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Linear Ranking for Linear Lasso Programs [article]

Matthias Heizmann, Jochen Hoenicke, Jan Leike, Andreas Podelski
2014 arXiv   pre-print
We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and an invariant.  ...  We present the---to the best of our knowledge---first method to synthesize termination arguments for lasso programs that uses linear arithmetic. We prove a completeness theorem.  ...  (ϕ rkBound ) For example, the lasso program depicted in Figure 1 has the ranking function f (x, y) = x with supporting invariant y ≥ 1. Linear lasso programs. Linear lasso programs.  ... 
arXiv:1401.5347v1 fatcat:h6plykinjncjxatu4yuzbiq7wy

Linear Ranking for Linear Lasso Programs [chapter]

Matthias Heizmann, Jochen Hoenicke, Jan Leike, Andreas Podelski
2013 Lecture Notes in Computer Science  
We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and an invariant.  ...  We present theto the best of our knowledge-first method to synthesize termination arguments for lasso programs that uses linear arithmetic. We prove a completeness theorem.  ...  (ϕ rkBound ) For example, the lasso program depicted in Figure 1 has the ranking function f (x, y) = x with supporting invariant y ≥ 1. Linear lasso programs. Linear lasso programs.  ... 
doi:10.1007/978-3-319-02444-8_26 fatcat:lueu7svi6nhklgnr44kxsakx4e

Ranking Function Synthesis for Linear Lasso Programs [article]

Jan Leike
2014 arXiv   pre-print
The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs.  ...  To our knowledge, the approach we propose is the most powerful technique of synthesis-based discovery of termination arguments for linear lasso programs and encompasses and enhances several methods having  ...  Furthermore, I extend my gratitude to Fabian Reiter and Pascal Raiola for their very helpful corrections and suggestions.  ... 
arXiv:1401.5351v1 fatcat:tkaut62lrbg3rfevblej2aw6hq

The Hardness of Finding Linear Ranking Functions for Lasso Programs

Amir M. Ben-Amram
2014 Electronic Proceedings in Theoretical Computer Science  
The lower bound for the rationals follows from a novel simulation of Boolean programs.  ...  Lower bounds are also given for the problem of deciding if a linear ranking-function supported by a particular form of inductive invariant exists.  ...  Ranking functions We now define linear ranking functions and the decision problem LINRF ρ , asking for the existence of a Linear Ranking Function for reachable states (the ρ reminds us of the lasso shape  ... 
doi:10.4204/eptcs.161.6 fatcat:hgvwrp5ynbc7difz4sghqnabnm

Low-Rank Regularization for Learning Gene Expression Programs

Guibo Ye, Mengfan Tang, Jian-Feng Cai, Qing Nie, Xiaohui Xie, Mark R. Muldoon
2013 PLoS ONE  
Efficient algorithms are derived to solve both the linear and nonlinear low-rank regularized problems.  ...  Imposing additional constraints with strong and biologically motivated regularizations is critical in developing reliable and effective algorithms for inferring gene expression programs.  ...  Acknowledgments We thank A Subramanian for providing us the connectivity map data and for helpful discussions. Author Contributions  ... 
doi:10.1371/journal.pone.0082146 pmid:24358148 pmcid:PMC3866120 fatcat:azsyrc4q7jdypg6sju6wbsenby

Geometric Nontermination Arguments [article]

Jan Leike, Matthias Heizmann
2016 arXiv   pre-print
For so-called linear lasso programs we can decide the existence of a geometric nontermination argument using a nonlinear algebraic ∃-constraint.  ...  We show that a deterministic conjunctive loop program with nonnegative eigenvalues is nonterminating if an only if there exists a geometric nontermination argument.  ...  A linear loop program is a linear lasso program L without stem, i.e., a linear lasso program such that the relation STEM is equivalent to true. Definition 2 (Deterministic Linear Lasso Program).  ... 
arXiv:1609.05207v1 fatcat:6v5qc5roxrc2ngri3fzqajgzay

Ranking Templates for Linear Loops

Jan Leike, Matthias Heizmann, Erika Abraham
2015 Logical Methods in Computer Science  
We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates.  ...  Our approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components.  ...  Ben-Amram for detailed comments on the Master's thesis [Lei13] from which this paper was derived. Moreover, we thank Andreas Podelski for his detailed feedback and helpful suggestions.  ... 
doi:10.2168/lmcs-11(1:16)2015 fatcat:jw3cdne6pbbrldnkav2mp72d5u

Geometric Nontermination Arguments [chapter]

Jan Leike, Matthias Heizmann
2018 Lecture Notes in Computer Science  
For so-called linear lasso programs we can decide the existence of a geometric nontermination argument using a nonlinear algebraic ∃-constraint.  ...  We show that a deterministic conjunctive loop program with nonnegative eigenvalues is nonterminating if an only if there exists a geometric nontermination argument.  ...  A linear loop program is a linear lasso program L without stem, i.e., a linear lasso program such that the relation STEM is equivalent to true. Definition 2 (Deterministic Linear Lasso Program).  ... 
doi:10.1007/978-3-319-89963-3_16 fatcat:h7jzitcykzgytot5nd67zmuiei

Geometric Series as Nontermination Arguments for Linear Lasso Programs [article]

Jan Leike, Matthias Heizmann
2014 arXiv   pre-print
We present a new kind of nontermination argument for linear lasso programs, called geometric nontermination argument.  ...  We show that every linear loop program that has a bounded infinite execution also has a geometric nontermination argument.  ...  Let P = (STEM, LOOP) be a linear lasso program and  ... 
arXiv:1405.4413v1 fatcat:hgco36m27fgqris3w6c7s55u44

A selective review of robust variable selection with applications in bioinformatics

Cen Wu, Shuangge Ma
2014 Briefings in Bioinformatics  
In this article, we provide a selective review of robust penalized variable selection approaches especially designed for high-dimensional data from bioinformatics and biomedical studies.  ...  In the analysis of such data, the standard modeling approaches can be challenged by the heavy-tailed errors and outliers in response variables, the contamination in predictors (which may be caused by, for  ...  Acknowledgements The authors thank the editor and three reviewers for careful review and insightful comments, which have led to significant improvement of this manuscript.  ... 
doi:10.1093/bib/bbu046 pmid:25479793 pmcid:PMC4570200 fatcat:5yflco36i5gixoroi27fpiove4

Penalized rank regression estimator with the smoothly clipped absolute deviation function

Jong-Tae Park, Kang-Mo Jung
2017 Communications for Statistical Applications and Methods  
The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty.  ...  The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection.  ...  All simulations are performed on R program.  ... 
doi:10.29220/csam.2017.24.6.673 fatcat:wsl57rcte5ax7n2ryiizhxvcbe

Core Course Analysis for Undergraduate Students in Mathematics [article]

Ritvik Kharkar, Jessica Tran, Charles Z. Marshak
2016 arXiv   pre-print
Ritvik Kharkar was supported by NSF grant DMS-1045536 and Jessica Tran was supported by the UC LEADS program.  ...  We also want to thank Mihai Cucuringu for initially helping us parse through the data and M. Puck Rombach for additional oversight and helpful discussions.  ...  Lasso regression uses an 1 penalty to ensure the coefficients for the linear model are sparse.  ... 
arXiv:1605.00328v1 fatcat:btaccjj5sjdybiul5bupg6gvqe

The Lasso Problem and Uniqueness [article]

Ryan J. Tibshirani
2012 arXiv   pre-print
Next, we derive a simple method for computing the component-wise uncertainty in lasso solutions of any given problem instance, based on linear programming.  ...  The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n.  ...  Acknowledgements The idea for computing bounds on the coefficients of lasso solutions was inspired by a similar idea of Max Jacob Grazier G'Sell, for bounding the uncertainty in maximum likelihood estimates  ... 
arXiv:1206.0313v2 fatcat:qihlywuh5basfj27c6k6veinoq

Risk prediction for prostate cancer recurrence through regularized estimation with simultaneous adjustment for nonlinear clinical effects

Qi Long, Matthias Chung, Carlos S. Moreno, Brent A. Johnson
2011 Annals of Applied Statistics  
We propose to build risk prediction scores through regularized rank estimation in partly linear AFT models, where high-dimensional data such as gene expression data are modeled linearly and important clinical  ...  While accelerated failure time (AFT) models are a useful tool for the analysis of censored outcome data, it assumes that covariate effects on the logarithm of time-to-event are linear, which is often unrealistic  ...  Acknowledgments We thank Editor Kafadar, an associate editor, and two referees for their helpful suggestions that greatly improved an earlier draft of this manuscript.  ... 
doi:10.1214/11-aoas458 pmid:22081781 pmcid:PMC3212400 fatcat:o23lwbeynzfz5cyq7ns23bwsfq

The lasso problem and uniqueness

Ryan J. Tibshirani
2013 Electronic Journal of Statistics  
Next, we derive a simple method for computing the component-wise uncertainty in lasso solutions of any given problem instance, based on linear programming.  ...  The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n.  ...  Acknowledgements The idea for computing bounds on the coefficients of lasso solutions was inspired by a similar idea of Max Jacob Grazier G'Sell, for bounding the uncertainty in maximum likelihood estimates  ... 
doi:10.1214/13-ejs815 fatcat:ywqou6ryjnhw3d47pr2avcrdyq
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