188,863 research outputs found
A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data
In many semiparametric models that are parameterized by two types of
parameters---a Euclidean parameter of interest and an infinite-dimensional
nuisance parameter---the two parameters are bundled together, that is, the
nuisance parameter is an unknown function that contains the parameter of
interest as part of its argument. For example, in a linear regression model for
censored survival data, the unspecified error distribution function involves
the regression coefficients. Motivated by developing an efficient estimating
method for the regression parameters, we propose a general sieve M-theorem for
bundled parameters and apply the theorem to deriving the asymptotic theory for
the sieve maximum likelihood estimation in the linear regression model for
censored survival data. The numerical implementation of the proposed estimating
method can be achieved through the conventional gradient-based search
algorithms such as the Newton--Raphson algorithm. We show that the proposed
estimator is consistent and asymptotically normal and achieves the
semiparametric efficiency bound. Simulation studies demonstrate that the
proposed method performs well in practical settings and yields more efficient
estimates than existing estimating equation based methods. Illustration with a
real data example is also provided.Comment: Published in at http://dx.doi.org/10.1214/11-AOS934 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Distributed Parameter Estimation via Pseudo-likelihood
Estimating statistical models within sensor networks requires distributed
algorithms, in which both data and computation are distributed across the nodes
of the network. We propose a general approach for distributed learning based on
combining local estimators defined by pseudo-likelihood components,
encompassing a number of combination methods, and provide both theoretical and
experimental analysis. We show that simple linear combination or max-voting
methods, when combined with second-order information, are statistically
competitive with more advanced and costly joint optimization. Our algorithms
have many attractive properties including low communication and computational
cost and "any-time" behavior.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
Dynamic Graph Stream Algorithms in Space
In this paper we study graph problems in dynamic streaming model, where the
input is defined by a sequence of edge insertions and deletions. As many
natural problems require space, where is the number of
vertices, existing works mainly focused on designing space
algorithms. Although sublinear in the number of edges for dense graphs, it
could still be too large for many applications (e.g. is huge or the graph
is sparse). In this work, we give single-pass algorithms beating this space
barrier for two classes of problems.
We present space algorithms for estimating the number of connected
components with additive error and
-approximating the weight of minimum spanning tree, for any
small constant . The latter improves previous
space algorithm given by Ahn et al. (SODA 2012) for connected graphs with
bounded edge weights.
We initiate the study of approximate graph property testing in the dynamic
streaming model, where we want to distinguish graphs satisfying the property
from graphs that are -far from having the property. We consider
the problem of testing -edge connectivity, -vertex connectivity,
cycle-freeness and bipartiteness (of planar graphs), for which, we provide
algorithms using roughly space, which is
for any constant .
To complement our algorithms, we present space
lower bounds for these problems, which show that such a dependence on
is necessary.Comment: ICALP 201
Approximate Span Programs
Span programs are a model of computation that have been used to design
quantum algorithms, mainly in the query model. For any decision problem, there
exists a span program that leads to an algorithm with optimal quantum query
complexity, but finding such an algorithm is generally challenging.
We consider new ways of designing quantum algorithms using span programs. We
show how any span program that decides a problem can also be used to decide
"property testing" versions of , or more generally, approximate the span
program witness size, a property of the input related to . For example,
using our techniques, the span program for OR, which can be used to design an
optimal algorithm for the OR function, can also be used to design optimal
algorithms for: threshold functions, in which we want to decide if the Hamming
weight of a string is above a threshold or far below, given the promise that
one of these is true; and approximate counting, in which we want to estimate
the Hamming weight of the input. We achieve these results by relaxing the
requirement that 1-inputs hit some target exactly in the span program, which
could make design of span programs easier.
We also give an exposition of span program structure, which increases the
understanding of this important model. One implication is alternative
algorithms for estimating the witness size when the phase gap of a certain
unitary can be lower bounded. We show how to lower bound this phase gap in some
cases.
As applications, we give the first upper bounds in the adjacency query model
on the quantum time complexity of estimating the effective resistance between
and , , of , and, when is a lower
bound on , by our phase gap lower bound, we can obtain , both using space
A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters
Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM-UA algorithm is a modified version of the original SCE-UA global optimization algorithm developed by Duan et al. [1992]. The SCEM-UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM-UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis-Hastings samplers
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