General bounds on statistical query learning and PAC learning with noise via hypothesis boosting

Specifying the objective function that an AI system should pursue can be challenging. Especially when the decisions to be made by the system have a moral component, input from multiple stakeholders is often required. We consider approaches that query them about their judgments in individual examples, and then aggregate these judgments into a general policy. We propose a formal learning-theoretic framework for this setting. We then give general results on how to translate classical results from PAC learning into results in our framework. Subsequently, we show that in some settings, better results can be obtained by working directly in our framework. Finally, we discuss how our model can be extended in a variety of ways for future research.

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Quantum learning with noise and decoherence: a robust quantum neural network

10.36227/techrxiv.11398458.v1 ◽

2019 ◽

Author(s):

Elizabeth Behrman ◽

Nam Nguyen ◽

James Steck

Keyword(s):

Neural Network ◽

Quantum Computing ◽

Large Scale ◽

Learning Approaches ◽

Quantum Neural Network ◽

Quantum Learning ◽

Learning With Noise ◽

Robustness To Noise ◽

Robust To Noise ◽

Arbitrary Quantum

<p>Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work in a quantum context, and unwanted interactions with the environment can destroy coherence and thus the quantum nature of the computation. Because of the parallel and distributed nature of classical neural networks, they have long been successfully used to deal with incomplete or damaged data. In this work, we show that our model of a quantum neural network (QNN) is similarly robust to noise, and that, in addition, it is robust to decoherence. Moreover, robustness to noise and decoherence is not only maintained but improved as the size of the system is increased. Noise and decoherence may even be of advantage in training, as it helps correct for overfitting. We demonstrate the robustness using entanglement as a means for pattern storage in a qubit array. Our results provide evidence that machine learning approaches can obviate otherwise recalcitrant problems in quantum computing. </p> <p> </p>

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On the Complexity of Learning a Class Ratio from Unlabeled Data

Journal of Artificial Intelligence Research ◽

10.1613/jair.1.12013 ◽

2020 ◽

Vol 69 ◽

Author(s):

Benjamin Fish ◽

Lev Reyzin

Keyword(s):

Computational Complexity ◽

Unlabeled Data ◽

Training Data ◽

Pac Learning ◽

Vc Dimension ◽

Standard Set

In the problem of learning a class ratio from unlabeled data, which we call CR learning, the training data is unlabeled, and only the ratios, or proportions, of examples receiving each label are given. The goal is to learn a hypothesis that predicts the proportions of labels on the distribution underlying the sample. This model of learning is applicable to a wide variety of settings, including predicting the number of votes for candidates in political elections from polls. In this paper, we formally define this class and resolve foundational questions regarding the computational complexity of CR learning and characterize its relationship to PAC learning. Among our results, we show, perhaps surprisingly, that for finite VC classes what can be efficiently CR learned is a strict subset of what can be learned efficiently in PAC, under standard complexity assumptions. We also show that there exist classes of functions whose CR learnability is independent of ZFC, the standard set theoretic axioms. This implies that CR learning cannot be easily characterized (like PAC by VC dimension).

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