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Linear Ranking for Linear Lasso Programs
[article]
2014
arXiv
pre-print
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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]
2013
Lecture Notes in Computer Science
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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]
2014
arXiv
pre-print
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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
2014
Electronic Proceedings in Theoretical Computer Science
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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
2013
PLoS ONE
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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]
2016
arXiv
pre-print
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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
2015
Logical Methods in Computer Science
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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]
2018
Lecture Notes in Computer Science
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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]
2014
arXiv
pre-print
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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
2014
Briefings in Bioinformatics
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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
2017
Communications for Statistical Applications and Methods
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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]
2016
arXiv
pre-print
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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]
2012
arXiv
pre-print
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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
2011
Annals of Applied Statistics
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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
2013
Electronic Journal of Statistics
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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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