Nuances in Margin Conditions Determine Gains in Active Learning

Kpotufe, Samory; Gao, Yuan; Zhao, Yunfan

doi:10.48550/arxiv.2110.08418

Cited by 2 publications

(6 citation statements)

References 7 publications

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“…The parameter ζ 0 should be considered as a extremely small quantity, where the extreme case corresponds to ζ 0 = 0 (which still allow arbitrary probability for region {x ∈ X : η(x) = 1/2}). The special case with ζ 0 = 0 is recently studied in (Kpotufe et al, 2021), where the authors conclude that no active learners can outperform the passive counterparts in the nonparametric regime. We show next, in the parametric regime (with function approximation), active learning with proper abstention (Algorithm 1) overcomes these noise-seeking conditions.…”

Section: Abstention To Avoid Noise-seekingmentioning

confidence: 99%

Efficient Active Learning with Abstention

Zhu¹,

Nowak²

2022

Preprint

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The goal of active learning is to achieve the same accuracy achievable by passive learning, while using much fewer labels. Exponential savings in label complexity are provably guaranteed in very special cases, but fundamental lower bounds show that such improvements are impossible in general. This suggests a need to explore alternative goals for active learning. Learning with abstention is one such alternative. In this setting, the active learning algorithm may abstain from prediction in certain cases and incur an error that is marginally smaller than 1 2 . We develop the first computationally efficient active learning algorithm with abstention. Furthermore, the algorithm is guaranteed to only abstain on hard examples (where the true label distribution is close to a fair coin), a novel property we term "proper abstention" that also leads to a host of other desirable characteristics. The option to abstain reduces the label complexity by an exponential factor, with no assumptions on the distribution, relative to passive learning algorithms and/or active learning that are not allowed to abstain. A key feature of the algorithm is that it avoids the undesirable "noise-seeking" behavior often seen in active learning. We also explore extensions that achieve constant label complexity and deal with model misspecification.

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Section: Abstention To Avoid Noise-seekingmentioning

confidence: 99%

Efficient Active Learning with Abstention

Zhu¹,

Nowak²

2022

Preprint

View full text Add to dashboard Cite

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“…The unit ball in the Sobolev space is defined as W α,∞ 1 (X ) := {f : f W α,∞ ≤ 1}. Following the convention of nonparametric active learning (Castro and Nowak, 2008;Minsker, 2012;Locatelli et al, 2017Locatelli et al, , 2018Shekhar et al, 2021;Kpotufe et al, 2021), we assume X = [0, 1] d and η ∈ W α,∞ 1 (X ) (except in Section 4).…”

Section: Problem Settingmentioning

confidence: 99%

“…These work mainly focus on the parametric regime (e.g., learning with a set of linear classifiers), and their label complexities rely on the boundedness of the so-called disagreement coefficient (Hanneke, 2007(Hanneke, , 2014Friedman, 2009). Active learning in the nonparametric regime has been analyzed in Castro and Nowak (2008); Minsker (2012); Locatelli et al (2017Locatelli et al ( , 2018; Kpotufe et al (2021). These algorithms rely on partitioning of the input space X ⊆ [0, 1] d into exponentially (in dimension) many small cubes, and then conduct local mean (or some higher-order statistics) estimation within each small cube.…”

Section: Related Workmentioning

confidence: 99%

“…• New perspective on nonparametric learning. Nonparametric learning of smooth functions have been mainly approached by partitioning-based methods (Tsybakov, 2004;Audibert and Tsybakov, 2007;Castro and Nowak, 2008;Minsker, 2012;Locatelli et al, 2017Locatelli et al, , 2018Kpotufe et al, 2021) : Partition the unit cube [0, 1] d into exponentially (in dimension) many sub-cubes and conduct local mean estimation within each sub-cube (which additionally requires a strictly stronger membership querying oracle). Our results show that, in both passive and active settings, one can learn globally with a set of neural networks and achieve near minimax optimal label complexities.…”

Section: Update Active Set Hmentioning

confidence: 99%

“…We obtain insights from the nonparametric setting where the conditional probability (of taking a positive label) is assumed to be a smooth function (Tsybakov, 2004;Audibert and Tsybakov, 2007). Previous nonparametric active learning algorithms proceed by partitioning the action space into exponentially many sub-regions (e.g., partitioning the unit cube [0, 1] d into ε −d sub-cubes each with volume ε d ), and then conducting local mean (or some higher-order statistics) estimation within each sub-region (Castro and Nowak, 2008;Minsker, 2012;Locatelli et al, 2017Locatelli et al, , 2018Shekhar et al, 2021;Kpotufe et al, 2021). We show that, with an appropriately chosen set of neural networks that globally approximates the smooth regression function, one can in fact recover the minimax label complexity for active learning, up to disagreement coefficient (Hanneke, 2007(Hanneke, , 2014 and other logarithmic factors.…”

Section: Introductionmentioning

confidence: 99%

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Active Learning with Neural Networks: Insights from Nonparametric Statistics

Zhu¹,

Nowak²

2022

Preprint

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Deep neural networks have great representation power, but typically require large numbers of training examples. This motivates deep active learning methods that can significantly reduce the amount of labeled training data. Empirical successes of deep active learning have been recently reported in the literature, however, rigorous label complexity guarantees of deep active learning have remained elusive. This constitutes a significant gap between theory and practice. This paper tackles this gap by providing the first near-optimal label complexity guarantees for deep active learning. The key insight is to study deep active learning from the nonparametric classification perspective. Under standard low noise conditions, we show that active learning with neural networks can provably achieve the minimax label complexity, up to disagreement coefficient and other logarithmic terms. When equipped with an abstention option, we further develop an efficient deep active learning algorithm that achieves polylog( 1 ε ) label complexity, without any low noise assumptions. We also provide extensions of our results beyond the commonly studied Sobolev/Hölder spaces and develop label complexity guarantees for learning in Radon BV 2 spaces, which have recently been proposed as natural function spaces associated with neural networks.

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Nuances in Margin Conditions Determine Gains in Active Learning

Cited by 2 publications

References 7 publications

Efficient Active Learning with Abstention

Efficient Active Learning with Abstention

Active Learning with Neural Networks: Insights from Nonparametric Statistics

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