65,426 research outputs found
An approximate dynamic programming approach to food security of communities following hazards
Food security can be threatened by extreme natural hazard events for
households of all social classes within a community. To address food security
issues following a natural disaster, the recovery of several elements of the
built environment within a community, including its building portfolio, must be
considered. Building portfolio restoration is one of the most challenging
elements of recovery owing to the complexity and dimensionality of the problem.
This study introduces a stochastic scheduling algorithm for the identification
of optimal building portfolio recovery strategies. The proposed approach
provides a computationally tractable formulation to manage multi-state,
large-scale infrastructure systems. A testbed community modeled after Gilroy,
California, is used to illustrate how the proposed approach can be implemented
efficiently and accurately to find the near-optimal decisions related to
building recovery following a severe earthquake.Comment: As opposed to the preemptive scheduling problem, which was addressed
in multiple works by us, we deal with a non-preemptive stochastic scheduling
problem in this work. Submitted to 13th International Conference on
Applications of Statistics and Probability in Civil Engineering, ICASP13
Seoul, South Korea, May 26-30, 201
Community Detection in Hypergraphs, Spiked Tensor Models, and Sum-of-Squares
We study the problem of community detection in hypergraphs under a stochastic
block model. Similarly to how the stochastic block model in graphs suggests
studying spiked random matrices, our model motivates investigating statistical
and computational limits of exact recovery in a certain spiked tensor model. In
contrast with the matrix case, the spiked model naturally arising from
community detection in hypergraphs is different from the one arising in the
so-called tensor Principal Component Analysis model. We investigate the
effectiveness of algorithms in the Sum-of-Squares hierarchy on these models.
Interestingly, our results suggest that these two apparently similar models
exhibit significantly different computational to statistical gaps.Comment: In proceedings of 2017 International Conference on Sampling Theory
and Applications (SampTA
Sparse recovery by reduced variance stochastic approximation
In this paper, we discuss application of iterative Stochastic Optimization
routines to the problem of sparse signal recovery from noisy observation. Using
Stochastic Mirror Descent algorithm as a building block, we develop a
multistage procedure for recovery of sparse solutions to Stochastic
Optimization problem under assumption of smoothness and quadratic minoration on
the expected objective. An interesting feature of the proposed algorithm is its
linear convergence of the approximate solution during the preliminary phase of
the routine when the component of stochastic error in the gradient observation
which is due to bad initial approximation of the optimal solution is larger
than the "ideal" asymptotic error component owing to observation noise "at the
optimal solution." We also show how one can straightforwardly enhance
reliability of the corresponding solution by using Median-of-Means like
techniques. We illustrate the performance of the proposed algorithms in
application to classical problems of recovery of sparse and low rank signals in
linear regression framework. We show, under rather weak assumption on the
regressor and noise distributions, how they lead to parameter estimates which
obey (up to factors which are logarithmic in problem dimension and confidence
level) the best known to us accuracy bounds
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