong to a
low-dimensional manifold (the so-called model) which is stable under small
perturbations of the function. This property is crucial to make the underlying
low-complexity model robust to small noise. We show that a generalized
"irrepresentable condition" implies stable model selection under small noise
perturbations in the observations and the design matrix, when the
regularization parameter is tuned proportionally to the noise level. This
condition is shown to be almost a necessary condition. We then show that this
condition implies model consistency of the regularized estimator. That is, with
a probability tending to one as the number of measurements increases, the
regularized estimator belongs to the correct low-dimensional model manifold.
This work unifies and generalizes several previous ones, where model
consistency is known to hold for sparse, group sparse, total variation and
low-rank regularizations
Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module
The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project
Joint Cooperative Spectrum Sensing and MAC Protocol Design for Multi-channel Cognitive Radio Networks
In this paper, we propose a semi-distributed cooperative spectrum sen sing
(SDCSS) and channel access framework for multi-channel cognitive radio networks
(CRNs). In particular, we c onsider a SDCSS scheme where secondary users (SUs)
perform sensing and exchange sensing outcomes with ea ch other to locate
spectrum holes. In addition, we devise the p -persistent CSMA-based cognitive
MAC protocol integrating the SDCSS to enable efficient spectrum sharing among
SUs. We then perform throughput analysis and develop an algorithm to determine
the spectrum sensing and access parameters to maximize the throughput for a
given allocation of channel sensing sets. Moreover, we consider the spectrum
sensing set optimization problem for SUs to maxim ize the overall system
throughput. We present both exhaustive search and low-complexity greedy
algorithms to determine the sensing sets for SUs and analyze their complexity.
We also show how our design and analysis can be extended to consider reporting
errors. Finally, extensive numerical results are presented to demonstrate the
sig nificant performance gain of our optimized design framework with respect to
non-optimized designs as well as the imp acts of different protocol parameters
on the throughput performance.Comment: accepted for publication EURASIP Journal on Wireless Communications
and Networking, 201
Continuous-time Proportional-Integral Distributed Optimization for Networked Systems
In this paper we explore the relationship between dual decomposition and the
consensus-based method for distributed optimization. The relationship is
developed by examining the similarities between the two approaches and their
relationship to gradient-based constrained optimization. By formulating each
algorithm in continuous-time, it is seen that both approaches use a gradient
method for optimization with one using a proportional control term and the
other using an integral control term to drive the system to the constraint set.
Therefore, a significant contribution of this paper is to combine these methods
to develop a continuous-time proportional-integral distributed optimization
method. Furthermore, we establish convergence using Lyapunov stability
techniques and utilizing properties from the network structure of the
multi-agent system.Comment: 23 Pages, submission to Journal of Control and Decision, under
review. Takes comments from previous review process into account. Reasons for
a continuous approach are given and minor technical details are remedied.
Largest revision is reformatting for the Journal of Control and Decisio
Swarm-Based Spatial Sorting
Purpose: To present an algorithm for spatially sorting objects into an
annular structure. Design/Methodology/Approach: A swarm-based model that
requires only stochastic agent behaviour coupled with a pheromone-inspired
"attraction-repulsion" mechanism. Findings: The algorithm consistently
generates high-quality annular structures, and is particularly powerful in
situations where the initial configuration of objects is similar to those
observed in nature. Research limitations/implications: Experimental evidence
supports previous theoretical arguments about the nature and mechanism of
spatial sorting by insects. Practical implications: The algorithm may find
applications in distributed robotics. Originality/value: The model offers a
powerful minimal algorithmic framework, and also sheds further light on the
nature of attraction-repulsion algorithms and underlying natural processes.Comment: Accepted by the Int. J. Intelligent Computing and Cybernetic
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