4,292 research outputs found
Computational Complexity versus Statistical Performance on Sparse Recovery Problems
We show that several classical quantities controlling compressed sensing
performance directly match classical parameters controlling algorithmic
complexity. We first describe linearly convergent restart schemes on
first-order methods solving a broad range of compressed sensing problems, where
sharpness at the optimum controls convergence speed. We show that for sparse
recovery problems, this sharpness can be written as a condition number, given
by the ratio between true signal sparsity and the largest signal size that can
be recovered by the observation matrix. In a similar vein, Renegar's condition
number is a data-driven complexity measure for convex programs, generalizing
classical condition numbers for linear systems. We show that for a broad class
of compressed sensing problems, the worst case value of this algorithmic
complexity measure taken over all signals matches the restricted singular value
of the observation matrix which controls robust recovery performance. Overall,
this means in both cases that, in compressed sensing problems, a single
parameter directly controls both computational complexity and recovery
performance. Numerical experiments illustrate these points using several
classical algorithms.Comment: Final version, to appear in information and Inferenc
The D1-triangulation in simplicial variable dimension algorithms for computing solutions of nonlinear equations
Nonlinear Equations
Progressive Analytics: A Computation Paradigm for Exploratory Data Analysis
Exploring data requires a fast feedback loop from the analyst to the system,
with a latency below about 10 seconds because of human cognitive limitations.
When data becomes large or analysis becomes complex, sequential computations
can no longer be completed in a few seconds and data exploration is severely
hampered. This article describes a novel computation paradigm called
Progressive Computation for Data Analysis or more concisely Progressive
Analytics, that brings at the programming language level a low-latency
guarantee by performing computations in a progressive fashion. Moving this
progressive computation at the language level relieves the programmer of
exploratory data analysis systems from implementing the whole analytics
pipeline in a progressive way from scratch, streamlining the implementation of
scalable exploratory data analysis systems. This article describes the new
paradigm through a prototype implementation called ProgressiVis, and explains
the requirements it implies through examples.Comment: 10 page
On the performance of a hybrid genetic algorithm in dynamic environments
The ability to track the optimum of dynamic environments is important in many
practical applications. In this paper, the capability of a hybrid genetic
algorithm (HGA) to track the optimum in some dynamic environments is
investigated for different functional dimensions, update frequencies, and
displacement strengths in different types of dynamic environments. Experimental
results are reported by using the HGA and some other existing evolutionary
algorithms in the literature. The results show that the HGA has better
capability to track the dynamic optimum than some other existing algorithms.Comment: This paper has been submitted to Applied Mathematics and Computation
on May 22, 2012 Revised version has been submitted to Applied Mathematics and
Computation on March 1, 201
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