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On the hardness of evading combinations of linear classifiers

David Stevens, Daniel Lowd
2013 Proceedings of the 2013 ACM workshop on Artificial intelligence and security - AISec '13  
This problem setting has been formally analyzed for linear classifiers with discrete features and convex-inducing classifiers with continuous features, but never for non-linear classifiers with discrete  ...  In this paper, we extend previous ACRE learning results to convex polytopes representing unions or intersections of linear classifiers.  ...  These results show while the disjunctive classifiers may sometimes be harder to defeat than the linear classifiers, the conjunctive ones tend to be much easier.  ... 
doi:10.1145/2517312.2517318 dblp:conf/ccs/StevensL13 fatcat:gleitxuhhvh7pg6bqipjmnmaja

A Convex Analysis Framework for Blind Separation of Non-Negative Sources

Tsung-Han Chan, Wing-Kin Ma, Chong-Yung Chi, Yue Wang
2008 IEEE Transactions on Signal Processing  
It is a good assumption for source signals exhibiting sparsity or high contrast, and thus is considered realistic to many real-world problems such as multichannel biomedical imaging.  ...  Under local dominance and several standard assumptions, we apply convex analysis to establish a new BSS criterion, which states that the source signals can be perfectly identified (in a blind fashion)  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers and the associate editor in charge for their thoughtful comments, which have improved this paper.  ... 
doi:10.1109/tsp.2008.928937 fatcat:z74a7cmzf5gz7j47k4omhfme2u

Modeling Generalization in Machine Learning: A Methodological and Computational Study [article]

Pietro Barbiero and Giovanni Squillero and Alberto Tonda
2020 arXiv   pre-print
and extrapolated predictions.  ...  Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine learning predictions.  ...  On the other hand, the test accuracy of RF seems much harder to predict, and associated with the average class-wise correlation among features (ρ) only.  ... 
arXiv:2006.15680v1 fatcat:2zoduqaogzchpfihed5i6hvexa

Distance-weighted discrimination

J. S. Marron
2015 Wiley Interdisciplinary Reviews: Computational Statistics  
This leads naturally to the development of Distance Weighted Discrimination, which is based on Second Order Cone Programming, a modern computationally intensive optimization method.  ...  High Dimension Low Sample Size statistical analysis is becoming increasingly important in a wide range of applied contexts.  ...  Marron was grateful for the chance to spend a year in the exciting research environment of the School of Operations Research and Industrial Engineering, from which this collaboration is a direct result  ... 
doi:10.1002/wics.1345 fatcat:ctqewoiiira7tootmoinnnyesq

QPLIB: a library of quadratic programming instances

Fabio Furini, Emiliano Traversi, Pietro Belotti, Antonio Frangioni, Ambros Gleixner, Nick Gould, Leo Liberti, Andrea Lodi, Ruth Misener, Hans Mittelmann, Nikolaos V. Sahinidis, Stefan Vigerske (+1 others)
2018 Mathematical Programming Computation  
On the other hand, an instance is classified as non-convex if the objective function is non-convex and/or at least one of the constraints is non-convex, and convex otherwise.  ...  This is, however, reasonable, considering how quadratic constraints can, in general, be expected to be much more computationally challenging than linear ones, especially if nonconvex.  ...  The file format The QPLIB format is defined in Table 8 , with the notation of §2. The data is in free format (blanks separate values), but must occur in the order given here.  ... 
doi:10.1007/s12532-018-0147-4 fatcat:7q7dunjewffb3ca2am6kmuf4im

Complete search in continuous global optimization and constraint satisfaction

Arnold Neumaier
2004 Acta Numerica  
Then a discussion of important problem transformations follows, in particular of linear, convex, and semilinear (= mixed integer linear) relaxations that are important for handling larger problems.  ...  After giving motivations for and important examples of applications of global optimization, a precise problem definition is given, and a general form of the traditional first-order necessary conditions  ...  This survey is part of work done in the context of the COCONUT project (COCONUT 2001) sponsored by the European Union, with the goal of integrating various existing complete approaches to global optimization  ... 
doi:10.1017/s0962492904000194 fatcat:phckdsbkevdahcawdroqwwgoeq

Fifteen observations on the structure of energy-minimizing gaits in many simple biped models

M. Srinivasan
2010 Journal of the Royal Society Interface  
A popular hypothesis regarding legged locomotion is that humans and other large animals walk and run in a manner that minimizes the metabolic energy expenditure for locomotion.  ...  For many of these models, walking-like gaits are optimal at low speeds and running-like gaits at higher speeds, so a gait transition is optimal.  ...  So, it is not surprising that essentially no qualitative changes are found in the optimal gaits for a linear additive force cost.  ... 
doi:10.1098/rsif.2009.0544 pmid:20542957 pmcid:PMC3024815 fatcat:34d5rifuhrezhfqvh3ibh2ze54

Convex Optimization for Big Data: Scalable, randomized, and parallel algorithms for big data analytics

Volkan Cevher, Stephen Becker, Mark Schmidt
2014 IEEE Signal Processing Magazine  
This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks.  ...  We provide an overview of this emerging field, describe contemporary approximation techniques like first-order methods and randomization for scalability, and survey the important role of parallel and distributed  ...  Acknowledgements Volkan Cevher's work is supported in part by the European Commission under grants MIRG-268398 and  ... 
doi:10.1109/msp.2014.2329397 fatcat:7np3knuhena2fd5o6tqjtpbzai

Sample-Optimal Identity Testing with High Probability

Ilias Diakonikolas, Themis Gouleakis, John Peebles, Eric Price, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
The fact that this simple "plug-in" estimator is sample-optimal is surprising, even in the constant δ case.  ...  Our new upper and lower bounds show that the optimal sample complexity of identity testing is for any n, ε, and δ.  ...  The reason is that the difference µ(p) − µ(U n ) can be much smaller than µ(p) and µ(U n ); it can even be arbitrarily small.  ... 
doi:10.4230/lipics.icalp.2018.41 dblp:conf/icalp/DiakonikolasGPP18 fatcat:fl776xeeobb5rm7geqlz2wd7dq

Optimization for deep learning: theory and algorithms [article]

Ruoyu Sun
2019 arXiv   pre-print
When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks.  ...  Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms.  ...  Srikant, Tian Ding and Dawei Li for discussions on various results reviewed in this article.  ... 
arXiv:1912.08957v1 fatcat:bdtx2o3qhfhthh2vyohkuwnxxa

Near-optimal Local Convergence of Alternating Gradient Descent-Ascent for Minimax Optimization [article]

Guodong Zhang, Yuanhao Wang, Laurent Lessard, Roger Grosse
2022 arXiv   pre-print
We prove that Alt-GDA achieves a near-optimal local convergence rate for strongly convex-strongly concave (SCSC) problems while Sim-GDA converges at a much slower rate.  ...  To our knowledge, this is the first result of any setting showing that Alt-GDA converges faster than Sim-GDA by more than a constant.  ...  However, bounding the spectral radius is much harder for Alt-GDA, since the algorithm involves two half steps, and the spectral radius of the matrix product can't be bounded straightforwardly in terms  ... 
arXiv:2102.09468v3 fatcat:77ys6uedr5gyxbrttd6o3ss57e

Approximated perspective relaxations: a project and lift approach

Antonio Frangioni, Fabio Furini, Claudio Gentile
2015 Computational optimization and applications  
The Perspective Reformulation (PR) of a Mixed-Integer NonLinear Program with semicontinuous variables is obtained by replacing each term in the (separable) objective function with its convex envelope.  ...  While the AP 2 R bound can be weaker than that of the PR, this approach can be applied in many more cases and allows direct use of off-the-shelf MINLP software; this is shown to be competitive with previously  ...  Optimization: Approaches and Applications", as well as of the European Union under the 7FP Marie Curie Initial Training Network n. 316647 "MINO: Mixed-Integer Nonlinear Optimization".  ... 
doi:10.1007/s10589-015-9787-8 fatcat:jju2kkzsezhabcl7t2wm5ennx4

The Mysteries of Security Games: Equilibrium Computation Becomes Combinatorial Algorithm Design [article]

Haifeng Xu
2016 arXiv   pre-print
In particular, we prove that, for any set system E, the following problems can be reduced to each other in polynomial time: (0) combinatorial optimization over E, (1) computing the minimax equilibrium  ...  The security game is a basic model for resource allocation in adversarial environments. Here there are two players, a defender and an attacker.  ...  ACKNOWLEDGMENTS We would like to thank Shaddin Dughmi, Milind Tambe and Vincent Conitzer for helpful discussions. We also thank the anonymous EC reviewers for helpful feedback and suggestions.  ... 
arXiv:1603.02377v2 fatcat:73ri5qo7cjg2ppt477adogkahm

Turning Up the Heat: The Discouraging Effect of Competition in Contests

Dawei Fang, Thomas Noe, Philipp Strack
2019 Journal of Political Economy  
We study contests in which contestants are homogeneous and have convex effort costs.  ...  Holding promotion contests at the division level rather than the firm level can boost employees' effort.  ...  performers rather than tilted toward top performers implies a much stronger boost in effort when costs are strictly convex than when costs are linear through the discouragement effect.  ... 
doi:10.1086/705670 fatcat:wlr6g2juvzbkdhcqqkg4db77ge

Robust Market Equilibria with Uncertain Preferences

Riley Murray, Christian Kroer, Alex Peysakhovich, Parikshit Shah
and allocations is computed that sets demand equal to supply.  ...  convex programming methods.  ...  This is surprising, since robust solutions are optimizing for a different objective than nominal Nash welfare.  ... 
doi:10.1609/aaai.v34i02.5595 fatcat:vyobefyrvvhv7lz7pj3jqxcad4
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