In this paper, we address a Monte Carlo algorithm for calculating the Shapley values of minimum cost spanning tree games. We provide tighter upper and lower bounds for the marginal cost vector and improve a previous study’s lower bound on the number of permutations required for the output of the algorithm to achieve a given accuracy with a given probability. In addition, we present computational experiments for estimating the lower bound on the number of permutations required by the Monte Carlo algorithm.
{"title":"MONTE CARLO ALGORITHM FOR CALCULATING THE SHAPLEY VALUES OF MINIMUM COST SPANNING TREE GAMES","authors":"Kazutoshi Ando, K. Takase","doi":"10.15807/jorsj.63.31","DOIUrl":"https://doi.org/10.15807/jorsj.63.31","url":null,"abstract":"In this paper, we address a Monte Carlo algorithm for calculating the Shapley values of minimum cost spanning tree games. We provide tighter upper and lower bounds for the marginal cost vector and improve a previous study’s lower bound on the number of permutations required for the output of the algorithm to achieve a given accuracy with a given probability. In addition, we present computational experiments for estimating the lower bound on the number of permutations required by the Monte Carlo algorithm.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41622463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In the one-way trading problem, we are asked to convert dollars into yen only by unidirectional conversions, while watching the exchange rate that fluctuates along time. The goal is to maximize the amount of yen we finally get, under the assumption that we are not informed of when the game ends. For this problem, an optimal algorithm was proposed by El-Yaniv et al. In this paper we formulate this problem into a linear optimization problem (linear program) and reduce derivation of an optimal algorithm to solving the linear optimization problem. This reveals that the optimality of the algorithm follows from the duality theorem. Our analysis demonstrates how infinite-dimensional linear optimization helps to design algorithms.
{"title":"ONE-WAY TRADING PROBLEMS VIA LINEAR OPTIMIZATION","authors":"H. Fujiwara, Naohiro Araki, Hiroaki Yamamoto","doi":"10.15807/jorsj.63.1","DOIUrl":"https://doi.org/10.15807/jorsj.63.1","url":null,"abstract":"Abstract In the one-way trading problem, we are asked to convert dollars into yen only by unidirectional conversions, while watching the exchange rate that fluctuates along time. The goal is to maximize the amount of yen we finally get, under the assumption that we are not informed of when the game ends. For this problem, an optimal algorithm was proposed by El-Yaniv et al. In this paper we formulate this problem into a linear optimization problem (linear program) and reduce derivation of an optimal algorithm to solving the linear optimization problem. This reveals that the optimality of the algorithm follows from the duality theorem. Our analysis demonstrates how infinite-dimensional linear optimization helps to design algorithms.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67215450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Akifumi Kira, Naoyuki Kamiyama, H. Anai, H. Iwashita, Kotaro Ohori
We consider Stackelberg patrolling security games in which a security guard and an intruder walk around a facility. In these games, at each timepoint, the guard earns a reward (intruder incurs a cost) depending on their locations at that time. The objective of the guard (resp., the intruder) is to patrol (intrude) the facility so that the total sum of rewards is maximized (minimized). We study three cases: In Case 1, the guard chooses a scheduled route first and then the intruder chooses a scheduled route after perfectly observing the guard’s choice. In Case 2, the guard randomizes her scheduled routes and then intruder observes its probability distribution and also randomize his scheduled routes. In Case 3, the guard randomizes her scheduled routes as well, but the intruder sequentially observes the location of the guard and reroutes to reach one of his targets. We show that the intruder’s best response problem in Cases 1 and 2 and Case 3 can be formulated as a shortest path problem and a Markov decision process, respectively. Moreover, the equilibrium problem in each case reduces to a polynomial-sized mixed integer linear programming, linear programming, and bilinear programming problem, respectively.
{"title":"ON DYNAMIC PATROLLING SECURITY GAMES","authors":"Akifumi Kira, Naoyuki Kamiyama, H. Anai, H. Iwashita, Kotaro Ohori","doi":"10.15807/jorsj.62.152","DOIUrl":"https://doi.org/10.15807/jorsj.62.152","url":null,"abstract":"We consider Stackelberg patrolling security games in which a security guard and an intruder walk around a facility. In these games, at each timepoint, the guard earns a reward (intruder incurs a cost) depending on their locations at that time. The objective of the guard (resp., the intruder) is to patrol (intrude) the facility so that the total sum of rewards is maximized (minimized). We study three cases: In Case 1, the guard chooses a scheduled route first and then the intruder chooses a scheduled route after perfectly observing the guard’s choice. In Case 2, the guard randomizes her scheduled routes and then intruder observes its probability distribution and also randomize his scheduled routes. In Case 3, the guard randomizes her scheduled routes as well, but the intruder sequentially observes the location of the guard and reroutes to reach one of his targets. We show that the intruder’s best response problem in Cases 1 and 2 and Case 3 can be formulated as a shortest path problem and a Markov decision process, respectively. Moreover, the equilibrium problem in each case reduces to a polynomial-sized mixed integer linear programming, linear programming, and bilinear programming problem, respectively.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48610628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Separable convex resource allocation problem aims at finding an allocation of a discrete resource to several activities that minimizes a separable convex function representing the total cost or the total loss. In this paper, we consider the separable convex resource allocation problem with an additional constraint that the L1-distance between a given vector and a feasible solution is bounded by a given positive constant. We prove that the simplest separable convex resource allocation problem with the L1-distance constraint can be reformulated as a submodular resource allocation problem. This result implies that the problem can be solved in polynomial time by existing algorithms for the submodular resource allocation problem. We present specialized implementations of the existing algorithms and analyze their running time.
{"title":"SEPARABLE CONVEX RESOURCE ALLOCATION PROBLEM WITH L1-DISTANCE CONSTRAINT","authors":"N. Minamikawa, A. Shioura","doi":"10.15807/JORSJ.62.109","DOIUrl":"https://doi.org/10.15807/JORSJ.62.109","url":null,"abstract":"Separable convex resource allocation problem aims at finding an allocation of a discrete resource to several activities that minimizes a separable convex function representing the total cost or the total loss. In this paper, we consider the separable convex resource allocation problem with an additional constraint that the L1-distance between a given vector and a feasible solution is bounded by a given positive constant. We prove that the simplest separable convex resource allocation problem with the L1-distance constraint can be reformulated as a submodular resource allocation problem. This result implies that the problem can be solved in polynomial time by existing algorithms for the submodular resource allocation problem. We present specialized implementations of the existing algorithms and analyze their running time.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41432246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper proposes a continuous network model for determining the size of the toll area and toll level in cordon and area road pricing. Cordon pricing charges a toll to vehicles passing a cordon line surrounding a designated area, whereas area pricing charges a toll to all vehicles driving inside the area. Analytical expressions for the traffic volume and toll revenue are obtained for a circular city with a radial-arc network. The analytical expressions demonstrate how the size of the toll area and toll level affect the traffic volume and toll revenue. Comparing cordon and area pricing shows that area pricing is superior to cordon pricing in both reducing traffic volume in the toll area and generating revenue.
{"title":"CORDON AND AREA ROAD PRICING IN RADIAL-ARC NETWORK","authors":"M. Miyagawa","doi":"10.15807/JORSJ.62.121","DOIUrl":"https://doi.org/10.15807/JORSJ.62.121","url":null,"abstract":"Abstract This paper proposes a continuous network model for determining the size of the toll area and toll level in cordon and area road pricing. Cordon pricing charges a toll to vehicles passing a cordon line surrounding a designated area, whereas area pricing charges a toll to all vehicles driving inside the area. Analytical expressions for the traffic volume and toll revenue are obtained for a circular city with a radial-arc network. The analytical expressions demonstrate how the size of the toll area and toll level affect the traffic volume and toll revenue. Comparing cordon and area pricing shows that area pricing is superior to cordon pricing in both reducing traffic volume in the toll area and generating revenue.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44949317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The payoff of option is determined by the future price of underlying asset and therefore the option prices contain the forward looking information. Implied distribution is a forward looking distribution of the underlying asset derived from option prices. There are a lot of studies estimating implied distribution in the risk neutral probability framework. However, a risk neutral probability generally differs from a real world probability, which represents actual investors view about asset return. Recently, Ross (2015) has showed remarkable theorem, named “Recovery Theorem”. It enables us to estimate the real world probability distribution from option prices under a particular assumption about representative investor's risk preferences. However, it is not easy to derive the appropriate estimators because it is necessary to solve an ill-posed problem in estimation process. This paper discusses about the method to estimate a real world distribution accurately with the Recovery Theorem. The previous studies propose the methods to estimate the real world distribution, whereas they do not investigate on the estimation accuracy. Hence, we test the effectiveness of the Tikhonov method used by Audrino et al. (2015) in the numerical analysis with hypothetical data. We propose a new method to derive the more accurate solution by configuring the regularization term considering prior information and compare it with the Tikhonov method. Moreover, we discuss regularization parameter selection to get the accurate real world distribution. We find the following three points through the numerical analysis. (1) To stabilize the solution by introducing regularization term is an effective method in terms of estimating a real world distribution with the Recovery Theorem. (2) Proposed method can estimate a real world distribution more accurately than the Tikhonov method. (3) We can offer the appropriate solutions even if the number of maturities is less than that of states.
期权的收益是由标的资产的未来价格决定的，因此期权价格包含了前瞻性信息。隐含分布是从期权价格推导出的标的资产的前瞻性分布。在风险中性概率框架下对隐含分布的估计已有大量的研究。然而，风险中性概率通常不同于现实世界的概率，它代表了投资者对资产回报的实际看法。最近，Ross(2015)提出了一个引人注目的定理，命名为“恢复定理”。它使我们能够在一个关于代表性投资者风险偏好的特定假设下，从期权价格估计真实世界的概率分布。然而，由于在估计过程中需要解决一个不适定问题，因此推导出合适的估计量并不容易。本文讨论了用恢复定理准确估计实际分布的方法。以往的研究提出了估计真实世界分布的方法，但没有对估计的精度进行研究。因此，我们使用假设数据测试Audrino et al.(2015)在数值分析中使用的Tikhonov方法的有效性。我们提出了一种新的方法，通过配置考虑先验信息的正则化项来获得更精确的解，并与Tikhonov方法进行了比较。此外，我们还讨论了正则化参数的选择，以获得准确的真实世界分布。通过数值分析，我们发现以下三点。(1)引入正则化项稳定解是利用恢复定理估计实际分布的一种有效方法。(2)与Tikhonov方法相比，该方法可以更准确地估计真实世界的分布。(3)即使期限少于国家，我们也可以提供相应的解决方案。
{"title":"ESTIMATING FORWARD LOOKING DISTRIBUTION WITH THE ROSS RECOVERY THEOREM","authors":"Takuya Kiriu, Norio Hibiki","doi":"10.15807/JORSJ.62.83","DOIUrl":"https://doi.org/10.15807/JORSJ.62.83","url":null,"abstract":"The payoff of option is determined by the future price of underlying asset and therefore the option prices contain the forward looking information. Implied distribution is a forward looking distribution of the underlying asset derived from option prices. There are a lot of studies estimating implied distribution in the risk neutral probability framework. However, a risk neutral probability generally differs from a real world probability, which represents actual investors view about asset return. Recently, Ross (2015) has showed remarkable theorem, named “Recovery Theorem”. It enables us to estimate the real world probability distribution from option prices under a particular assumption about representative investor's risk preferences. However, it is not easy to derive the appropriate estimators because it is necessary to solve an ill-posed problem in estimation process. This paper discusses about the method to estimate a real world distribution accurately with the Recovery Theorem. The previous studies propose the methods to estimate the real world distribution, whereas they do not investigate on the estimation accuracy. Hence, we test the effectiveness of the Tikhonov method used by Audrino et al. (2015) in the numerical analysis with hypothetical data. We propose a new method to derive the more accurate solution by configuring the regularization term considering prior information and compare it with the Tikhonov method. Moreover, we discuss regularization parameter selection to get the accurate real world distribution. We find the following three points through the numerical analysis. (1) To stabilize the solution by introducing regularization term is an effective method in terms of estimating a real world distribution with the Recovery Theorem. (2) Proposed method can estimate a real world distribution more accurately than the Tikhonov method. (3) We can offer the appropriate solutions even if the number of maturities is less than that of states.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44486401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, baseball is formulated as a finite Markov game with approximately 6.45 million states. We give an effective dynamic programming algorithm which computes Markov perfect equilibria and the value functions of the game for both teams in 2 second per game. Optimal decision making can be found depending on the situation—for example, for the batting team, whether batting for a hit, stealing a base or sacrifice bunting will maximize their win percentage, or for the fielding team, whether to pitch to or intentionally walk a batter, yields optimal results. In addition, our algorithm makes it possible to compute the optimal batting order, in consideration of strategy optimization such as a sacrifice bunt or a stolen base. The authors believe that this baseball model is also useful as a benchmark instance for evaluating the performances of (multi-agent) Reinforcement Learning methods.
{"title":"A DYNAMIC PROGRAMMING ALGORITHM FOR OPTIMIZING BASEBALL STRATEGIES","authors":"Akifumi Kira, Keisuke Inakawa, Toshiharu Fujita","doi":"10.15807/JORSJ.62.64","DOIUrl":"https://doi.org/10.15807/JORSJ.62.64","url":null,"abstract":"In this paper, baseball is formulated as a finite Markov game with approximately 6.45 million states. We give an effective dynamic programming algorithm which computes Markov perfect equilibria and the value functions of the game for both teams in 2 second per game. Optimal decision making can be found depending on the situation—for example, for the batting team, whether batting for a hit, stealing a base or sacrifice bunting will maximize their win percentage, or for the fielding team, whether to pitch to or intentionally walk a batter, yields optimal results. In addition, our algorithm makes it possible to compute the optimal batting order, in consideration of strategy optimization such as a sacrifice bunt or a stolen base. The authors believe that this baseball model is also useful as a benchmark instance for evaluating the performances of (multi-agent) Reinforcement Learning methods.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.62.64","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48615475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the knapsack sharing problem (KSP), formulated previously, we considered a game-theoretic situation in which two or more players (agents) compete for their share of capacity in a knapsack with their respective sets of items. As an extension of this problem, we formulate the extended knapsack sharing problem (XKSP). This is actually a family of KSP-like problems, and we present a dynamic programmingbased (DP-based), pseudo-polynomial time algorithm to solve XKSP to optimality in a unified way. XKSP is shown to be NP-hard, but due to the existence of this pseudo-polynomial time algorithm, it is only weakly NP-hard. Next, we develop an algorithm to solve the problem approximately in polynomial time by decomposing it into a series of subproblems. Furthermore, we introduce a scaling factor into the DP computation to obtain a fully polynomial time approximation scheme (FPTAS) for XKSP with two agents. Extension to the case of more than two agents is discussed, together with a non-DP-based PTAS.
{"title":"DP-BASED ALGORITHM AND FPTAS FOR THE KNAPSACK SHARING AND RELATED PROBLEMS","authors":"S. Kataoka, Takeo Yamada","doi":"10.15807/JORSJ.62.1","DOIUrl":"https://doi.org/10.15807/JORSJ.62.1","url":null,"abstract":"In the knapsack sharing problem (KSP), formulated previously, we considered a game-theoretic situation in which two or more players (agents) compete for their share of capacity in a knapsack with their respective sets of items. As an extension of this problem, we formulate the extended knapsack sharing problem (XKSP). This is actually a family of KSP-like problems, and we present a dynamic programmingbased (DP-based), pseudo-polynomial time algorithm to solve XKSP to optimality in a unified way. XKSP is shown to be NP-hard, but due to the existence of this pseudo-polynomial time algorithm, it is only weakly NP-hard. Next, we develop an algorithm to solve the problem approximately in polynomial time by decomposing it into a series of subproblems. Furthermore, we introduce a scaling factor into the DP computation to obtain a fully polynomial time approximation scheme (FPTAS) for XKSP with two agents. Extension to the case of more than two agents is discussed, together with a non-DP-based PTAS.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.62.1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43247876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In revenue management, there are models which aim to maximize revenue by controlling policy for uncertain demands throughout a booking horizon. The models are called dynamic models. One of the applications of the dynamic models is reservation system which offers available seats for customers’ requests. Recently, the system has allowed us to choose our booking seat position. However, the dynamic models in revenue management have not been included customers’ selection behavior for seating position. This paper proposes choice-based seating position model with undistinguished multi-lines that is a dynamic model considered with the customers’ selection behavior for seating positions. Approximate solutions for this model are calculated by Choice-based Deterministic Linear Programming (CDLP) and decomposition approximation which are used in choice-based network revenue management models. This paper suggests that CDLP is more effective than decomposition approximation for the choice-based seating position model, even through some reports in revenue management suggested that decomposition approximation could derive higher revenue than CDLP in their models.
{"title":"CHOICE-BASED SEATING POSITION MODEL WITH UNDISTINGUISHED MULTI-LINES IN REVENUE MANAGEMENT","authors":"Yu Ogasawara, Masamichi Kon","doi":"10.15807/JORSJ.62.37","DOIUrl":"https://doi.org/10.15807/JORSJ.62.37","url":null,"abstract":"In revenue management, there are models which aim to maximize revenue by controlling policy for uncertain demands throughout a booking horizon. The models are called dynamic models. One of the applications of the dynamic models is reservation system which offers available seats for customers’ requests. Recently, the system has allowed us to choose our booking seat position. However, the dynamic models in revenue management have not been included customers’ selection behavior for seating position. This paper proposes choice-based seating position model with undistinguished multi-lines that is a dynamic model considered with the customers’ selection behavior for seating positions. Approximate solutions for this model are calculated by Choice-based Deterministic Linear Programming (CDLP) and decomposition approximation which are used in choice-based network revenue management models. This paper suggests that CDLP is more effective than decomposition approximation for the choice-based seating position model, even through some reports in revenue management suggested that decomposition approximation could derive higher revenue than CDLP in their models.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44413760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Variable selection is the process of finding variables relevant to a given dataset in model construction. One of the techniques for variable selection is exponentially evaluating many models with a goodness-of-fit (GOF) measure, for example, Akaike information criterion (AIC). The model with the lowest GOF value is considered as the best model. We proposed a mixed integer nonlinear programming approach to AIC minimization for linear regression and showed that the approach outperformed existing approaches in terms of computational time [13]. In this study, we apply the approach in [13] to AIC minimization for logistic regression and explain that a few of the techniques developed previously [13], for example, relaxation and a branching rule, can be used for the AIC minimization. The proposed approach requires solving relaxation problems, which are unconstrained convex problems. We apply an iterative method with an effective initial guess to solve these problems. We implement the proposed approach via SCIP, which is a noncommercial optimization software and a branch-and-bound framework. We compare the proposed approach with a piecewise linear approximation approach developed by Sato and others [16]. The results of computational experiments show that the proposed approach finds the model with the lowest AIC value if the number of candidates for variables is 45 or lower.
{"title":"APPLICATION OF A MIXED INTEGER NONLINEAR PROGRAMMING APPROACH TO VARIABLE SELECTION IN LOGISTIC REGRESSION","authors":"K. Kimura","doi":"10.15807/JORSJ.62.15","DOIUrl":"https://doi.org/10.15807/JORSJ.62.15","url":null,"abstract":"Variable selection is the process of finding variables relevant to a given dataset in model construction. One of the techniques for variable selection is exponentially evaluating many models with a goodness-of-fit (GOF) measure, for example, Akaike information criterion (AIC). The model with the lowest GOF value is considered as the best model. We proposed a mixed integer nonlinear programming approach to AIC minimization for linear regression and showed that the approach outperformed existing approaches in terms of computational time [13]. In this study, we apply the approach in [13] to AIC minimization for logistic regression and explain that a few of the techniques developed previously [13], for example, relaxation and a branching rule, can be used for the AIC minimization. The proposed approach requires solving relaxation problems, which are unconstrained convex problems. We apply an iterative method with an effective initial guess to solve these problems. We implement the proposed approach via SCIP, which is a noncommercial optimization software and a branch-and-bound framework. We compare the proposed approach with a piecewise linear approximation approach developed by Sato and others [16]. The results of computational experiments show that the proposed approach finds the model with the lowest AIC value if the number of candidates for variables is 45 or lower.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49561130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：