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Optimal Approximation – Smoothness Tradeoffs for Soft-Max Functions [article]

Alessandro Epasto, Mohammad Mahdian, Vahab Mirrokni, Manolis Zampetakis
2020 arXiv   pre-print
We introduce a soft-max function, called "piecewise linear soft-max", with optimal tradeoff between approximation, measured in terms of worst-case additive approximation and smoothness, measured with respect  ...  Our goal is to identify the optimal approximation-smoothness tradeoffs for different measures of approximation and smoothness.  ...  We explore the tradeoff between the approximation guarantee of a soft-max function and its smoothness.  ... 
arXiv:2010.11450v1 fatcat:2z4noyrbq5gcvjmb47ylb3tw3q

Quantum Algorithms for Scientific Computing and Approximate Optimization [article]

Stuart Hadfield
2018 arXiv   pre-print
The remaining two deal with quantum algorithms for approximate optimization.  ...  We study the performance of the quantum approximate optimization algorithm (QAOA), and show a generalization of QAOA, the quantum alternating operator ansatz, particularly suitable for constrained optimization  ...  QUANTUM APPROXIMATE OPTIMIZATION WITH HARD AND SOFT CONSTRAINTS 147 approximate solution y.  ... 
arXiv:1805.03265v1 fatcat:7ycpl3byjrg73kn4jpzg5ajiwy

Approximate Reduction from AUC Maximization to 1-Norm Soft Margin Optimization [chapter]

Daiki Suehiro, Kohei Hatano, Eiji Takimoto
2011 Lecture Notes in Computer Science  
Then, for the soft margin case, we show that the problem is approximately reduced to a soft margin optimization problem over p + n instances for which the resulting linear classifier is guaranteed to have  ...  In this paper, we give (approximate) reductions from the problems to hard/soft margin optimization problems of linear size.  ...  The authors would like to Manfred Warmuth for the stimulating discussion regarding the initial results. We would also like to Masayuki Takeda for his financial support.  ... 
doi:10.1007/978-3-642-24412-4_26 fatcat:fpebotuetrgprdyt7blry3qm5q

Multi denoising approximate message passing for optimal recovery with lower computational cost

Alessandro Perelli, Mike E. Davies
2017 2017 25th European Signal Processing Conference (EUSIPCO)  
Another work [5] examined the time-data tradeoff for image interpolation problem,  ...  composite optimization problems with lower complexity [4] .  ...  Another work [5] examined the time-data tradeoff for image interpolation problem, by varying the amount of smoothing applied to the convex optimization problem.  ... 
doi:10.23919/eusipco.2017.8081586 dblp:conf/eusipco/PerelliD17 fatcat:4vnvic5s6jfbvicupkppql4ly4

Parallel and Distributed Successive Convex Approximation Methods for Big-Data Optimization [article]

Gesualdo Scutari, Ying Sun
2018 arXiv   pre-print
The presented framework unifies and generalizes several existing SCA methods, making them appealing for a parallel/distributed implementation while offering a flexible selection of function approximants  ...  Recent years have witnessed a surge of interest in parallel and distributed optimization methods for large-scale systems.  ...  smooth, optimization.  ... 
arXiv:1805.06963v1 fatcat:fbjziifyezdixoudqgi2sbfpum

Parameter Optimization for Local Polynomial Approximation based Intersection Confidence Interval Filter Using Genetic Algorithm: An Application for Brain MRI Image De-Noising

Nilanjan Dey, Amira Ashour, Samsad Beagum, Dimitra Pistola, Mitko Gospodinov, Еvgeniya Gospodinova, João Tavares
2015 Journal of Imaging  
The present study proposed a novel technique for parameter optimization of LPA-ICI filter using genetic algorithm (GA) for brain MR images de-noising.  ...  Local polynomial approximation based intersection confidence interval (LPA-ICI) filter is one of the effective de-noising filters.  ...  Acknowledgments The authors would like to thank the Editor and anonymous reviewers for their valuable comments and suggestions, which were helpful in improving the paper.  ... 
doi:10.3390/jimaging1010060 fatcat:vqvo6mbh25e7fht722dkgfswti

Designing Statistical Estimators That Balance Sample Size, Risk, and Computational Cost

John J. Bruer, Joel A. Tropp, Volkan Cevher, Stephen R. Becker
2015 IEEE Journal on Selected Topics in Signal Processing  
We propose to achieve this tradeoff by varying the amount of smoothing applied to the optimization problem.  ...  Index Terms-Smoothing methods, statistical estimation, convex optimization, regularized regression, image interpolation, resource tradeoffs I.  ...  Bottou and Bousquet [5] show that approximate optimization algorithms exhibit a tradeoff between small-and large-scale problems. Agarwal et al.  ... 
doi:10.1109/jstsp.2015.2400412 fatcat:5fhnxoncpba2he2byppzqo5s2q

A Maximal Correlation Approach to Imposing Fairness in Machine Learning [article]

Joshua Lee, Yuheng Bu, Prasanna Sattigeri, Rameswar Panda, Gregory Wornell, Leonid Karlinsky, Rogerio Feris
2020 arXiv   pre-print
criteria, which admit optimization algorithms for both discrete and continuous variables which are more computationally efficient than existing algorithms.  ...  We show that these algorithms provide smooth performance-fairness tradeoff curves and perform competitively with state-of-the-art methods on both discrete datasets (COMPAS, Adult) and continuous datasets  ...  Note that for the first soft-HGR term, we use g, h to denote the maximal correlation functions, and g , h to denote the functions for the second term.  ... 
arXiv:2012.15259v1 fatcat:elrk55akqvaqfaw34mg2ztqem4

A Maximal Correlation Framework for Fair Machine Learning

Joshua Lee, Yuheng Bu, Prasanna Sattigeri, Rameswar Panda, Gregory W. Wornell, Leonid Karlinsky, Rogerio Schmidt Feris
2022 Entropy  
criteria, which admit optimization algorithms for both discrete and continuous variables that are more computationally efficient than existing algorithms.  ...  We show that these algorithms provide smooth performance–fairness tradeoff curves and perform competitively with state-of-the-art methods on both discrete datasets (COMPAS, Adult) and continuous datasets  ...  to a current situation, which can be a difficult process if the tradeoff curve is not smooth.  ... 
doi:10.3390/e24040461 pmid:35455124 pmcid:PMC9027582 fatcat:e7uael4zlvhwzea4isjy3jqxhi

A factor graph approach to iterative channel estimation and LDPC decoding over fading channels

Huaning Niu, Manyuan Shen, J.A. Ritcey, Hui Liu
2005 IEEE Transactions on Wireless Communications  
This letter provides a comparative study of joint channel estimation and low-density parity-check decoding algorithms for flat Rayleigh fading channels based on the receiver factor graphs.  ...  Two approaches for joint channel estimation and decoding are proposed. Intensive simulation studies are carried out to evaluate the receiver sensitivity to the choice of the factor graph.  ...  Following the notation in [7] , the optimal receiver for this model, with respect to bit error probability iŝ u i = arg max u i p(u i |y) = arg max ξ u:u i =ξ h p(u, h|y). (4) Because of the systematic  ... 
doi:10.1109/twc.2005.850273 fatcat:tmou2y23jzfavohx6z2qpyx4iy

Spartan: Differentiable Sparsity via Regularized Transportation [article]

Kai Sheng Tai, Taipeng Tian, Ser-Nam Lim
2022 arXiv   pre-print
This scheme realizes an exploration-exploitation tradeoff: early in training, the learner is able to explore various sparsity patterns, and as the soft top-k approximation is gradually sharpened over the  ...  Spartan is based on a combination of two techniques: (1) soft top-k masking of low-magnitude parameters via a regularized optimal transportation problem and (2) dual averaging-based parameter updates with  ...  Our use of the soft top-k operation is related to prior methods that use the logistic sigmoid function as a differentiable approximation to the step function for sparse training [29; 35; 1] .  ... 
arXiv:2205.14107v1 fatcat:et7ejsljjzgdbf4f24vjid7agy

Soft-Input Soft-Output Single Tree-Search Sphere Decoding [article]

Christoph Studer, Helmut Bölcskei
2009 arXiv   pre-print
Furthermore, we propose a new method for correcting approximate LLRs --resulting from sub-optimal detectors-- which (often significantly) improves detection performance at low additional computational  ...  Soft-input soft-output (SISO) detection algorithms form the basis for iterative decoding.  ...  From Fig. 4 , we can conclude that LLR clipping allows for a smooth performance/complexity tradeoff, adjustable through a single parameter, namely the LLR clipping parameter L max .  ... 
arXiv:0906.0840v1 fatcat:32p3ocmunnfnvmgx527f2si4xq

An Efficient Method for Large-Scale Gate Sizing

S. Joshi, S. Boyd
2008 IEEE Transactions on Circuits and Systems Part 1: Regular Papers  
A simple implementation of our algorithm can size a 10 000 gate circuit in 25 s, a 100 000 gate circuit in 4 min, and a million gate circuit in 40 min, approximately.  ...  In this paper, we describe a new method for solving this problem that handles far larger circuits, up to a million gates, and is far faster.  ...  large-scale GP solver that was used to calculate the exact optimal solutions for the test circuits as well as P. Parakh, B. Deprey, and I.  ... 
doi:10.1109/tcsi.2008.920087 fatcat:aan3rq72r5fcnhbg5vju7oqaq4

The information bottleneck and geometric clustering [article]

DJ Strouse, David J Schwab
2020 arXiv   pre-print
We also show that, in particular limits of our model parameters, clustering with DIB and IB is equivalent to k-means and EM fitting of a GMM with hard and soft assignments, respectively.  ...  We also introduce a novel method to choose the number of clusters, based on identifying solutions where the tradeoff between number of clusters used and spatial information preserved is strongest.  ...  To see the correspondence between GMMs/k-means and IB, consider that IB can be viewed as DIB with the hard max replaced by a soft max (see eqn 7.)  ... 
arXiv:1712.09657v2 fatcat:7vz2gpkjiraezjm6ifudn2phhy

Spectral Efficiency and Energy Efficiency of OFDM Systems: Impact of Power Amplifiers and Countermeasures

Jingon Joung, Chin Keong Ho, Sumei Sun
2014 IEEE Journal on Selected Areas in Communications  
In other words, the Pareto-optimal tradeoff boundary of the SE-EE curve is very narrow.  ...  An ideal PA that is always linear and incurs no additional power consumption can be shown to yield a decreasing convex function in the SE-EE tradeoff.  ...  Proposition 7: The Pareto-optimality of the approximated SE-EE tradeoff is characterized as follows: i) For min{ ξ ⋆ EE , ξ ⋆ SE } ≤ ξ ≤ max{ ξ ⋆ EE , ξ ⋆ SE }, the corresponding approximated SE-EE tradeoff  ... 
doi:10.1109/jsac.2014.141203 fatcat:vlsgi4znsbct5ojvcynuarukte
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