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No Subclass Left Behind: Fine-Grained Robustness in Coarse-Grained Classification Problems [article]

Nimit S. Sohoni, Jared A. Dunnmon, Geoffrey Angus, Albert Gu, Christopher Ré
2022 arXiv   pre-print
We theoretically characterize the performance of GEORGE in terms of the worst-case generalization error across any subclass.  ...  We empirically validate GEORGE on a mix of real-world and benchmark image classification datasets, and show that our approach boosts worst-case subclass accuracy by up to 22 percentage points compared  ...  Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.  ... 
arXiv:2011.12945v2 fatcat:as3wlcijpnfqfp5qn4ax4t5gti

Page 2355 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
For instance, the error functions used in the worst-case and in the average-case settings are given by supy p<, ||S(/) — U(f)||, and (Sp IS(P) — U(S)\? u(af))'”, respectively.  ...  The settings con- sidered are: worst-case, average-case, probabilistic, randomized.  ... 

Linear Semi-Supervised Dimensionality Reduction with Pairwise Constraint for Multiple Subclasses

Bin TONG, Weifeng JIA, Yanli JI, Einoshin SUZUKI
2012 IEICE transactions on information and systems  
We propose a new method, called Subclass-oriented Dimensionality Reduction with Pairwise Constraints (SODRPaC), for dimensionality reduction.  ...  are likely to be located in different groups.  ...  to be suitable for the data of multiple subclasses.  ... 
doi:10.1587/transinf.e95.d.812 fatcat:t5cchlyilfbkleotnm2v7duzt4

Page 2782 of Mathematical Reviews Vol. , Issue 80G [page]

1980 Mathematical Reviews  
worst case general complexity; O(n) for planar graphs), the vector ud(-) (O(n*/*) average case complexity with probabilities as above) and Boolean squaring of the adjacency matrix for G (O(n'°8’) worst  ...  The latter technique leads to a minimum circuit algorithm of O(n’) worst case performance.  ... 

Page 5099 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
We also give exponential worst-case running time bounds for deterministic algorithms to solve each of these problems.  ...  Lorenzo Traldi (1-LFYC; Easton, PA) 2000g:68057 68Q25 68Q15 Serna, Maria (E-UPB-LI; Barcelona); Xhafa, Fatos (E-UPB-LI; Barcelona) On the average case complexity of some P-complete problems.  ... 

Extended SWN solvers in GreatSPN

S. Donatelli, J.M. Ilie, S. Baarir, M. Beccuti, C. Delamare, C. Dutheillet, G. Franceschinis, R. Gaeta, P. Moreaux
2004 First International Conference on the Quantitative Evaluation of Systems, 2004. QEST 2004. Proceedings.  
Well-formed nets and their stochastic timed extension, take advantage of symmetries to allow efficient solution techniques for both qualitative and quantitative properties.  ...  In this paper, we present a suite of new software tools based on the original SWN solver of the GreatSPN tool which implement these new features.  ...  In this case, SR is sufficient to represent a whole ESM, allowing to discard the eventualities. The ESRG cannot be larger than the SRG but in the worst case its construction can take more time.  ... 
doi:10.1109/qest.2004.1348049 dblp:conf/qest/IlieBBDDDFGM04 fatcat:jhxldibc4fd47arbke6dzqbuki

Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class

Bernhard Nebel
1997 Constraints  
While the worst-case computational properties of Allen's calculus for qualitative temporal reasoning have been analyzed quite extensively, the determination of the empirical e ciency of algorithms for  ...  While the worst-case computational properties of Allen's calculus and fragments of it have been quite extensively analyzed Golumbic and Shamir, 1993; Ladkin and Maddux, 1994; Nebel and B urckert, 1995;  ...  Acknowledgements I would like to thank Peter Ladkin for discussions concerning the problems discussed in this paper and Peter van Beek for discussions and making available the  ... 
doi:10.1007/bf00137869 fatcat:rzdvlwuxrbarvhdzxvjjbxaujq

Subclass Marginal Fisher Analysis

Anastasios Maronidis, Anastasios Tefas, Ioannis Pitas
2015 2015 IEEE Symposium Series on Computational Intelligence  
Through a series of experiments on various real-world datasets, it is shown that SMFA outperforms in most of the cases the state-of-the-art demonstrating the potential of exploiting subclass neighbourhood  ...  Full terms of use are available: Abstract-Subspace learning techniques have been extensively used for dimensionality reduction (DR) in many pattern classification problem domains.  ...  In this paper, extending the GE framework [7] so as to include subclass information, we propose a novel Subclass Marginal Fisher Analysis (SMFA) algorithm for supervised dimensionality reduction.  ... 
doi:10.1109/ssci.2015.198 dblp:conf/ssci/MaronidisTP15 fatcat:sgzfxhz7dzg4td2d66fxvjggfe

On basing one-way functions on NP-hardness

Adi Akavia, Oded Goldreich, Shafi Goldwasser, Dana Moshkovitz
2006 Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC '06  
We believe that our results illustrate the gain of directly studying the context of one-way functions rather than inferring results for it from a the general study of worst-case to average-case reductions  ...  We consider the possibility of basing one-way functions on NP-Hardness; that is, we study possible reductions from a worst-case decision problem to the task of average-case inverting a polynomial-time  ...  Dana Moshkovitz is grateful to Muli Safra for supporting her visit to MIT, where this research has been initiated.  ... 
doi:10.1145/1132516.1132614 dblp:conf/stoc/AkaviaGGM06 fatcat:jxdclcu33jgrrks26r6ke2ay4a

On Worst‐Case to Average‐Case Reductions for NP Problems

Andrej Bogdanov, Luca Trevisan
2006 SIAM journal on computing (Print)  
Our result implies that the average-case hardness of a problem in NP or the security of a one-way function cannot be based on the worst-case complexity of an NP-complete problem via non-adaptive reductions  ...  A self-corrector for a language L with respect to a distribution D is a worst-case to averagecase reduction that transforms any given algorithm that correctly decides L on most inputs (with respect to  ...  Acknowledgments We thank Madhu Sudan for suggesting the relevance of [IL90] , Oded Goldreich for stressing the relevance of our result to the question of basing cryptography on NP-hardness, and Amit Sahai  ... 
doi:10.1137/s0097539705446974 fatcat:2wtotkshpjfz5c3uvuglnqfmfm

Average-Case Complexity [article]

Andrej Bogdanov, Luca Trevisan
2021 arXiv   pre-print
While the relation between worst-case and average-case complexity for general NP problems remains open, there has been progress in understanding the relation between different "degrees" of average-case  ...  A major open question whether the existence of hard-on-average problems in NP can be based on the P≠NP assumption or on related worst-case assumptions.  ...  Acknowledgements We thanks Scott Aaronson, Jonathan Katz, Chris Moore and the anonymous referee for their helpful comments.  ... 
arXiv:cs/0606037v3 fatcat:ishwc6ck2vhztpfb5z3bjywehi

Average-case intractability vs. worst-case intractability [chapter]

Johannes Köbler, Rainer Schuler
1998 Lecture Notes in Computer Science  
We use the assumption that all sets in NP (or other levels of the polynomial-time hierarchy) have e cient average-case algorithms to derive collapse consequences for MA, AM, and various subclasses of P  ...  As a further consequence we show for C 2 fP(PP); PSPACEg that C is not tractable in the average-case unless C = P.  ...  This means that for C = P(PP), C is not tractable on the average unless C is tractable in the worst-case.  ... 
doi:10.1007/bfb0055799 fatcat:x4jqsloj4be2fmn5pdze6yglby

Throughput-centric routing algorithm design

Brian Towles, William J. Dally, Stephen Boyd
2003 Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03  
Expanding the analysis of tori to average-case throughput reveals that there is a weak tradeoff between average-case and worst-case throughput.  ...  Specifically, both the IVAL and 2TURN algorithms developed for the worst-case also have good average-case throughput.  ...  A similar optimization for edge-symmetric topologies yields a reduction in the number of worst-case throughput constraints to O(CN ).  ... 
doi:10.1145/777441.777444 fatcat:c3xsnonktfbdzo4zww4lb7zl5e

Throughput-centric routing algorithm design

Brian Towles, William J. Dally, Stephen Boyd
2003 Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures - SPAA '03  
Expanding the analysis of tori to average-case throughput reveals that there is a weak tradeoff between average-case and worst-case throughput.  ...  Specifically, both the IVAL and 2TURN algorithms developed for the worst-case also have good average-case throughput.  ...  A similar optimization for edge-symmetric topologies yields a reduction in the number of worst-case throughput constraints to O(CN ).  ... 
doi:10.1145/777412.777444 dblp:conf/spaa/TowlesDB03 fatcat:x7jaghbqpjeazndoohpwchulue

Automatic Bayesian Classification of Healthy Controls, Bipolar Disorder, and Schizophrenia Using Intrinsic Connectivity Maps From fMRI Data

J I Arribas, V D Calhoun, T Adali
2010 IEEE Transactions on Biomedical Engineering  
The average 3-way correct classification rate is in the range of 70 − 72%, for the test set, remaining close to the estimated Bayesian optimal correct classification rate theoretical upper bound of about  ...  dimension of the input patterns to a number comparable to the limited number of subjects available for each of the three classes.  ...  Arribas wishes to thank Pedro Rodriguez, Univ. Maryland Baltimore County, MD, USA for the help in preprocessing the fMRI data and Dr. Xi-Lin Li, Univ.  ... 
doi:10.1109/tbme.2010.2080679 pmid:20876002 pmcid:PMC2982883 fatcat:il4dzba6zjhthiy2jcw35vv4ee
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