14,299 research outputs found
Money demand and relative prices during episodes of hyperinflation
Inflation (Finance) ; Money ; Prices
A Statistical Perspective on Algorithmic Leveraging
One popular method for dealing with large-scale data sets is sampling. For
example, by using the empirical statistical leverage scores as an importance
sampling distribution, the method of algorithmic leveraging samples and
rescales rows/columns of data matrices to reduce the data size before
performing computations on the subproblem. This method has been successful in
improving computational efficiency of algorithms for matrix problems such as
least-squares approximation, least absolute deviations approximation, and
low-rank matrix approximation. Existing work has focused on algorithmic issues
such as worst-case running times and numerical issues associated with providing
high-quality implementations, but none of it addresses statistical aspects of
this method.
In this paper, we provide a simple yet effective framework to evaluate the
statistical properties of algorithmic leveraging in the context of estimating
parameters in a linear regression model with a fixed number of predictors. We
show that from the statistical perspective of bias and variance, neither
leverage-based sampling nor uniform sampling dominates the other. This result
is particularly striking, given the well-known result that, from the
algorithmic perspective of worst-case analysis, leverage-based sampling
provides uniformly superior worst-case algorithmic results, when compared with
uniform sampling. Based on these theoretical results, we propose and analyze
two new leveraging algorithms. A detailed empirical evaluation of existing
leverage-based methods as well as these two new methods is carried out on both
synthetic and real data sets. The empirical results indicate that our theory is
a good predictor of practical performance of existing and new leverage-based
algorithms and that the new algorithms achieve improved performance.Comment: 44 pages, 17 figure
Current Dissipation in Thin Superconducting Wires: Accurate Numerical Evaluation Using the String Method
Current dissipation in thin superconducting wires is numerically evaluated by
using the string method, within the framework of time-dependent Ginzburg-Landau
equation with a Langevin noise term. The most probable transition pathway
between two neighboring current-carrying metastable states, continuously
linking the Langer-Ambegaokar saddle-point state to a state in which the order
parameter vanishes somewhere, is found numerically. We also give a numerically
accurate algorithm to evaluate the prefactors for the rate of current-reducing
transitions.Comment: 25 pages, 5 figure
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