Linear Factor

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Subhabrata Sen - One of the best experts on this subject based on the ideXlab platform.

  • near optimal disjoint path facility location through set cover by pairs
    Operations Research, 2020
    Co-Authors: David S Johnson, Lee Breslau, Ilias Diakonikolas, Nick Duffield, Mohammadtaghi Hajiaghayi, Howard Karloff, Mauricio G C Resende, Subhabrata Sen
    Abstract:

    In this paper, we consider two special cases of the “cover-by-pairs” optimization problem that arises when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems arise in a network traffic-monitoring scheme proposed by Breslau et al. and have potential applications to content distribution. The “set-disjoint” variant applies to networks that use the open shortest path first routing protocol, and the “path-disjoint” variant applies when multiprotocol label switching routing is enabled, making better solutions possible at the cost of greater operational expense. Although we can prove that no polynomial-time algorithm can guarantee good solutions for either version, we are able to provide heuristics that do very well in practice on instances with real-world network structure. Fast implementations of the heuristics, made possible by exploiting mathematical observations about the relationship between the network instances and the corresponding instances of the cover-by-pairs problem, allow us to perform an extensive experimental evaluation of the heuristics and what the solutions they produce tell us about the effectiveness of the proposed monitoring scheme. For the set-disjoint variant, we validate our claim of near-optimality via a new lower-bounding integer programming formulation. Although computing this lower bound requires solving the NP-hard hitting set problem and can underestimate the optimal value by a Linear Factor in the worst case, it can be computed quickly by CPLEX, and it equals the optimal solution value for all the instances in our extensive test bed.

  • near optimal disjoint path facility location through set cover by pairs
    arXiv: Data Structures and Algorithms, 2016
    Co-Authors: David S Johnson, Lee Breslau, Ilias Diakonikolas, Nick Duffield, Mohammadtaghi Hajiaghayi, Howard Karloff, Mauricio G C Resende, Subhabrata Sen
    Abstract:

    In this paper we consider two special cases of the "cover-by-pairs" optimization problem that arise when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems arise in a network traffic monitoring scheme proposed by Breslau et al. and have potential applications to content distribution. The "set-disjoint" variant applies to networks that use the OSPF routing protocol, and the "path-disjoint" variant applies when MPLS routing is enabled, making better solutions possible at the cost of greater operational expense. Although we can prove that no polynomial-time algorithm can guarantee good solutions for either version, we are able to provide heuristics that do very well in practice on instances with real-world network structure. Fast implementations of the heuristics, made possible by exploiting mathematical observations about the relationship between the network instances and the corresponding instances of the cover-by-pairs problem, allow us to perform an extensive experimental evaluation of the heuristics and what the solutions they produce tell us about the effectiveness of the proposed monitoring scheme. For the set-disjoint variant, we validate our claim of near-optimality via a new lower-bounding integer programming formulation. Although computing this lower bound requires solving the NP-hard Hitting Set problem and can underestimate the optimal value by a Linear Factor in the worst case, it can be computed quickly by CPLEX, and it equals the optimal solution value for all the instances in our extensive testbed.

Soosung Hwang - One of the best experts on this subject based on the ideXlab platform.

  • testing Linear Factor models on individual stocks using the average f test
    European Journal of Finance, 2014
    Co-Authors: Soosung Hwang, Stephen E. Satchell
    Abstract:

    In this paper, we propose the average F -statistic for testing Linear asset pricing models. The average pricing error, captured in the statistic, is of more interest than the ex post maximum pricing error of the multivariate F -statistic that is associated with extreme long and short positions and excessively sensitive to small perturbations in the estimates of asset means and covariances. The average F -test can be applied to thousands of individual stocks and thus is free from the information loss or the data-snooping biases from grouping. This test is robust to ellipticity, and more importantly, our simulation and bootstrapping results show that the power of the average F -test continues to increase as the number of stocks increases. Empirical tests using individual stocks from 1967 to 2006 demonstrate that the popular four-Factor model (i.e. Fama-French three Factors and momentum) is rejected in two sub-periods from 1967 to 1971 and from 1982 to 1986.

  • testing Linear Factor models on individual stocks using the average f test
    Social Science Research Network, 2012
    Co-Authors: Soosung Hwang, Stephen Satchell
    Abstract:

    We propose the average F statistic for testing Linear asset pricing models. The average pricing error, captured in the the statistic, is of more interest than the ex post maximum pricing error of the multivariate F statistic that is associated with extreme long and short positions and excessively sensitive to small perturbations in the estimates of asset means and covariances. The average F test can be applied to thousands of individual stocks and thus is free from the information loss or the data snooping biases from grouping. This test is robust to ellipticity, and more importantly, our simulation and bootstrapping results show that the power of average F test continues to increase as the number of stocks increases. Empirical tests using individual stocks from 1967 to 2006 demonstrate that the popular four Factor model (i.e. Fama-French three Factors and momentum) is rejected two sub-periods from from 1967 to 1971 and from 1982 to 1986.

  • fishing with a licence an empirical search for asset pricing Factors
    2008
    Co-Authors: Soosung Hwang, Alexandre Rubesam
    Abstract:

    We study the question of which asset pricing Factors should be included in Linear Factor asset pricing model. We develop a simple multivariate extension of a Bayesian variable selection procedure from the statistics literature to estimate posterior probabilities of asset pricing Factors using many assets at once. Using a dataset of thousands of individual stocks in the US market, we calculate posterior probabilities of 12 Factors which have been suggested in the literature. Our results indicate strong and robust evidence that a Linear Factor model should include the excess market return, the size and the liquidity Factors, and only weak evidence that the idiosyncratic volatility and downside risk Factors matter. We find that the famous Fama and French (1993, 1996) HML Factor has high posterior probability only if portfolios formed on book-to-market ratio are used.

Stephen Satchell - One of the best experts on this subject based on the ideXlab platform.

  • testing Linear Factor models on individual stocks using the average f test
    Social Science Research Network, 2012
    Co-Authors: Soosung Hwang, Stephen Satchell
    Abstract:

    We propose the average F statistic for testing Linear asset pricing models. The average pricing error, captured in the the statistic, is of more interest than the ex post maximum pricing error of the multivariate F statistic that is associated with extreme long and short positions and excessively sensitive to small perturbations in the estimates of asset means and covariances. The average F test can be applied to thousands of individual stocks and thus is free from the information loss or the data snooping biases from grouping. This test is robust to ellipticity, and more importantly, our simulation and bootstrapping results show that the power of average F test continues to increase as the number of stocks increases. Empirical tests using individual stocks from 1967 to 2006 demonstrate that the popular four Factor model (i.e. Fama-French three Factors and momentum) is rejected two sub-periods from from 1967 to 1971 and from 1982 to 1986.

Daniel Cremers - One of the best experts on this subject based on the ideXlab platform.

  • visual inertial mapping with non Linear Factor recovery
    International Conference on Robotics and Automation, 2020
    Co-Authors: Vladyslav Usenko, Nikolaus Demmel, David Schubert, Jorg Stuckler, Daniel Cremers
    Abstract:

    Cameras and inertial measurement units are complementary sensors for ego-motion estimation and environment mapping. Their combination makes visual-inertial odometry (VIO) systems more accurate and robust. For globally consistent mapping, however, combining visual and inertial information is not straightforward. To estimate the motion and geometry with a set of images large baselines are required. Because of that, most systems operate on keyframes that have large time intervals between each other. Inertial data on the other hand quickly degrades with the duration of the intervals and after several seconds of integration, it typically contains only little useful information. In this letter, we propose to extract relevant information for visual-inertial mapping from visual-inertial odometry using non-Linear Factor recovery. We reconstruct a set of non-Linear Factors that make an optimal approximation of the information on the trajectory accumulated by VIO. To obtain a globally consistent map we combine these Factors with loop-closing constraints using bundle adjustment. The VIO Factors make the roll and pitch angles of the global map observable, and improve the robustness and the accuracy of the mapping. In experiments on a public benchmark, we demonstrate superior performance of our method over the state-of-the-art approaches.

  • visual inertial mapping with non Linear Factor recovery
    arXiv: Computer Vision and Pattern Recognition, 2019
    Co-Authors: Vladyslav Usenko, Nikolaus Demmel, David Schubert, Jorg Stuckler, Daniel Cremers
    Abstract:

    Cameras and inertial measurement units are complementary sensors for ego-motion estimation and environment mapping. Their combination makes visual-inertial odometry (VIO) systems more accurate and robust. For globally consistent mapping, however, combining visual and inertial information is not straightforward. To estimate the motion and geometry with a set of images large baselines are required. Because of that, most systems operate on keyframes that have large time intervals between each other. Inertial data on the other hand quickly degrades with the duration of the intervals and after several seconds of integration, it typically contains only little useful information. In this paper, we propose to extract relevant information for visual-inertial mapping from visual-inertial odometry using non-Linear Factor recovery. We reconstruct a set of non-Linear Factors that make an optimal approximation of the information on the trajectory accumulated by VIO. To obtain a globally consistent map we combine these Factors with loop-closing constraints using bundle adjustment. The VIO Factors make the roll and pitch angles of the global map observable, and improve the robustness and the accuracy of the mapping. In experiments on a public benchmark, we demonstrate superior performance of our method over the state-of-the-art approaches.

David S Johnson - One of the best experts on this subject based on the ideXlab platform.

  • near optimal disjoint path facility location through set cover by pairs
    Operations Research, 2020
    Co-Authors: David S Johnson, Lee Breslau, Ilias Diakonikolas, Nick Duffield, Mohammadtaghi Hajiaghayi, Howard Karloff, Mauricio G C Resende, Subhabrata Sen
    Abstract:

    In this paper, we consider two special cases of the “cover-by-pairs” optimization problem that arises when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems arise in a network traffic-monitoring scheme proposed by Breslau et al. and have potential applications to content distribution. The “set-disjoint” variant applies to networks that use the open shortest path first routing protocol, and the “path-disjoint” variant applies when multiprotocol label switching routing is enabled, making better solutions possible at the cost of greater operational expense. Although we can prove that no polynomial-time algorithm can guarantee good solutions for either version, we are able to provide heuristics that do very well in practice on instances with real-world network structure. Fast implementations of the heuristics, made possible by exploiting mathematical observations about the relationship between the network instances and the corresponding instances of the cover-by-pairs problem, allow us to perform an extensive experimental evaluation of the heuristics and what the solutions they produce tell us about the effectiveness of the proposed monitoring scheme. For the set-disjoint variant, we validate our claim of near-optimality via a new lower-bounding integer programming formulation. Although computing this lower bound requires solving the NP-hard hitting set problem and can underestimate the optimal value by a Linear Factor in the worst case, it can be computed quickly by CPLEX, and it equals the optimal solution value for all the instances in our extensive test bed.

  • near optimal disjoint path facility location through set cover by pairs
    arXiv: Data Structures and Algorithms, 2016
    Co-Authors: David S Johnson, Lee Breslau, Ilias Diakonikolas, Nick Duffield, Mohammadtaghi Hajiaghayi, Howard Karloff, Mauricio G C Resende, Subhabrata Sen
    Abstract:

    In this paper we consider two special cases of the "cover-by-pairs" optimization problem that arise when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems arise in a network traffic monitoring scheme proposed by Breslau et al. and have potential applications to content distribution. The "set-disjoint" variant applies to networks that use the OSPF routing protocol, and the "path-disjoint" variant applies when MPLS routing is enabled, making better solutions possible at the cost of greater operational expense. Although we can prove that no polynomial-time algorithm can guarantee good solutions for either version, we are able to provide heuristics that do very well in practice on instances with real-world network structure. Fast implementations of the heuristics, made possible by exploiting mathematical observations about the relationship between the network instances and the corresponding instances of the cover-by-pairs problem, allow us to perform an extensive experimental evaluation of the heuristics and what the solutions they produce tell us about the effectiveness of the proposed monitoring scheme. For the set-disjoint variant, we validate our claim of near-optimality via a new lower-bounding integer programming formulation. Although computing this lower bound requires solving the NP-hard Hitting Set problem and can underestimate the optimal value by a Linear Factor in the worst case, it can be computed quickly by CPLEX, and it equals the optimal solution value for all the instances in our extensive testbed.