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Large deviations in the perceptron model and consequences for active learning

Authors: Cui, Hugo; Saglietti, Luca; Zdeborovà, Lenka;

Large deviations in the perceptron model and consequences for active learning

Abstract

Abstract Active learning (AL) is a branch of machine learning that deals with problems where unlabeled data is abundant yet obtaining labels is expensive. The learning algorithm has the possibility of querying a limited number of samples to obtain the corresponding labels, subsequently used for supervised learning. In this work, we consider the task of choosing the subset of samples to be labeled from a fixed finite pool of samples. We assume the pool of samples to be a random matrix and the ground truth labels to be generated by a single-layer teacher random neural network. We employ replica methods to analyze the large deviations for the accuracy achieved after supervised learning on a subset of the original pool. These large deviations then provide optimal achievable performance boundaries for any AL algorithm. We show that the optimal learning performance can be efficiently approached by simple message-passing AL algorithms. We also provide a comparison with the performance of some other popular active learning strategies.

Keywords

FOS: Computer and information sciences, ACTIVE LEARNING, LARGE DEVIATIONS, PERCEPTRON MODEL, MESSAGE-PASSING ALGORITHMS, Computer Science - Machine Learning, Active learning, Large Deviations, Active learning Large Deviations Perceptron Model Message-passing algorithms, FOS: Physical sciences, PERCEPTRON MODEL, LARGE DEVIATIONS, ACTIVE LEARNING, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Perceptron Model, Message-passing algorithms, [PHYS] Physics [physics], Machine Learning (cs.LG)

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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Average
Green
gold