316 research outputs found
Potts model, parametric maxflow and k-submodular functions
The problem of minimizing the Potts energy function frequently occurs in
computer vision applications. One way to tackle this NP-hard problem was
proposed by Kovtun [19,20]. It identifies a part of an optimal solution by
running maxflow computations, where is the number of labels. The number
of "labeled" pixels can be significant in some applications, e.g. 50-93% in our
tests for stereo. We show how to reduce the runtime to maxflow
computations (or one {\em parametric maxflow} computation). Furthermore, the
output of our algorithm allows to speed-up the subsequent alpha expansion for
the unlabeled part, or can be used as it is for time-critical applications.
To derive our technique, we generalize the algorithm of Felzenszwalb et al.
[7] for {\em Tree Metrics}. We also show a connection to {\em -submodular
functions} from combinatorial optimization, and discuss {\em -submodular
relaxations} for general energy functions.Comment: Accepted to ICCV 201
Complexity of Discrete Energy Minimization Problems
Discrete energy minimization is widely-used in computer vision and machine
learning for problems such as MAP inference in graphical models. The problem,
in general, is notoriously intractable, and finding the global optimal solution
is known to be NP-hard. However, is it possible to approximate this problem
with a reasonable ratio bound on the solution quality in polynomial time? We
show in this paper that the answer is no. Specifically, we show that general
energy minimization, even in the 2-label pairwise case, and planar energy
minimization with three or more labels are exp-APX-complete. This finding rules
out the existence of any approximation algorithm with a sub-exponential
approximation ratio in the input size for these two problems, including
constant factor approximations. Moreover, we collect and review the
computational complexity of several subclass problems and arrange them on a
complexity scale consisting of three major complexity classes -- PO, APX, and
exp-APX, corresponding to problems that are solvable, approximable, and
inapproximable in polynomial time. Problems in the first two complexity classes
can serve as alternative tractable formulations to the inapproximable ones.
This paper can help vision researchers to select an appropriate model for an
application or guide them in designing new algorithms.Comment: ECCV'16 accepte
Testing for Common Breaks in a Multiple Equations System
The issue addressed in this paper is that of testing for common breaks across
or within equations of a multivariate system. Our framework is very general and
allows integrated regressors and trends as well as stationary regressors. The
null hypothesis is that breaks in different parameters occur at common
locations and are separated by some positive fraction of the sample size unless
they occur across different equations. Under the alternative hypothesis, the
break dates across parameters are not the same and also need not be separated
by a positive fraction of the sample size whether within or across equations.
The test considered is the quasi-likelihood ratio test assuming normal errors,
though as usual the limit distribution of the test remains valid with
non-normal errors. Of independent interest, we provide results about the rate
of convergence of the estimates when searching over all possible partitions
subject only to the requirement that each regime contains at least as many
observations as some positive fraction of the sample size, allowing break dates
not separated by a positive fraction of the sample size across equations.
Simulations show that the test has good finite sample properties. We also
provide an application to issues related to level shifts and persistence for
various measures of inflation to illustrate its usefulness.Comment: 44 pages, 2 tables and 1 figur
Correlations and projective measurements in maximally entangled multipartite states
Multipartite quantum states constitute the key resource for quantum
computation. The understanding of their internal structure is thus of great
importance in the field of quantum information. This paper aims at examining
the structure of multipartite maximally entangled pure states, using tools with
a simple and intuitive physical meaning, namely, projective measurements and
correlations. We first show how, in such states, a very simple relation arises
between post-measurement expectation values and pre-measurement correlations.
We then infer the consequences of this relation on the structure of the
recently introduced \textit{entanglement metric}, allowing us to provide an
upper bound for the \textit{persistency of entanglement}. The dependence of
these features on the chosen measurement axis is underlined, and two simple
optimization procedures are proposed, to find those maximizing the
correlations. Finally, we apply our procedures onto some prototypical examples
Testing for common breaks in a multiple equations system
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that breaks in different parameters occur at common locations and are separated by some positive fraction of the sample size unless they occur across different equations. Under the alternative hypothesis, the break dates across parameters are not the same and also need not be separated by a positive fraction of the sample size whether within or across equations. The test considered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Of independent interest, we provide results about the rate of convergence of the estimates when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as some positive fraction of the sample size, allowing break dates not separated by a positive fraction of the sample size across equations. Simulations show that the test has good finite sample properties. We also provide an application to issues related to level shifts and persistence for various measures of inflation to illustrate its usefulness.Accepted manuscrip
Testing for common breaks in a multiple equations system
The issue addressed in this paper is that of testing for common breaks across or within equations. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that some subsets of the parameters (either regression coe cients or elements of the covariance matrix of the errors) share one or more common break dates, with the break dates in the system asymptotically distinct so that each regime is separated by some positive fraction of the sample size. Under the alternative hypothesis, the break dates are not the same and also need not be separated by a positive fraction of the sample size. The test considered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Also of independent interest, we provide results about the consistency and rate of convergence when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as the number of parameters in the model. Simulation results show that the test has good nite sample properties. We also provide an application to various measures of in ation to illustrate its usefulness
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