4,312 research outputs found
Numerical Analysis of the Non-uniform Sampling Problem
We give an overview of recent developments in the problem of reconstructing a
band-limited signal from non-uniform sampling from a numerical analysis view
point. It is shown that the appropriate design of the finite-dimensional model
plays a key role in the numerical solution of the non-uniform sampling problem.
In the one approach (often proposed in the literature) the finite-dimensional
model leads to an ill-posed problem even in very simple situations. The other
approach that we consider leads to a well-posed problem that preserves
important structural properties of the original infinite-dimensional problem
and gives rise to efficient numerical algorithms. Furthermore a fast multilevel
algorithm is presented that can reconstruct signals of unknown bandwidth from
noisy non-uniformly spaced samples. We also discuss the design of efficient
regularization methods for ill-conditioned reconstruction problems. Numerical
examples from spectroscopy and exploration geophysics demonstrate the
performance of the proposed methods
Non-Uniform Stochastic Average Gradient Method for Training Conditional Random Fields
We apply stochastic average gradient (SAG) algorithms for training
conditional random fields (CRFs). We describe a practical implementation that
uses structure in the CRF gradient to reduce the memory requirement of this
linearly-convergent stochastic gradient method, propose a non-uniform sampling
scheme that substantially improves practical performance, and analyze the rate
of convergence of the SAGA variant under non-uniform sampling. Our experimental
results reveal that our method often significantly outperforms existing methods
in terms of the training objective, and performs as well or better than
optimally-tuned stochastic gradient methods in terms of test error.Comment: AI/Stats 2015, 24 page
An early warning system for multivariate time series with sparse and non-uniform sampling
In this paper we propose a new early warning test statistic, the ratio of
deviations (RoD), which is defined to be the root mean squared of successive
differences divided by the standard deviation. We show that RoD and
autocorrelation are asymptotically related, and this relationship motivates the
use of RoD to predict Hopf bifurcations in multivariate systems before they
occur. We validate the use of RoD on synthetic data in the novel situation
where the data is sparse and non-uniformly sampled. Additionally, we adapt the
method to be used on high-frequency time series by sampling, and demonstrate
the proficiency of RoD as a classifier.Comment: 14 pages, 8 figure
Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling
Accelerated coordinate descent is widely used in optimization due to its
cheap per-iteration cost and scalability to large-scale problems. Up to a
primal-dual transformation, it is also the same as accelerated stochastic
gradient descent that is one of the central methods used in machine learning.
In this paper, we improve the best known running time of accelerated
coordinate descent by a factor up to . Our improvement is based on a
clean, novel non-uniform sampling that selects each coordinate with a
probability proportional to the square root of its smoothness parameter. Our
proof technique also deviates from the classical estimation sequence technique
used in prior work. Our speed-up applies to important problems such as
empirical risk minimization and solving linear systems, both in theory and in
practice.Comment: same result, but polished writin
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