Cristian Gatu - Academia.edu (original) (raw)
Papers by Cristian Gatu
Computational Statistics & Data Analysis, Mar 1, 2014
Computing in Economics and Finance, 2002
Statistical model selection problems arises in diverse areas. Some of the selection methods have ... more Statistical model selection problems arises in diverse areas. Some of the selection methods have exponential complexities and thus, are computationally demanding. The purpose of this thesis is to propose computationally efficient and numerical reliable algorithms used in statistical model selection. Particular emphasis is given to the computationally intensive model selection strategies which evaluate regression trees and have combinatorial solutions. The computational efficiency of the proposed algorithms has been investigated by detailed complexity analysis. Parallel algorithms to compute all possible subset regression models are designed, implemented and analyzed. A branch-and-bound strategy that computes the best-subset regression models corresponding to each number of variables is proposed. A heuristic version of this strategy is developed. It is based on a tolerance parameter when deciding to cut a subtree. Experimental results which support the theoretical results of the new ...
Comprehensive R Archive Network (CRAN), Feb 7, 2021
International Journal of Computer Mathematics, 2016
L'utilisation des écrans tactiles et en particulier les claviers logiciels est extrêmement compli... more L'utilisation des écrans tactiles et en particulier les claviers logiciels est extrêmement compliquée pour les nonvoyants qui manquent de repères physiques sur ce type d'appareil. Nous proposons dans cet article une solution clavier logicielle qui propose une liste de mots pouvant correspondre au mot recherché à partir de frappes approximatives des utilisateurs non-voyants. Cette technique évite ainsi à l'utilisateur d'explorer le clavier en permanence pour trouver précisément les caractères à saisir. Une première évaluation nous permet de montrer que notre système est efficace pour les mots de plus de quatre caractères. Il permet aussi d'éviter certains types d'erreur de frappe. Mots Clés Saisie de texte ; déficience visuelle ; écran tactile ; dispositifs mobiles ; clavier logiciel ; système déductif.
COMPSTAT 2008
ABSTRACT A strategy is proposed for finding the most significant linear regression submodel for f... more ABSTRACT A strategy is proposed for finding the most significant linear regression submodel for fat-structure data, that is when the number of variables n exceeds the number of available observations m. The method consists of two stages. First, a heuristic is employed to preselect a number of variables n S such that n S ≤m. The second stage performs an exhaustive search on the reduced list of variables. It employs a regression tree structure that generates all possible subset models. Non-optimal subtrees are pruned using a branch-and-bound device. Cross validation experiments on a real biomedical dataset are presented and analyzed.
Advances in Computational Management Science, 2007
Optimisation Models and Methods: A Supply Chain Network Perspective for Electric Power Generation... more Optimisation Models and Methods: A Supply Chain Network Perspective for Electric Power Generation, Supply, Transmission, and Consumption.- Worst-Case Modelling for Management Decisions under Incomplete Information, with Application to Electricity Spot Markets.- An Approximate Winner Determination Algorithm for Hybrid Procurement Mechanisms in Logistics.- Proximal-ACCPM: A Versatile Oracle Based Optimization Method.- A Survey of Different Integer Programming Formulations of the Travelling Salesman Problem.- Econometric Modelling and Prediction: The Threshold Accepting Optimization Algorithm in Economics and Statistics.- The Autocorrelation Functions in SETARMA Models.- Trend Estimation and De-Trending.- Non-Dyadic Wavelet Analysis.- Measuring Core Inflation by Multivariate Structural Time Series Models.- Financial Modelling: Random Portfolios for Performance Measurement.- Real Options with Random Controls, Rare Events, and Risk-to-Ruin.
Computational Statistics & Data Analysis, 2010
Second special issue on statistical algorithms and software Computational Statistics and Data Ana... more Second special issue on statistical algorithms and software Computational Statistics and Data Analysis has long published articles on algorithms and software. Recently it published its first Special Issue on Statistical Algorithms and Software (Gatu et al., 2007a). The 15 papers in the issue included, among others: Gatu et al. (2007b) on all possible regression submodels;
Computational Statistics & Data Analysis, 2007
Computational Management Science, 2005
Algorithms for computing the subset Vector Autoregressive (VAR) models are proposed. These algori... more Algorithms for computing the subset Vector Autoregressive (VAR) models are proposed. These algorithms can be used to choose a subset of the most statistically-significant variables of a VAR model. In such cases, the selection criteria are based on the residual sum of squares or the estimated residual covariance matrix. The VAR model with zero coefficient restrictions is formulated as a Seemingly Unrelated Regressions (SUR) model. Furthermore, the SUR model is transformed into one of smaller size, where the exogenous matrices comprise columns of a triangular matrix. Efficient algorithms which exploit the common columns of the exogenous matrices, sparse structure of the variance-covariance of the disturbances and special properties of the SUR models are investigated. The main computational tool of the selection strategies is the generalized QR decomposition and its modification.
Journal of Computational and Graphical Statistics, 2010
A new algorithm to solve exact least trimmed squares (LTS) regression is presented. The adding ro... more A new algorithm to solve exact least trimmed squares (LTS) regression is presented. The adding row algorithm (ARA) extends existing methods that compute the LTS estimator for a given coverage. It employs a tree-based strategy to compute a set of LTS regressors for a range of coverage values. Thus, prior knowledge of the optimal coverage is not required. New nodes in the regression tree are generated by updating the QR decomposition of the data matrix after adding one observation to the regression model. The ARA is enhanced by employing a branch and bound strategy. The branch and bound algorithm is an exhaustive algorithm that uses a cutting test to prune nonoptimal subtrees. It significantly improves over the ARA in computational performance. Observation preordering throughout the traversal of the regression tree is investigated. A computationally efficient and numerically stable calculation of the bounds using Givens rotations is designed around the QR decomposition, avoiding the need to explicitly update the triangular factor when an observation is added. This reduces the overall computational load of the preordering device by approximately half. A solution is proposed to allow preordering when the model is underdetermined. It employs pseudo-orthogonal rotations to downdate the QR decomposition. The strategies are illustrated by example. Experimental results confirm the computational efficiency of the proposed algorithms. Supplemental materials (R package and formal proofs) are available online.
A regression graph to enumerate and evaluate all possible subset regression models is introduced.... more A regression graph to enumerate and evaluate all possible subset regression models is introduced. The graph is a generalization of a regression tree. All the spanning trees of the graph are minimum spanning trees and provide an optimal computational procedure for generating all possible submodels. Each minimum spanning tree has a different structure and characteristics. An adaptation of a branch-and-bound algorithm which computes the best-subset models using the regression graph framework is proposed. Experimental results and comparison with an existing method based on a regression tree are presented and discussed.
An efficient branch-and-bound algorithm for computing the best-subset regression models is propos... more An efficient branch-and-bound algorithm for computing the best-subset regression models is proposed. The algorithm avoids the computation of the whole regression tree that generates all possible subset models. It is formally shown that if the branch-and-bound test holds, then the current subtree together with its right-hand side subtrees are cut. This reduces significantly the computational burden of the proposed algorithm when compared to an existing leaps-and-bounds method which generates two trees. Specifically, the proposed algorithm, which is based on orthogonal transformations, outperforms by O(n 3) the leapsand-bounds strategy. The criteria used in identifying the best subsets are based on monotone functions of the residual sum of squares (RSS) such as R 2, adjusted R 2, mean square error of prediction, and Cp. Strategies and heuristics that improve the computational performance of the proposed algorithm are investigated. A computationally efficient heuristic version of the b...
Journal of Statistical Software
An R package for computing the all-subsets regression problem is presented. The proposed algorith... more An R package for computing the all-subsets regression problem is presented. The proposed algorithms are based on computational strategies recently developed. A novel algorithm for the best-subset regression problem selects subset models based on a predetermined criterion. The package user can choose from exact and from approximation algorithms. The core of the package is written in C++ and provides an efficient implementation of all the underlying numerical computations. A case study and benchmark results illustrate the usage and the computational efficiency of the package. Originally published in the Journal of Statistical Software (Hofmann et al. 2020).
Computational Economics, 2016
A new strategy for deriving the three-stage least squares (3SLS) estimator of the simultaneous eq... more A new strategy for deriving the three-stage least squares (3SLS) estimator of the simultaneous equations model (SEM) is proposed. The main numerical tool employed is the generalized singular value decomposition. This provides a numerical estimation procedure which can tackle efficiently the particular case when the variance-covariance matrix is singular. The proposed algorithm is further adapted to deal with the special case of the block-recursive SEM. The block diagonal structure of the variance-covariance matrix is exploited in order to reduce significantly the computational burden. Experimental results are presented to illustrate the computational efficiency of the new estimation strategy when compared with the equivalent method that ignores the block-recursive structure of the SEM.
S Financial networks Anna Nagurney, University of Massachusetts, USA In this tutorial we discuss ... more S Financial networks Anna Nagurney, University of Massachusetts, USA In this tutorial we discuss models, qualitative properties, as well as algorithms for the study and computation of a variety of nancial equilibrium problems which can be visualized as network problems. In particular, we identify the network structure of the individual portfolio optimization problems faced by each sector, construct the network of the nancial economy in equilibrium, and also discuss decomposition procedures which resolve the largescale problems into network subproblems of special structure, each of which can be solved simultaneously and in closed form. In addition, we provide dynamic adjustment processes and propose dicrete-time algorithms for the tracking of the trajectories. Applications of nancial networks to single-country problems and international problems will be discussed. In addition, some recent work on multicriteria decision-making within this context will be highlighted. Portfolio construction, index tracking and optimization: computational issues Stavros Siokos, Portfolio Construction Group, Schroder Salomon Smith Barney, London, UK Issues in creating strategic-integrated asset/liability management Jerome L. Kreuser, The RisKontrol Group GmbH, Bern Switzerland In 1996 the World Bank undertook a research project to develop strategic-integrated asset/liability management tools for the analysis of risk for central banks and ministries of nance in developing countries. These tools required the research of some new technology as traditional tools were unsatisfactory for the kinds of analysis required. This talk will discuss the results of that work including the use of dynamic stochastic programming models, the development of an integrated environment, technology transfer, and implementation issues. Swarm and huscarls: a case-study in high-performance computing in nancial institutions Cyril Godart, Paribas, London, UK Through the presentation of SWARM and Huscarls, a PC based parallel system, we present some re ections and aspects of high performance computing in nancial institutions and investment banks. We show that this kind of parallel architecture is suitable for these 4 institutions because it is cost e ective compared with massive parallel systems. But taking full advantage of this type of architecture goes through a new type of parallel library with higher level functionalities than the message-passing capability. The library we describe in this article inherit from the recent concepts in computer science which are related to objectoriented concepts, template coding and reactive applications. The right combination of all these aspects leads to astonishing e ciency in term of ease to parallel code development. We shall highlight the main points which should be taken into account when developing these kinds of high-level parallel libraries, which in a previous article we described as \parallel event-driven applications". Concretely, this means that the development of the parallel library can keep the pace with the sequential one with very few persons dedicated to this speci c coding. One of the other feature of the system we are describing is that it is running in live on traders and researchers machines and more strikingly on machines running the Microsoft Windows NT operating system. We show why and how HPC is introduced in institutions which are increasingly demanding on computer power. Volatility forecasting using genetic programming Olivier V. Pictet, Dynamic Asset Management, Geneva, Switzerland, Oliver Masutti and Gilles Zumbach, Olsen & Associates, Zurich, Switzerland This study uses Genetic Programming (GP) to discover new types of volatility forecasting models for nancial time series. We improve on the standard GP approach by introducing types in the GP trees, and by optimizing the program constants with a gradient search. These two modi cations improve signi cantly the convergence properties of the algorithm. Moreover, the typing is used to impose a well de ned parity of the solutions so that only meaningful volatility models are build from the price time series. The volatility models are searched with data sampled at hourly frequency, and the optimization criterion is based on the in-sample forecasting quality of the average daily volatility. The heterogeneity of the nancial markets is introduced into the models by price change information measured at di erent frequencies. Finally, the results are compared to standard models like GARCH(1,1). Multivariate GARCH: solving hard maximum likelihood problems using a genetic algorithm Patrick Burns,Global Quantitative Research, Schroder Salomon Smith Barney, London, UK The Multivariate BEKK GARCH model provides a setting of an optimisation of a differentiable function that can have multiple local minima and hundreds of parameters. The strategy is to use a genetic algorithm to nd a solution that is very close to the optimum, and then use a derivative-based…
Computational Statistics & Data Analysis, Mar 1, 2014
Computing in Economics and Finance, 2002
Statistical model selection problems arises in diverse areas. Some of the selection methods have ... more Statistical model selection problems arises in diverse areas. Some of the selection methods have exponential complexities and thus, are computationally demanding. The purpose of this thesis is to propose computationally efficient and numerical reliable algorithms used in statistical model selection. Particular emphasis is given to the computationally intensive model selection strategies which evaluate regression trees and have combinatorial solutions. The computational efficiency of the proposed algorithms has been investigated by detailed complexity analysis. Parallel algorithms to compute all possible subset regression models are designed, implemented and analyzed. A branch-and-bound strategy that computes the best-subset regression models corresponding to each number of variables is proposed. A heuristic version of this strategy is developed. It is based on a tolerance parameter when deciding to cut a subtree. Experimental results which support the theoretical results of the new ...
Comprehensive R Archive Network (CRAN), Feb 7, 2021
International Journal of Computer Mathematics, 2016
L'utilisation des écrans tactiles et en particulier les claviers logiciels est extrêmement compli... more L'utilisation des écrans tactiles et en particulier les claviers logiciels est extrêmement compliquée pour les nonvoyants qui manquent de repères physiques sur ce type d'appareil. Nous proposons dans cet article une solution clavier logicielle qui propose une liste de mots pouvant correspondre au mot recherché à partir de frappes approximatives des utilisateurs non-voyants. Cette technique évite ainsi à l'utilisateur d'explorer le clavier en permanence pour trouver précisément les caractères à saisir. Une première évaluation nous permet de montrer que notre système est efficace pour les mots de plus de quatre caractères. Il permet aussi d'éviter certains types d'erreur de frappe. Mots Clés Saisie de texte ; déficience visuelle ; écran tactile ; dispositifs mobiles ; clavier logiciel ; système déductif.
COMPSTAT 2008
ABSTRACT A strategy is proposed for finding the most significant linear regression submodel for f... more ABSTRACT A strategy is proposed for finding the most significant linear regression submodel for fat-structure data, that is when the number of variables n exceeds the number of available observations m. The method consists of two stages. First, a heuristic is employed to preselect a number of variables n S such that n S ≤m. The second stage performs an exhaustive search on the reduced list of variables. It employs a regression tree structure that generates all possible subset models. Non-optimal subtrees are pruned using a branch-and-bound device. Cross validation experiments on a real biomedical dataset are presented and analyzed.
Advances in Computational Management Science, 2007
Optimisation Models and Methods: A Supply Chain Network Perspective for Electric Power Generation... more Optimisation Models and Methods: A Supply Chain Network Perspective for Electric Power Generation, Supply, Transmission, and Consumption.- Worst-Case Modelling for Management Decisions under Incomplete Information, with Application to Electricity Spot Markets.- An Approximate Winner Determination Algorithm for Hybrid Procurement Mechanisms in Logistics.- Proximal-ACCPM: A Versatile Oracle Based Optimization Method.- A Survey of Different Integer Programming Formulations of the Travelling Salesman Problem.- Econometric Modelling and Prediction: The Threshold Accepting Optimization Algorithm in Economics and Statistics.- The Autocorrelation Functions in SETARMA Models.- Trend Estimation and De-Trending.- Non-Dyadic Wavelet Analysis.- Measuring Core Inflation by Multivariate Structural Time Series Models.- Financial Modelling: Random Portfolios for Performance Measurement.- Real Options with Random Controls, Rare Events, and Risk-to-Ruin.
Computational Statistics & Data Analysis, 2010
Second special issue on statistical algorithms and software Computational Statistics and Data Ana... more Second special issue on statistical algorithms and software Computational Statistics and Data Analysis has long published articles on algorithms and software. Recently it published its first Special Issue on Statistical Algorithms and Software (Gatu et al., 2007a). The 15 papers in the issue included, among others: Gatu et al. (2007b) on all possible regression submodels;
Computational Statistics & Data Analysis, 2007
Computational Management Science, 2005
Algorithms for computing the subset Vector Autoregressive (VAR) models are proposed. These algori... more Algorithms for computing the subset Vector Autoregressive (VAR) models are proposed. These algorithms can be used to choose a subset of the most statistically-significant variables of a VAR model. In such cases, the selection criteria are based on the residual sum of squares or the estimated residual covariance matrix. The VAR model with zero coefficient restrictions is formulated as a Seemingly Unrelated Regressions (SUR) model. Furthermore, the SUR model is transformed into one of smaller size, where the exogenous matrices comprise columns of a triangular matrix. Efficient algorithms which exploit the common columns of the exogenous matrices, sparse structure of the variance-covariance of the disturbances and special properties of the SUR models are investigated. The main computational tool of the selection strategies is the generalized QR decomposition and its modification.
Journal of Computational and Graphical Statistics, 2010
A new algorithm to solve exact least trimmed squares (LTS) regression is presented. The adding ro... more A new algorithm to solve exact least trimmed squares (LTS) regression is presented. The adding row algorithm (ARA) extends existing methods that compute the LTS estimator for a given coverage. It employs a tree-based strategy to compute a set of LTS regressors for a range of coverage values. Thus, prior knowledge of the optimal coverage is not required. New nodes in the regression tree are generated by updating the QR decomposition of the data matrix after adding one observation to the regression model. The ARA is enhanced by employing a branch and bound strategy. The branch and bound algorithm is an exhaustive algorithm that uses a cutting test to prune nonoptimal subtrees. It significantly improves over the ARA in computational performance. Observation preordering throughout the traversal of the regression tree is investigated. A computationally efficient and numerically stable calculation of the bounds using Givens rotations is designed around the QR decomposition, avoiding the need to explicitly update the triangular factor when an observation is added. This reduces the overall computational load of the preordering device by approximately half. A solution is proposed to allow preordering when the model is underdetermined. It employs pseudo-orthogonal rotations to downdate the QR decomposition. The strategies are illustrated by example. Experimental results confirm the computational efficiency of the proposed algorithms. Supplemental materials (R package and formal proofs) are available online.
A regression graph to enumerate and evaluate all possible subset regression models is introduced.... more A regression graph to enumerate and evaluate all possible subset regression models is introduced. The graph is a generalization of a regression tree. All the spanning trees of the graph are minimum spanning trees and provide an optimal computational procedure for generating all possible submodels. Each minimum spanning tree has a different structure and characteristics. An adaptation of a branch-and-bound algorithm which computes the best-subset models using the regression graph framework is proposed. Experimental results and comparison with an existing method based on a regression tree are presented and discussed.
An efficient branch-and-bound algorithm for computing the best-subset regression models is propos... more An efficient branch-and-bound algorithm for computing the best-subset regression models is proposed. The algorithm avoids the computation of the whole regression tree that generates all possible subset models. It is formally shown that if the branch-and-bound test holds, then the current subtree together with its right-hand side subtrees are cut. This reduces significantly the computational burden of the proposed algorithm when compared to an existing leaps-and-bounds method which generates two trees. Specifically, the proposed algorithm, which is based on orthogonal transformations, outperforms by O(n 3) the leapsand-bounds strategy. The criteria used in identifying the best subsets are based on monotone functions of the residual sum of squares (RSS) such as R 2, adjusted R 2, mean square error of prediction, and Cp. Strategies and heuristics that improve the computational performance of the proposed algorithm are investigated. A computationally efficient heuristic version of the b...
Journal of Statistical Software
An R package for computing the all-subsets regression problem is presented. The proposed algorith... more An R package for computing the all-subsets regression problem is presented. The proposed algorithms are based on computational strategies recently developed. A novel algorithm for the best-subset regression problem selects subset models based on a predetermined criterion. The package user can choose from exact and from approximation algorithms. The core of the package is written in C++ and provides an efficient implementation of all the underlying numerical computations. A case study and benchmark results illustrate the usage and the computational efficiency of the package. Originally published in the Journal of Statistical Software (Hofmann et al. 2020).
Computational Economics, 2016
A new strategy for deriving the three-stage least squares (3SLS) estimator of the simultaneous eq... more A new strategy for deriving the three-stage least squares (3SLS) estimator of the simultaneous equations model (SEM) is proposed. The main numerical tool employed is the generalized singular value decomposition. This provides a numerical estimation procedure which can tackle efficiently the particular case when the variance-covariance matrix is singular. The proposed algorithm is further adapted to deal with the special case of the block-recursive SEM. The block diagonal structure of the variance-covariance matrix is exploited in order to reduce significantly the computational burden. Experimental results are presented to illustrate the computational efficiency of the new estimation strategy when compared with the equivalent method that ignores the block-recursive structure of the SEM.
S Financial networks Anna Nagurney, University of Massachusetts, USA In this tutorial we discuss ... more S Financial networks Anna Nagurney, University of Massachusetts, USA In this tutorial we discuss models, qualitative properties, as well as algorithms for the study and computation of a variety of nancial equilibrium problems which can be visualized as network problems. In particular, we identify the network structure of the individual portfolio optimization problems faced by each sector, construct the network of the nancial economy in equilibrium, and also discuss decomposition procedures which resolve the largescale problems into network subproblems of special structure, each of which can be solved simultaneously and in closed form. In addition, we provide dynamic adjustment processes and propose dicrete-time algorithms for the tracking of the trajectories. Applications of nancial networks to single-country problems and international problems will be discussed. In addition, some recent work on multicriteria decision-making within this context will be highlighted. Portfolio construction, index tracking and optimization: computational issues Stavros Siokos, Portfolio Construction Group, Schroder Salomon Smith Barney, London, UK Issues in creating strategic-integrated asset/liability management Jerome L. Kreuser, The RisKontrol Group GmbH, Bern Switzerland In 1996 the World Bank undertook a research project to develop strategic-integrated asset/liability management tools for the analysis of risk for central banks and ministries of nance in developing countries. These tools required the research of some new technology as traditional tools were unsatisfactory for the kinds of analysis required. This talk will discuss the results of that work including the use of dynamic stochastic programming models, the development of an integrated environment, technology transfer, and implementation issues. Swarm and huscarls: a case-study in high-performance computing in nancial institutions Cyril Godart, Paribas, London, UK Through the presentation of SWARM and Huscarls, a PC based parallel system, we present some re ections and aspects of high performance computing in nancial institutions and investment banks. We show that this kind of parallel architecture is suitable for these 4 institutions because it is cost e ective compared with massive parallel systems. But taking full advantage of this type of architecture goes through a new type of parallel library with higher level functionalities than the message-passing capability. The library we describe in this article inherit from the recent concepts in computer science which are related to objectoriented concepts, template coding and reactive applications. The right combination of all these aspects leads to astonishing e ciency in term of ease to parallel code development. We shall highlight the main points which should be taken into account when developing these kinds of high-level parallel libraries, which in a previous article we described as \parallel event-driven applications". Concretely, this means that the development of the parallel library can keep the pace with the sequential one with very few persons dedicated to this speci c coding. One of the other feature of the system we are describing is that it is running in live on traders and researchers machines and more strikingly on machines running the Microsoft Windows NT operating system. We show why and how HPC is introduced in institutions which are increasingly demanding on computer power. Volatility forecasting using genetic programming Olivier V. Pictet, Dynamic Asset Management, Geneva, Switzerland, Oliver Masutti and Gilles Zumbach, Olsen & Associates, Zurich, Switzerland This study uses Genetic Programming (GP) to discover new types of volatility forecasting models for nancial time series. We improve on the standard GP approach by introducing types in the GP trees, and by optimizing the program constants with a gradient search. These two modi cations improve signi cantly the convergence properties of the algorithm. Moreover, the typing is used to impose a well de ned parity of the solutions so that only meaningful volatility models are build from the price time series. The volatility models are searched with data sampled at hourly frequency, and the optimization criterion is based on the in-sample forecasting quality of the average daily volatility. The heterogeneity of the nancial markets is introduced into the models by price change information measured at di erent frequencies. Finally, the results are compared to standard models like GARCH(1,1). Multivariate GARCH: solving hard maximum likelihood problems using a genetic algorithm Patrick Burns,Global Quantitative Research, Schroder Salomon Smith Barney, London, UK The Multivariate BEKK GARCH model provides a setting of an optimisation of a differentiable function that can have multiple local minima and hundreds of parameters. The strategy is to use a genetic algorithm to nd a solution that is very close to the optimum, and then use a derivative-based…