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Diminishable Parameterized Problems and Strict Polynomial Kernelization [article]

Henning Fernau, Till Fluschnik, Danny Hermelin, Andreas Krebs, Hendrik Molter, Rolf Niedermeier
2017 arXiv   pre-print
In particular, we show that various (multicolored) graph problems and Turing machine computation problems do not admit strict polynomial kernels unless P = NP.  ...  To this end, a key concept we use are diminishable problems; these are parameterized problems that allow to decrease the parameter of the input instance by at least one in polynomial time, thereby outputting  ...  It is not difficult to show that the existence of a parameter diminisher and a strict polynomial kernel for an NP-hard parameterized problem implies P = NP.  ... 
arXiv:1611.03739v3 fatcat:7vjx4mbcnbbq3o22is5eyb75ge

Kernelization Lower Bounds for Finding Constant-Size Subgraphs [chapter]

Till Fluschnik, George B. Mertzios, André Nichterlein
2018 Lecture Notes in Computer Science  
We prove that a linear-time computable strict kernel of truly subcubic size for this problem violates the popular APSP-conjecture.  ...  In this paper, we provide a first conceptual study on limits of kernelization for several polynomial-time solvable problems.  ...  We thank Holger Dell (MPI Saarbrücken) for fruitful discussion on Section 2.1 and Rolf Niedermeier for discussions leading to this work.  ... 
doi:10.1007/978-3-319-94418-0_19 fatcat:xpvzr6o6vbfezbm5uxurw76bvq

Kernelization Lower Bounds for Finding Constant-Size Subgraphs [article]

Till Fluschnik, George B. Mertzios, André Nichterlein
2018 arXiv   pre-print
We prove that a linear-time computable strict kernel of truly subcubic size for this problem violates the popular APSP-conjecture.  ...  In this paper, we provide a first conceptual study on limits of kernelization for several polynomial-time solvable problems.  ...  We thank Holger Dell (Saarland University) for fruitful discussion on Section 2 and Rolf Niedermeier for discussions leading to this work.  ... 
arXiv:1710.07601v2 fatcat:osz3kbyu2jfttpbli6eqzlm564

Parameterized enumeration, transversals, and imperfect phylogeny reconstruction

Peter Damaschke
2006 Theoretical Computer Science  
We study parameterized enumeration problems where we are interested in all solutions of limited size rather than just some solution of minimum cardinality.  ...  Two novel concepts are the notion of a full kernel that contains all small solutions and implicit enumeration of solutions in form of compressed descriptions.  ...  Acknowledgments I wish to thank the referees for numerous comments that helped to give the paper more shape and to clarify several details.  ... 
doi:10.1016/j.tcs.2005.10.004 fatcat:d2uypviamjgtzix6jqjmw6l4vu

Optimally Compressed Nonparametric Online Learning [article]

Alec Koppel, Amrit Singh Bedi, Ketan Rajawat, Brian M. Sadler
2020 arXiv   pre-print
The asymptotic bias depends on a compression parameter that trades off memory and accuracy.  ...  We survey online compression tools which bring their memory under control and attain approximate convergence.  ...  Then, we detail how the problem specializes when the estimator admits a kernel parameterization.  ... 
arXiv:1909.11555v2 fatcat:z2tl34d7nbazdlzfmwrsw5rzfu

Volterra models and three-layer perceptrons

V.Z. Marmarelis, X. Zhao
1997 IEEE Transactions on Neural Networks  
Index Terms-Laguerre kernel expansion, nonlinear system modeling, polynomial activation functions, separable Volterra network, three-layer perceptrons, Volterra kernels, Volterra models.  ...  A variant of TLP with polynomial activation functions-termed "separable Volterra networks" (SVN's)-is found particularly useful in deriving explicit relations with DVM and in obtaining practicable models  ...  The main limitations of this approach are the practical inability to extend kernel estimation to orders higher than third (due to increasing dimensionality of kernel representation) and the strict input  ... 
doi:10.1109/72.641465 pmid:18255744 fatcat:pilr3cee5bakvbuvsho4uogev4

The union of minimal hitting sets: Parameterized combinatorial bounds and counting

Peter Damaschke, Leonid Molokov
2009 Journal of Discrete Algorithms  
We show that this union is relevant for certain combinatorial inference problems and give worst-case bounds on its size, depending on r and k.  ...  For r = 2 our result is tight, and for each r 3 we have an asymptotically optimal bound and make progress regarding the constant factor. The exact worst-case size for r 3 remains an open problem.  ...  Partial support also came from the Swedish Research Council (Vetenskapsrådet), grant no. 2007-6437, "Combinatorial inference algorithms -parameterization and clustering".  ... 
doi:10.1016/j.jda.2009.01.003 fatcat:yccolf6rjvb6tjgcwgd4lsznbq

Enforcing necessary non-negativity constraints for common diffusion MRI models using sum of squares programming

Tom Dela Haije, Evren Özarslan, Aasa Feragen
2019 NeuroImage  
We formulate such constraints for the mean apparent propagator model and for spherical deconvolution, guaranteeing strict non-negativity of the corresponding diffusion propagators.  ...  These constraints can all be verified and enforced at reasonable computational costs using semidefinite programming.  ...  (a) In the proposed method, the small negative lobes that can typically be seen near the center of each glyph are entirely absent, and thus the problem of spurious peaks is greatly diminished.  ... 
doi:10.1016/j.neuroimage.2019.116405 pmid:31846758 fatcat:alivw6fdfbetzjdithfpqyvfzq

Ensemble-based probabilistic forecasting at Horns Rev

Pierre Pinson, Henrik Madsen
2009 Wind Energy  
This model employs local polynomial regression, and is adaptively estimated with an orthogonal fitting method.  ...  The obtained ensemble forecasts of wind power are then converted into predictive distributions with an original adaptive kernel dressing method.  ...  The authors are finally grateful to two anonymous reviewers and to an editor for their helpful comments and suggestions.  ... 
doi:10.1002/we.309 fatcat:gk5qpk2izbel3epa55qqhk72tu

Parsimonious Online Learning with Kernels via sparse projections in function space

Alec Koppel, Garrett Warnell, Ethan Stump, Alejandro Ribeiro
2017 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
We evaluate POLK for kernel multi-class logistic regression and kernel hinge-loss classification on three canonical data sets: a synthetic Gaussian mixture model, the MNIST hand-written digits, and the  ...  The method, called parsimonious online learning with kernels (POLK), provides a controllable tradeoff between its solution accuracy and the amount of memory it requires.  ...  Common choices κ include the polynomial kernel and the radial basis kernel, i.e., κ(x, x ) = x T x + b c and κ(x, x ) = exp − x−x 2 2 2c 2 , respectively, where x, x ∈ X .  ... 
doi:10.1109/icassp.2017.7953042 dblp:conf/icassp/KoppelWSR17 fatcat:lyseor55anfnhj55o3pqiiddxm

Sparse solutions of sparse linear systems: Fixed-parameter tractability and an application of complex group testing

Peter Damaschke
2013 Theoretical Computer Science  
We give different branching algorithms based on the close relationship to the hitting set problem in fixed-rank hypergraphs. For r = 2 the problem is simple.  ...  For 0, 1-matrices A we can also compute an O(rk r ) kernel. For systems of linear inequalities we get an FPT result in the combined parameter d, k, where d is the total number of minimal solutions.  ...  Acknowledgments This work has been supported by the Swedish Research Council (Vetenskapsrådet), grant no. 2010-4661 "Generalized and fast search strategies for parameterized problems", and the questions  ... 
doi:10.1016/j.tcs.2012.07.001 fatcat:pht3ay5bnve5zedkq34h5utjue

Ray Casting Algebraic Surfaces using the Frustum Form

Martin Reimers, Johan Seland
2008 Computer graphics forum (Print)  
A key point of our approach is a polynomial form adapted to the view frustum.  ...  For polynomials in Bernstein form, several methods are based on subdivision, e.g. Lane and Riesenfeld [LR81], Rockwood et al. [RHD89] and Schneider [Sch90], see [Spe94] for an overview.  ...  It has the variation diminishing property: the number of zeros, counting multiplicities, exceeds the number of strict sign changes in the coefficients.  ... 
doi:10.1111/j.1467-8659.2008.01133.x fatcat:ziamr6s5urfcncobpdclzg3hum

Decision Support in Car Leasing: a Forecasting Model for Residual Value Estimation

Stefan Lessmann, Mariana Listiani, Stefan Voß
2010 International Conference on Information Systems  
We explore the organizational and technical requirements associated with this forecasting task and develop a prediction model that complies with identified application constraints.  ...  The model is rigorously tested within an empirical study and compared to established benchmarks.  ...  We consider linear, polynomial and radial basis function (RBF) kernels in this work and formally introduce these in Appendix I.  ... 
dblp:conf/icis/LessmannLV10 fatcat:ygjiimhpsbcavkm2xxgqo4nnle

B-spline techniques for volatility modeling [article]

Sylvain Corlay
2015 arXiv   pre-print
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an  ...  We use a B-spline parameterization of the Radon-Nikodym derivative of the underlying's risk-neutral probability density with respect to a roughly calibrated base model.  ...  In other words, the multiplicity of a knot diminishes the regularity of the spanned set of piecewise polynomial functions at the corresponding breakpoint. Remark (Basis truncation).  ... 
arXiv:1306.0995v4 fatcat:qdd6txg4srcm5c4tz4ucbnshd4

B-spline techniques for volatility modeling

Sylvain Corlay
2016 Journal of Computational Finance  
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an  ...  We use a B-spline parameterization of the Radon-Nikodym derivative of the underlying's risk-neutral probability density with respect to a roughly calibrated base model.  ...  In other words, the multiplicity of a knot diminishes the regularity of the spanned set of piecewise polynomial functions at the corresponding breakpoint. Remark (Basis truncation).  ... 
doi:10.21314/jcf.2016.207 fatcat:5ysctpvj2zdkrfd2ryeq643cbq
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