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108
Process Mining Based on Regions of Languages
"... Abstract. In this paper we give an overview, how to apply region based methods for the synthesis of Petri nets from languages to process mining. The research domain of process mining aims at constructing a process model from an event log, such that the process model can reproduce the log, and does n ..."
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Abstract. In this paper we give an overview, how to apply region based methods for the synthesis of Petri nets from languages to process mining. The research domain of process mining aims at constructing a process model from an event log, such that the process model can reproduce the log, and does not allow for much more behaviour than shown in the log. We here consider Petri nets to represent process models. Event logs can be interpreted as finite languages. Region based synthesis methods can be used to construct a Petri net from a language generating the minimal net behaviour including the given language. Therefore, it seems natural to apply such methods in the process mining domain. There are several different region based methods in literature yielding different Petri nets. We adapt these methods to the process mining domain and compare them concerning efficiency and usefulness of the resulting Petri net. 1
Bayesian support vector regression using a unified loss function
 IEEE Transactions on Neural Networks
, 2004
"... In this paper, we use a unified loss function, called the soft insensitive loss function, for Bayesian support vector regression. We follow standard Gaussian processes for regression to set up the Bayesian framework, in which the unified loss function is used in the likelihood evaluation. Under this ..."
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Cited by 20 (2 self)
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In this paper, we use a unified loss function, called the soft insensitive loss function, for Bayesian support vector regression. We follow standard Gaussian processes for regression to set up the Bayesian framework, in which the unified loss function is used in the likelihood evaluation. Under this framework, the maximum a posteriori estimate of the function values corresponds to the solution of an extended support vector regression problem. The overall approach has the merits of support vector regression such as convex quadratic programming and sparsity in solution representation. It also has the advantages of Bayesian methods for model adaptation and error bars of its predictions. Experimental results on simulated and realworld data sets indicate that the approach works well even on large data sets.
The InteriorPoint Revolution in Constrained Optimization
 of Appl. Optim
, 1998
"... Interior methods are a central, striking feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interiorpoint techniques were widely used during the 1960s to solve nonlinearly constrained problems. However, their use for linear ..."
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Interior methods are a central, striking feature of the constrained optimization landscape today, but it was not always so. Primarily in the form of barrier methods, interiorpoint techniques were widely used during the 1960s to solve nonlinearly constrained problems. However, their use for linear programming was not even contemplated because of the total dominance of the simplex method. During the 1970s, barrier methods were superseded by newly emerging, apparently more efficient alternatives such as augmented Lagrangian and sequential quadratic programming methods. By the early 1980s, barrier methods were almost universally regarded as a closed chapter in the history of optimization. This picture changed dramatically in the mid1980s. In 1984, Karmarkar announced a fast polynomialtime interior method for linear programming; in 1985, a formal connection was established between his method and classical barrier methods. Since then, the new incarnations of interior methods ha...
Modelling Compression with Discourse Constraints
, 2007
"... Sentence compression holds promise for many applications ranging from summarisation to subtitle generation. The task is typically performed on isolated sentences without taking the surrounding context into account, even though most applications would operate over entire documents. In this paper we p ..."
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Cited by 20 (3 self)
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Sentence compression holds promise for many applications ranging from summarisation to subtitle generation. The task is typically performed on isolated sentences without taking the surrounding context into account, even though most applications would operate over entire documents. In this paper we present a discourse informed model which is capable of producing document compressions that are coherent and informative. Our model is inspired by theories of local coherence and formulated within the framework of Integer Linear Programming. Experimental results show significant improvements over a stateoftheart discourse agnostic approach.
Optimal Power Control in Interference Limited Fading Wireless Channels with Outage Probability Specifications
, 2000
"... We propose a new method of power control for interference limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explictly takes into account the statistical variation of both the received signal and interference power, and optimally allocates powe ..."
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Cited by 16 (2 self)
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We propose a new method of power control for interference limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explictly takes into account the statistical variation of both the received signal and interference power, and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair. We establish several results for this type of problem. For the case
Regression Models for Ordinal Data: A Machine Learning Approach
, 1999
"... In contrast to the standard machine learning tasks of classification and metric regression we investigate the problem of predicting variables of ordinal scale, a setting referred to as ordinal regression. The task of ordinal regression arises frequently in the social sciences and in information retr ..."
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Cited by 16 (3 self)
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In contrast to the standard machine learning tasks of classification and metric regression we investigate the problem of predicting variables of ordinal scale, a setting referred to as ordinal regression. The task of ordinal regression arises frequently in the social sciences and in information retrieval where human preferences play a major role. Also many multiclass problems are really problems of ordinal regression due to an ordering of the classes. Although the problem is rather novel to the Machine Learning Community it has been widely considered in Statistics before. All the statistical methods rely on a probability model of a latent (unobserved) variable and on the condition of stochastic ordering. In this paper we develop a distribution independent formulation of the problem and give uniform bounds for our risk functional. The main difference to classification is the restriction that the mapping of objects to ranks must be transitive and asymmetric. Combining our theoretical framework with results from measurement theory we present an approach that is based on a mapping from objects to scalar utility values and thus guarantees transitivity and asymmetry. Applying the principle of Structural Risk Minimization as employed in Support Vector Machines we derive a new learning algorithm based on large margin rank boundaries for the task of ordinal regression. Our method is easily extended to nonlinear utility functions. We give experimental results for an Information Retrieval task of learning the order of documents with respect to an initial query. Moreover, we show that our algorithm outperforms more naive approaches to ordinal regression such as Support Vector Classification and Support Vector Regression in the case of more than two ranks.
Frontiers of stochastically nondominated portfolios
 Econometrica
, 2003
"... Abstract. We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose mean–risk models which are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of secondorder ..."
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Cited by 15 (3 self)
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Abstract. We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution. We propose mean–risk models which are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of secondorder stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean–risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations. 1.
INTERIOR POINT METHODS FOR COMBINATORIAL OPTIMIZATION
, 1995
"... Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivale ..."
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Cited by 14 (9 self)
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Research on using interior point algorithms to solve combinatorial optimization and integer programming problems is surveyed. This paper discusses branch and cut methods for integer programming problems, a potential reduction method based on transforming an integer programming problem to an equivalent nonconvex quadratic programming problem, interior point methods for solving network flow problems, and methods for solving multicommodity flow problems, including an interior point column generation algorithm.
Interior Point Methods: Current Status And Future Directions
, 1997
"... This article provides a synopsis of the major developments in interior point methods for mathematical programming in the last thirteen years, and discusses current and future research directions in interior point methods, with a brief selective guide to the research literature. AMS Subject Classific ..."
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Cited by 13 (0 self)
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This article provides a synopsis of the major developments in interior point methods for mathematical programming in the last thirteen years, and discusses current and future research directions in interior point methods, with a brief selective guide to the research literature. AMS Subject Classification: 90C, 90C05, 90C60 Keywords: Linear Programming, Newton's Method, Interior Point Methods, Barrier Method, Semidefinite Programming, SelfConcordance, Convex Programming, Condition Numbers 1 An earlier version of this article has previously appeared in OPTIMA  Mathematical Programming Society Newsletter No. 51, 1996 2 M.I.T. Sloan School of Management, Building E40149A, Cambridge, MA 02139, USA. email: rfreund@mit.edu 3 The Institute of Statistical Mathematics, 467 MinamiAzabu, Minatoku, Tokyo 106 JAPAN. email: mizuno@ism.ac.jp INTERIOR POINT METHODS 1 1 Introduction and Synopsis The purpose of this article is twofold: to provide a synopsis of the major developments in ...
Policy teaching through reward function learning
 In Proc. 10th ACM Conf. on Electronic Commerce
, 2009
"... Policy teaching considers a Markov Decision Process setting in which an interested party aims to influence an agent’s decisions by providing limited incentives. In this paper, we consider the specific objective of inducing a prespecified desired policy. We examine both the case in which the agent’s ..."
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Cited by 12 (7 self)
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Policy teaching considers a Markov Decision Process setting in which an interested party aims to influence an agent’s decisions by providing limited incentives. In this paper, we consider the specific objective of inducing a prespecified desired policy. We examine both the case in which the agent’s reward function is known and unknown to the interested party, presenting a linear program for the former case and formulating an active, indirect elicitation method for the latter. We provide conditions for logarithmic convergence, and present a polynomial time algorithm that ensures logarithmic convergence with arbitrarily high probability. We also offer practical elicitation heuristics that can be formulated as linear programs, and demonstrate their effectiveness on a policy teaching problem in a simulated ad network setting. We extend our methods to handle partial observations and partial target policies, and provide a gametheoretic interpretation of our methods for handling strategic agents.