93,320 research outputs found
Parallel sparse interpolation using small primes
To interpolate a supersparse polynomial with integer coefficients, two
alternative approaches are the Prony-based "big prime" technique, which acts
over a single large finite field, or the more recently-proposed "small primes"
technique, which reduces the unknown sparse polynomial to many low-degree dense
polynomials. While the latter technique has not yet reached the same
theoretical efficiency as Prony-based methods, it has an obvious potential for
parallelization. We present a heuristic "small primes" interpolation algorithm
and report on a low-level C implementation using FLINT and MPI.Comment: Accepted to PASCO 201
Subsquares Approach - Simple Scheme for Solving Overdetermined Interval Linear Systems
In this work we present a new simple but efficient scheme - Subsquares
approach - for development of algorithms for enclosing the solution set of
overdetermined interval linear systems. We are going to show two algorithms
based on this scheme and discuss their features. We start with a simple
algorithm as a motivation, then we continue with a sequential algorithm. Both
algorithms can be easily parallelized. The features of both algorithms will be
discussed and numerically tested.Comment: submitted to PPAM 201
Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach
In this work, we propose a new policy iteration algorithm for pricing
Bermudan options when the payoff process cannot be written as a function of a
lifted Markov process. Our approach is based on a modification of the
well-known Longstaff Schwartz algorithm, in which we basically replace the
standard least square regression by a Wiener chaos expansion. Not only does it
allow us to deal with a non Markovian setting, but it also breaks the
bottleneck induced by the least square regression as the coefficients of the
chaos expansion are given by scalar products on the L^2 space and can therefore
be approximated by independent Monte Carlo computations. This key feature
enables us to provide an embarrassingly parallel algorithm.Comment: The Journal of Computational Finance, Incisive Media, In pres
A randomised primal-dual algorithm for distributed radio-interferometric imaging
Next generation radio telescopes, like the Square Kilometre Array, will
acquire an unprecedented amount of data for radio astronomy. The development of
fast, parallelisable or distributed algorithms for handling such large-scale
data sets is of prime importance. Motivated by this, we investigate herein a
convex optimisation algorithmic structure, based on primal-dual
forward-backward iterations, for solving the radio interferometric imaging
problem. It can encompass any convex prior of interest. It allows for the
distributed processing of the measured data and introduces further flexibility
by employing a probabilistic approach for the selection of the data blocks used
at a given iteration. We study the reconstruction performance with respect to
the data distribution and we propose the use of nonuniform probabilities for
the randomised updates. Our simulations show the feasibility of the
randomisation given a limited computing infrastructure as well as important
computational advantages when compared to state-of-the-art algorithmic
structures.Comment: 5 pages, 3 figures, Proceedings of the European Signal Processing
Conference (EUSIPCO) 2016, Related journal publication available at
https://arxiv.org/abs/1601.0402
Local-Aggregate Modeling for Big-Data via Distributed Optimization: Applications to Neuroimaging
Technological advances have led to a proliferation of structured big data
that have matrix-valued covariates. We are specifically motivated to build
predictive models for multi-subject neuroimaging data based on each subject's
brain imaging scans. This is an ultra-high-dimensional problem that consists of
a matrix of covariates (brain locations by time points) for each subject; few
methods currently exist to fit supervised models directly to this tensor data.
We propose a novel modeling and algorithmic strategy to apply generalized
linear models (GLMs) to this massive tensor data in which one set of variables
is associated with locations. Our method begins by fitting GLMs to each
location separately, and then builds an ensemble by blending information across
locations through regularization with what we term an aggregating penalty. Our
so called, Local-Aggregate Model, can be fit in a completely distributed manner
over the locations using an Alternating Direction Method of Multipliers (ADMM)
strategy, and thus greatly reduces the computational burden. Furthermore, we
propose to select the appropriate model through a novel sequence of faster
algorithmic solutions that is similar to regularization paths. We will
demonstrate both the computational and predictive modeling advantages of our
methods via simulations and an EEG classification problem.Comment: 41 pages, 5 figures and 3 table
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