The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Yair Weiss - One of the best experts on this subject based on the ideXlab platform.
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tighter Linear Program relaxations for high order graphical models
arXiv: Artificial Intelligence, 2013Co-Authors: Elad Mezuman, Daniel Tarlow, Amir Globerson, Yair WeissAbstract:Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a Linear Program (LP) relaxation with unary consistency constraints between the HOP and the individual variables. In many cases, the resulting relaxations are loose, and in these cases the results of inference can be poor. It is thus desirable to look for more accurate ways of performing inference in these models. In this work, we study the LP relaxations that result from enforcing additional consistency constraints between the HOP and the rest of the model. We address theoretical questions about the strength of the resulting relaxations compared to the relaxations that arise in standard approaches, and we develop practical and efficient message passing algorithms for optimizing the LPs. Empirically, we show that the LPs with additional consistency constraints lead to more accurate inference on some challenging problems that include a combination of low order and high order terms.
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tighter Linear Program relaxations for high order graphical models
Uncertainty in Artificial Intelligence, 2013Co-Authors: Elad Mezuman, Daniel Tarlow, Amir Globerson, Yair WeissAbstract:Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a Linear Program (LP) relaxation with unary consistency constraints between the HOP and the individual variables. In many cases, the resulting relaxations are loose, and in these cases the results of inference can be poor. It is thus desirable to look for more accurate ways of performing inference. In this work, we study the LP relaxations that result from enforcing additional consistency constraints between the HOP and the rest of the model. We address theoretical questions about the strength of the resulting relaxations compared to the relaxations that arise in standard approaches, and we develop practical and efficient message passing algorithms for optimizing the LPs. Empirically, we show that the LPs with additional consistency constraints lead to more accurate inference on some challenging problems that include a combination of low order and high order terms.
Shi Hongxing - One of the best experts on this subject based on the ideXlab platform.
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study on the model of grey matrix game based on grey mixed strategy solution of grey Linear Program model on grey matrix game
IEEE International Conference on Fuzzy Systems, 2008Co-Authors: Zhang Yuanyuan, Fang Zhigeng, Liu Sifen, Wu Xin, Shi HongxingAbstract:The key to grey matrix game lies in the solution of grey Linear Program model. On this paper, we have proved the necessary and sufficient condition of the existence of grey basic feasible solution in grey Linear Program problem. We have also certified that grey basic feasible solution corresponds to grey apex of grey feasible field. Then, having proved that any point of grey convex set can be Linearly expressed by the grey apex of the grey convex set, we proved that grey optimal value of the objective function corresponds to the grey apex of the grey convex in the grey Linear Program problem of the grey matrix game. Therefore, grey optimal value of it certainly corresponds to some unity grey numbers of grey element in the grey game matrix Atilde(otimes).
Michael Chertkov - One of the best experts on this subject based on the ideXlab platform.
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Linear Programming based detectors for two dimensional intersymbol interference channels
International Symposium on Information Theory, 2011Co-Authors: Shrinivas Kudekar, Jason K Johnson, Michael ChertkovAbstract:We present and study Linear Programming based detectors for two-dimensional intersymbol interference channels. Interesting instances of two-dimensional intersymbol interference channels are magnetic storage, optical storage and Wyner's cellular network model. We show that the optimal maximum a posteriori detection in such channels lends itself to a natural Linear Programming based sub-optimal detector. We call this the Pairwise Linear Program detector. Our experiments show that the Pairwise Linear Program detector performs poorly. We then propose two methods to strengthen our detector. These detectors are based on systematically enhancing the Pairwise Linear Program. The first one, the Block Linear Program detector adds higher order potential functions in an exhaustive manner, as constraints, to the Pairwise Linear Program detector. We show by experiments that the Block Linear Program detector has performance close to the optimal detector. We then develop another detector by adaptively adding frustrated cycles to the Pairwise Linear Program detector. Empirically, this detector also has performance close to the optimal one and turns out to be less complex then the Block Linear Program detector.
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Linear Programming based detectors for two dimensional intersymbol interference channels
arXiv: Information Theory, 2011Co-Authors: Shrinivas Kudekar, Jason K Johnson, Michael ChertkovAbstract:We present and study Linear Programming based detectors for two-dimensional intersymbol interference channels. Interesting instances of two-dimensional intersymbol interference channels are magnetic storage, optical storage and Wyner's cellular network model. We show that the optimal maximum a posteriori detection in such channels lends itself to a natural Linear Programming based sub-optimal detector. We call this the Pairwise Linear Program detector. Our experiments show that the Pairwise Linear Program detector performs poorly. We then propose two methods to strengthen our detector. These detectors are based on systematically enhancing the Pairwise Linear Program. The first one, the Block Linear Program detector adds higher order potential functions in an {\em exhaustive} manner, as constraints, to the Pairwise Linear Program detector. We show by experiments that the Block Linear Program detector has performance close to the optimal detector. We then develop another detector by {\em adaptively} adding frustrated cycles to the Pairwise Linear Program detector. Empirically, this detector also has performance close to the optimal one and turns out to be less complex then the Block Linear Program detector.
Jan Van Den Brand - One of the best experts on this subject based on the ideXlab platform.
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a deterministic Linear Program solver in current matrix multiplication time
Symposium on Discrete Algorithms, 2020Co-Authors: Jan Van Den BrandAbstract:Interior point algorithms for solving Linear Programs have been studied extensively for a long time [e.g. Karmarkar 1984; Lee, Sidford FOCS'14; Cohen, Lee, Song STOC'19]. For Linear Programs of the form minAx=b,x≥0 c┬x with n variables and d constraints, the generic case d = Ω(n) has recently been settled by Cohen, Lee and Song [STOC'19]. Their algorithm can solve Linear Programs in O(nω log(n/Δ)) expected time1, where Δ is the relative accuracy. This is essentially optimal as all known Linear system solvers require up to O(nΩ) time for solving Ax = b. However, for the case of deterministic solvers, the best upper bound is Vaidya's 30 years old O(n2.5 log(n/Δ)) bound [FOCS'89]. In this paper we show that one can also settle the deterministic setting by derandomizing Cohen et al.'s O(nω log(n/Δ))) time algorithm. This allows for a strict O(nω log(n/Δ)) time bound, instead of an expected one, and a simplified analysis, reducing the length of their proof of their central path method by roughly half. Derandomizing this algorithm was also an open question asked in Song's PhD Thesis. The main tool to achieve our result is a new data-structure that can maintain the solution to a Linear system in subquadratic time. More accurately we are able to maintain [MATH HERE] in subquadratic time under l2 multiplicative changes to the diagonal matrix U and the vector v. This type of change is common for interior point algorithms. Previous algorithms [e.g. Vaidya STOC'89; Lee, Sidford FOCS'15; Cohen, Lee, Song STOC'19] required Ω(n2) time for this task. In [Cohen, Lee, Song STOC'19] they managed to maintain the matrix [MATH HERE] in sub-quadratic time, but multiplying it with a dense vector to solve the Linear system still required Ω(n2) time. To improve the complexity of their Linear Program solver, they restricted the solver to only multiply sparse vectors via a random sampling argument. In comparison, our data-structure maintains the entire product [MATH HERE] additionally to just the matrix. Interestingly, this can be viewed as a simple modification of Cohen et al.'s data-structure, but it significantly simplifies their analysis of their central path method and makes their whole algorithm deterministic.
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a deterministic Linear Program solver in current matrix multiplication time
arXiv: Data Structures and Algorithms, 2019Co-Authors: Jan Van Den BrandAbstract:Interior point algorithms for solving Linear Programs have been studied extensively for a long time [e.g. Karmarkar 1984; Lee, Sidford FOCS'14; Cohen, Lee, Song STOC'19]. For Linear Programs of the form $\min_{Ax=b, x \ge 0} c^\top x$ with $n$ variables and $d$ constraints, the generic case $d = \Omega(n)$ has recently been settled by Cohen, Lee and Song [STOC'19]. Their algorithm can solve Linear Programs in $\tilde O(n^\omega \log(n/\delta))$ expected time, where $\delta$ is the relative accuracy. This is essentially optimal as all known Linear system solvers require up to $O(n^{\omega})$ time for solving $Ax = b$. However, for the case of deterministic solvers, the best upper bound is Vaidya's 30 years old $O(n^{2.5} \log(n/\delta))$ bound [FOCS'89]. In this paper we show that one can also settle the deterministic setting by derandomizing Cohen et al.'s $\tilde{O}(n^\omega \log(n/\delta))$ time algorithm. This allows for a strict $\tilde{O}(n^\omega \log(n/\delta))$ time bound, instead of an expected one, and a simplified analysis, reducing the length of their proof of their central path method by roughly half. Derandomizing this algorithm was also an open question asked in Song's PhD Thesis. The main tool to achieve our result is a new data-structure that can maintain the solution to a Linear system in subquadratic time. More accurately we are able to maintain $\sqrt{U}A^\top(AUA^\top)^{-1}A\sqrt{U}\:v$ in subquadratic time under $\ell_2$ multiplicative changes to the diagonal matrix $U$ and the vector $v$. This type of change is common for interior point algorithms. Previous algorithms [e.g. Vaidya STOC'89; Lee, Sidford FOCS'15; Cohen, Lee, Song STOC'19] required $\Omega(n^2)$ time for this task. [...]
Ignaz Rutter - One of the best experts on this subject based on the ideXlab platform.
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an integer Linear Program for bend minimization in ortho radial drawings
Graph Drawing, 2020Co-Authors: Benjamin Niedermann, Ignaz RutterAbstract:An ortho-radial grid is described by concentric circles and straight-line spokes emanating from the circles’ center. An ortho-radial drawing is the analog of an orthogonal drawing on an ortho-radial grid. Such a drawing has an unbounded outer face and a central face that contains the origin. Building on the notion of an ortho-radial representation [1], we describe an integer-Linear Program (ILP) for computing bend-free ortho-radial representations with a given embedding and fixed outer and central face. Using the ILP as a building block, we introduce a pruning technique to compute bend-optimal ortho-radial drawings with a given embedding and a fixed outer face, but freely choosable central face. Our experiments show that, in comparison with orthogonal drawings using the same embedding and the same outer face, the use of ortho-radial drawings reduces the number of bends by \(43.8 \%\) on average. Further, our approach allows us to compute ortho-radial drawings of embedded graphs such as the metro system of Beijing or London within seconds.
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an integer Linear Program for bend minimization in ortho radial drawings
arXiv: Computational Geometry, 2020Co-Authors: Benjamin Niedermann, Ignaz RutterAbstract:An ortho-radial grid is described by concentric circles and straight-line spokes emanating from the circles' center. An ortho-radial drawing is the analog of an orthogonal drawing on an ortho-radial grid. Such a drawing has an unbounded outer face and a central face that contains the origin. Building on the notion of an ortho-radial representation (Barth et al., SoCG, 2017), we describe an integer-Linear Program (ILP) for computing bend-free ortho-radial representations with a given embedding and fixed outer and central face. Using the ILP as a building block, we introduce a pruning technique to compute bend-optimal ortho-radial drawings with a given embedding and a fixed outer face, but freely choosable central face. Our experiments show that, in comparison with orthogonal drawings using the same embedding and the same outer face, the use of ortho-radial drawings reduces the number of bends by 43.8% on average. Further, our approach allows us to compute ortho-radial drawings of embedded graphs such as the metro system of Beijing or London within seconds.
