Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

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Principles of Model Checking

Algebraically Closed Fields- Real Closed Fields- Semi-Algebraic Sets- Algebra- Decomposition of Semi-Algebraic Sets- Elements of Topology- Quantitative Semi-algebraic Geometry- Complexity of Basic Algorithms- Cauchy Index and Applications- Real Roots- Cylindrical Decomposition Algorithm- Polynomial System Solving- Existential Theory of the Reals- Quantifier Elimination- Computing Roadmaps and Connected Components of Algebraic Sets- Computing Roadmaps and Connected Components of Semi-algebraic Sets

Algorithms in real algebraic geometry

PREFACE Introduction and Background Less Is More Huan Liu and Hiroshi Motoda Background and Basics Supervised, Unsupervised, and Semi-Supervised Feature Selection Key Contributions and Organization of the Book Looking Ahead Unsupervised Feature Selection Jennifer G. Dy Introduction Clustering Feature Selection Feature Selection for Unlabeled Data Local Approaches Summary Randomized Feature Selection David J. Stracuzzi Introduction Types of Randomizations Randomized Complexity Classes Applying Randomization to Feature Selection The Role of Heuristics Examples of Randomized Selection Algorithms Issues in Randomization Summary Causal Feature Selection Isabelle Guyon, Constantin Aliferis, and Andre Elisseeff Introduction Classical "Non-Causal" Feature Selection The Concept of Causality Feature Relevance in Bayesian Networks Causal Discovery Algorithms Examples of Applications Summary, Conclusions, and Open Problems Extending Feature Selection Active Learning of Feature Relevance Emanuele Olivetti, Sriharsha Veeramachaneni, and Paolo Avesani Introduction Active Sampling for Feature Relevance Estimation Derivation of the Sampling Benefit Function Implementation of the Active Sampling Algorithm Experiments Conclusions and Future Work A Study of Feature Extraction Techniques Based on Decision Border Estimate Claudia Diamantini and Domenico Potena Introduction Feature Extraction Based on Decision Boundary Generalities about Labeled Vector Quantizers Feature Extraction Based on Vector Quantizers Experiments Conclusions Ensemble-Based Variable Selection Using Independent Probes Eugene Tuv, Alexander Borisov, and Kari Torkkola Introduction Tree Ensemble Methods in Feature Ranking The Algorithm: Ensemble-Based Ranking against Independent Probes Experiments Discussion Efficient Incremental-Ranked Feature Selection in Massive Data Roberto Ruiz, Jesus S. Aguilar-Ruiz, and Jose C. Riquelme Introduction Related Work Preliminary Concepts Incremental Performance over Ranking Experimental Results Conclusions Weighting and Local Methods Non-Myopic Feature Quality Evaluation with (R)ReliefF Igor Kononenko and Marko Robnik Sikonja Introduction From Impurity to Relief ReliefF for Classification and RReliefF for Regression Extensions Interpretation Implementation Issues Applications Conclusion Weighting Method for Feature Selection in k-Means Joshua Zhexue Huang, Jun Xu, Michael Ng, and Yunming Ye Introduction Feature Weighting in k-Means W-k-Means Clustering Algorithm Feature Selection Subspace Clustering with k-Means Text Clustering Related Work Discussions Local Feature Selection for Classification Carlotta Domeniconi and Dimitrios Gunopulos Introduction The Curse of Dimensionality Adaptive Metric Techniques Large Margin nearest Neighbor Classifiers Experimental Comparisons Conclusions Feature Weighting through Local Learning Yijun Sun Introduction Mathematical Interpretation of Relief Iterative Relief Algorithm Extension to Multiclass Problems Online Learning Computational Complexity Experiments Conclusion Text Classification and Clustering Feature Selection for Text Classification George Forman Introduction Text Feature Generators Feature Filtering for Classification Practical and Scalable Computation A Case Study Conclusion and Future Work A Bayesian Feature Selection Score Based on Naive Bayes Models Susana Eyheramendy and David Madigan Introduction Feature Selection Scores Classification Algorithms Experimental Settings and Results Conclusion Pairwise Constraints-Guided Dimensionality Reduction Wei Tang and Shi Zhong Introduction Pairwise Constraints-Guided Feature Projection Pairwise Constraints-Guided Co-Clustering Experimental Studies Conclusion and Future Work Aggressive Feature Selection by Feature Ranking Masoud Makrehchi and Mohamed S. Kamel Introduction Feature Selection by Feature Ranking Proposed Approach to Reducing Term Redundancy Experimental Results Summary Feature Selection in Bioinformatics Feature Selection for Genomic Data Analysis Lei Yu Introduction Redundancy-Based Feature Selection Empirical Study Summary A Feature Generation Algorithm with Applications to Biological Sequence Classification Rezarta Islamaj Dogan, Lise Getoor, and W. John Wilbur Introduction Splice-Site Prediction Feature Generation Algorithm Experiments and Discussion Conclusions An Ensemble Method for Identifying Robust Features for Biomarker Discovery Diana Chan, Susan M. Bridges, and Shane C. Burgess Introduction Biomarker Discovery from Proteome Profiles Challenges of Biomarker Identification Ensemble Method for Feature Selection Feature Selection Ensemble Results and Discussion Conclusion Model Building and Feature Selection with Genomic Data Hui Zou and Trevor Hastie Introduction Ridge Regression, Lasso, and Bridge Drawbacks of the Lasso The Elastic Net The Elastic-Net Penalized SVM Sparse Eigen-Genes Summary INDEX

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Computational Methods of Feature Selection

Extending and implementing the stable model semantics

Progress in neural recording techniques has allowed the number of simultaneously recorded neurons to double approximately every 7 years, mimicking Moore's law. Emerging data analysis techniques should consider both the computational costs and the potential for more accurate models associated with this exponential growth of the number of recorded neurons. Over the last five decades, progress in neural recording techniques has allowed the number of simultaneously recorded neurons to double approximately every 7 years, mimicking Moore's law. Such exponential growth motivates us to ask how data analysis techniques are affected by progressively larger numbers of recorded neurons. Traditionally, neurons are analyzed independently on the basis of their tuning to stimuli or movement. Although tuning curve approaches are unaffected by growing numbers of simultaneously recorded neurons, newly developed techniques that analyze interactions between neurons become more accurate and more complex as the number of recorded neurons increases. Emerging data analysis techniques should consider both the computational costs and the potential for more accurate models associated with this exponential growth of the number of recorded neurons.

How advances in neural recording affect data analysis

Once we have developed an algorithm (q.v.) for solving a computational problem and analyzed its worst-case time requirements as a function of the size of its input (most usefully, in terms of the O-notation; see ALGORITHMS, ANALYSIS OF), it is inevitable to ask the question: "Can we do better?" In a typical problem, we may be able to devise new algorithms for the problem that are more and more efficient. But eventually, this line of research often seems to hit an invisible barrier, a level beyond whch improvements are very difficult, seemingly impossible, to come by. After many unsuccessful attempts, algorithm designers inevitably start to wonder if there is something inherent in the problem that makes it impossible to devise algorithms that are faster than the current one. They may try to develop mathematical techniques for proving formally that there can be no algorithm for the given problem which runs faster than the current one. Such a proof would be valuable, as it would suggest that it is futile to keep working on improved algorithms for this problem, that further improvements are certainly impossible. The realm of mathematical models and techniques for establishing such impossibility proofs is called computational complexity.

Christos H. Papadimitriou

Papers

Computational Complexity