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Constructing Multiclass Classifiers using Binary Classifiers Under Log-Loss
[article]

2021
*
arXiv
*
pre-print

The

arXiv:2102.08184v2
fatcat:qwrc7f5eubf4pksmiylz3f7vzi
*construction*of*multiclass**classifiers*from*binary*elements is studied in this paper, and performance is quantified by the regret, defined with respect to the Bayes optimal*log*-*loss*. ... The first is one vs. all (OVA), for which we prove that the*multiclass*regret is upper bounded by the sum of*binary*regrets of the constituent*classifiers*. ... CONCLUDING REMARKS We have studied the problem of soft classification*under**log*-*loss*and have focused on*constructions*of*multiclass**classifiers*from*binary**classifiers*. ...##
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Error-Correcting Tournaments
[chapter]

2009
*
Lecture Notes in Computer Science
*

We present a family of pairwise tournaments reducing k-class classification to

doi:10.1007/978-3-642-04414-4_22
fatcat:et3ish4wfvg7vphxwnu3k3sonm
*binary*classification. ... These reductions are provably robust against a constant fraction of*binary*errors, and match the best possible computation and regret up to a constant. ... Utilizing this observation, we*construct*a reduction, called the Filter Tree, with the property that it*uses*O(*log*k)*binary*examples and O(*log*k) computation at training and test time with a*multiclass*...##
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Error-Correcting Tournaments
[article]

2010
*
arXiv
*
pre-print

We present a family of pairwise tournaments reducing k-class classification to

arXiv:0902.3176v4
fatcat:2jysxunlfne3dldzfukuxjreo4
*binary*classification. These reductions are provably robust against a constant fraction of*binary*errors. ... The results improve on the PECOC*construction*SECOC with an exponential improvement in computation, from O(k) to O(_2 k), and the removal of a square root in the regret dependence, matching the best possible ... Utilizing this observation, we*construct*a reduction, called the filter tree, which*uses*a O(*log*k) computation per*multiclass*example at both training and test time, and whose*multiclass*regret is bounded ...##
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Multiclass Learning by Probabilistic Embeddings

2002
*
Neural Information Processing Systems
*

Furthermore, the method of

dblp:conf/nips/DekelS02
fatcat:cvki6cpmevd2pfsu3x4fxqhwry
*multiclass*categorization*using*ECOC is shown to be an instance of Bunching. ... A key*construction*in the analysis of the algorithm is the notion of probabilistic output codes, a generalization of error correcting output codes (ECOC). ... then solving each*binary*problem individually to obtain a*multiclass**classifier*. ...##
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Multiclass classification of microarray data samples with a reduced number of genes

2011
*
BMC Bioinformatics
*

Conclusions: A comprehensive experimental work shows that the bound is indeed

doi:10.1186/1471-2105-12-59
pmid:21342522
pmcid:PMC3056725
fatcat:7i24ujejh5bt5ffks5i3mhlk7a
*useful*to induce accurate and sparse*multiclass**classifiers*for microarray data samples. ... The bound suggests that high-dimensional*binary*output domains might favor the existence of accurate and sparse*binary*mediated*multiclass**classifiers*for microarray data samples. ...*Multiclass**classifiers*for M ≥ 3 classes built from n*binary**classifiers*, n ≥ ⌈*log*2 M⌉ + 2, are considered. ...##
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Better multiclass classification via a margin-optimized single binary problem

2008
*
Pattern Recognition Letters
*

We develop a new

doi:10.1016/j.patrec.2008.06.012
fatcat:3ohttlc63zhy7lj4zkonb5q4r4
*multiclass*classification method that reduces the*multiclass*problem to a single*binary**classifier*(SBC). ... We provide a bound on the generalization error of the*multiclass**classifier*obtained with our*construction*and outline the conditions for its consistency. ... Risk Bound Let M (h α,µ , (x, y) ) be the*multiclass*0/1*loss*of the SBC*classifier*,*using*the hypothesis h α,µ for its*binary*decisions, over a*multiclass*example (x, y). ...##
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Efficient Loss-Based Decoding on Graphs For Extreme Classification
[article]

2018
*
arXiv
*
pre-print

We show how to find the sweet spot of this tradeoff

arXiv:1803.03319v2
fatcat:7j5auzag3fcnboqgkco4o54u5u
*using*only the training data. ... Our framework employs output codes induced by graphs, for which we show how to perform efficient*loss*-based decoding to potentially improve accuracy. ... Few well known*loss*functions are the hinge*loss*L(z) max (0, 1 − z),*used*by SVM, its square, the*log**loss*L (z)*log*(1 + e −z )*used*in logistic regression, and the exponential*loss*L (z) e −z*used*in ...##
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Consistent Classification with Generalized Metrics
[article]

2019
*
arXiv
*
pre-print

We propose a framework for

arXiv:1908.09057v1
fatcat:i473x56wvbbjjnivdejqmwwive
*constructing*and analyzing*multiclass*and multioutput classification metrics, i.e., involving multiple, possibly correlated*multiclass*labels. ... Further, we analyze averaging methodologies commonly*used*to compute multioutput metrics and characterize the corresponding Bayes optimal*classifiers*. ... Tewari and Bartlett [26] showed that*multiclass**classifiers**constructed**using*consistent*binary**classifiers*may still lead to inconsistent*multiclass*results. Narasimhan et al. ...##
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Consistent Multiclass Algorithms for Complex Performance Measures

2015
*
International Conference on Machine Learning
*

This setting includes as a special case all

dblp:conf/icml/NarasimhanRS015
fatcat:4bvqvdcy2zdijnekeyed7grble
*loss*-based performance measures, which are simply linear functions of the confusion matrix, but also includes more complex performance measures such as the*multiclass*... The resulting algorithms are provably consistent and outperform a*multiclass*version of the state-of-the-art SVMperf method in experiments; for large*multiclass*problems, the algorithms are also orders ... SA acknowledges support from the Department of Science & Technology (DST) of the Indian Government*under*a Ramanujan Fellowship, from the Indo-*US*Science & Technology Forum (IUSSTF), and from Yahoo in ...##
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Convex Optimization for Binary Classifier Aggregation in Multiclass Problems
[article]

2014
*
arXiv
*
pre-print

*Multiclass*problems are often decomposed into multiple

*binary*problems that are solved by individual

*binary*

*classifiers*whose results are integrated into a final answer. ... In this paper we present a convex optimization method for an optimal aggregation of

*binary*

*classifiers*to estimate class membership probabilities in

*multiclass*problems. ... Direct approach involves

*constructing*a discriminant function directly for the

*multiclass*problem. ...

##
###
Convex Optimization for Binary Classifier Aggregation in Multiclass Problems
[chapter]

2014
*
Proceedings of the 2014 SIAM International Conference on Data Mining
*

*Multiclass*problems are often decomposed into multiple

*binary*problems that are solved by individual

*binary*

*classifiers*whose results are integrated into a final answer. ... In this paper we present a convex optimization method for an optimal aggregation of

*binary*

*classifiers*to estimate class membership probabilities in

*multiclass*problems. ... Direct approach involves

*constructing*a discriminant function directly for the

*multiclass*problem. ...

##
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A cryptographic approach to black box adversarial machine learning
[article]

2020
*
arXiv
*
pre-print

Our

arXiv:1906.03231v2
fatcat:a5lwo22jhfbajhmivnbkhlzu54
*construction*crucially leverages hidden randomness in the*multiclass*-to-*binary*reduction. ... Our proof*constructs*a new security problem for random*binary**classifiers*which is easier to empirically verify and a reduction from the security of this new model to the security of the ensemble*classifier*... All random*binary**classifiers**used*in these experiments are the same architecture as the random*binary**classifiers*in Section 4.a. ...##
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On the Consistency of Output Code Based Learning Algorithms for Multiclass Learning Problems

2014
*
Annual Conference Computational Learning Theory
*

We focus on settings where the

dblp:conf/colt/RamaswamyBAW14
fatcat:jizxzymiizbghepw2to27orqte
*binary*problems are solved by minimizing a*binary*surrogate*loss*, and derive general conditions on the*binary*surrogate*loss**under*which the one-vs-all and all-pairs code ... We then consider general*multiclass*learning problems defined by a general*multiclass**loss*, and derive conditions on the output code matrix and*binary*surrogates*under*which the resulting algorithm is ... SA acknowledges support from the Department of Science & Technology (DST) of the Indian Government*under*a Ramanujan Fellowship, from the Indo-*US*Science & Technology Forum (IUSSTF), and from Yahoo in ...##
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Error limiting reductions between classification tasks

2005
*
Proceedings of the 22nd international conference on Machine learning - ICML '05
*

We

doi:10.1145/1102351.1102358
dblp:conf/icml/BeygelzimerDHLZ05
fatcat:pb2i5k7v4jaxrji4jj3wsgpkce
*use*this model to devise a new reduction from multi-class cost-sensitive classification to*binary*classification with the following guarantee: If the learned*binary**classifier*has error rate at most ... Since cost-sensitive classification can embed any bounded*loss*finite choice supervised learning task, this result shows that any such task can be solved*using*a*binary*classification oracle. ... (Tree error efficiency) For all*multiclass*problems (D, X, T ), if the*binary**classifiers*have*loss*rate , the tree reduction has*loss*rate at most*log*2 r. Proof. ...##
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Convex Calibrated Surrogates for the Multi-Label F-Measure
[article]

2020
*
arXiv
*
pre-print

limit of sufficient data) a Bayes optimal multi-label

arXiv:2009.07801v1
fatcat:jfk5shpu75aardsxrg6lxctaiq
*classifier*for the F-measure. ... In this paper, we explore the question of designing convex surrogate*losses*that are calibrated for the F-measure – specifically, that have the property that minimizing the surrogate*loss*yields (in the ... SA is also supported in part by the*US*National Institutes of Health (NIH)*under*Grant No. U01CA214411. ...
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