80,552 research outputs found
The optimal polarizations for achieving maximum contrast in radar images
There is considerable interest in determining the optimal polarizations that maximize contrast between two scattering classes in polarimetric radar images. A systematic approach is presented for obtaining the optimal polarimetric matched filter, i.e., that filter which produces maximum contrast between two scattering classes. The maximization procedure involves solving an eigenvalue problem where the eigenvector corresponding to the maximum contrast ratio is an optimal polarimetric matched filter. To exhibit the physical significance of this filter, it is transformed into its associated transmitting and receiving polarization states, written in terms of horizontal and vertical vector components. For the special case where the transmitting polarization is fixed, the receiving polarization which maximizes the contrast ratio is also obtained. Polarimetric filtering is then applies to synthetic aperture radar images obtained from the Jet Propulsion Laboratory. It is shown, both numerically and through the use of radar imagery, that maximum image contrast can be realized when data is processed with the optimal polarimeter matched filter
Worst-case Optimal Submodular Extensions for Marginal Estimation
Submodular extensions of an energy function can be used to efficiently
compute approximate marginals via variational inference. The accuracy of the
marginals depends crucially on the quality of the submodular extension. To
identify the best possible extension, we show an equivalence between the
submodular extensions of the energy and the objective functions of linear
programming (LP) relaxations for the corresponding MAP estimation problem. This
allows us to (i) establish the worst-case optimality of the submodular
extension for Potts model used in the literature; (ii) identify the worst-case
optimal submodular extension for the more general class of metric labeling; and
(iii) efficiently compute the marginals for the widely used dense CRF model
with the help of a recently proposed Gaussian filtering method. Using synthetic
and real data, we show that our approach provides comparable upper bounds on
the log-partition function to those obtained using tree-reweighted message
passing (TRW) in cases where the latter is computationally feasible.
Importantly, unlike TRW, our approach provides the first practical algorithm to
compute an upper bound on the dense CRF model.Comment: Accepted to AISTATS 201
Bayesian emulation for optimization in multi-step portfolio decisions
We discuss the Bayesian emulation approach to computational solution of
multi-step portfolio studies in financial time series. "Bayesian emulation for
decisions" involves mapping the technical structure of a decision analysis
problem to that of Bayesian inference in a purely synthetic "emulating"
statistical model. This provides access to standard posterior analytic,
simulation and optimization methods that yield indirect solutions of the
decision problem. We develop this in time series portfolio analysis using
classes of economically and psychologically relevant multi-step ahead portfolio
utility functions. Studies with multivariate currency, commodity and stock
index time series illustrate the approach and show some of the practical
utility and benefits of the Bayesian emulation methodology.Comment: 24 pages, 7 figures, 2 table
A Theoretical Analysis of Two-Stage Recommendation for Cold-Start Collaborative Filtering
In this paper, we present a theoretical framework for tackling the cold-start
collaborative filtering problem, where unknown targets (items or users) keep
coming to the system, and there is a limited number of resources (users or
items) that can be allocated and related to them. The solution requires a
trade-off between exploitation and exploration as with the limited
recommendation opportunities, we need to, on one hand, allocate the most
relevant resources right away, but, on the other hand, it is also necessary to
allocate resources that are useful for learning the target's properties in
order to recommend more relevant ones in the future. In this paper, we study a
simple two-stage recommendation combining a sequential and a batch solution
together. We first model the problem with the partially observable Markov
decision process (POMDP) and provide an exact solution. Then, through an
in-depth analysis over the POMDP value iteration solution, we identify that an
exact solution can be abstracted as selecting resources that are not only
highly relevant to the target according to the initial-stage information, but
also highly correlated, either positively or negatively, with other potential
resources for the next stage. With this finding, we propose an approximate
solution to ease the intractability of the exact solution. Our initial results
on synthetic data and the Movie Lens 100K dataset confirm the performance gains
of our theoretical development and analysis
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Measuring the impact of observations on the predictability of the Kuroshio Extension in a shallow-water model
In this paper sequential importance sampling is used to assess the impact of observations on a ensemble prediction for the decadal path transitions of the Kuroshio Extension (KE). This particle ļ¬ltering approach gives access to the probability density of the state vector, which allows us to determine the predictive power ā an entropy based measure ā of the ensemble prediction. The proposed set-up makes use of an ensemble that, at each time, samples the climatological probability distribution. Then, in a post-processing step, the impact of diļ¬erent sets of observations is measured by the increase in predictive power of the ensemble over the climatological signal during one-year. The method is applied in an identical-twin
experiment for the Kuroshio Extension using a reduced-gravity shallow water model. We investigate the impact of assimilating velocity observations from diļ¬erent locations during the elongated and the contracted meandering state of the KE. Optimal observations location correspond to regions with strong potential vorticity gradients. For the elongated state the optimal location is in the ļ¬rst meander of the KE. During the contracted state of the KE it is located south of Japan, where the Kuroshio separates from the coast
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