Proof(Foundations of Machine Learning): For any\epsilon>0, define\mathcal{H}_\epsilon=\{h \in \mathcal{H}:R(h)>\epsilon\}, as long as we draw the training setS,i.i.d., we haveP[\hat R_S(h)=0]\leq (1-\epsilon)^m. That is, we have the probability less than(1-\epsilo...
定义1.3 PAC-学习(PAC-learning):我们说一个概念集合 C 是PAC可学习的,当且仅当存在一个算法 $\mathcal{A}$ 以及一个多项式函数 $poly(\cdot,\cdot,\cdot,\cdot)$,使得对任意的 $\epsilon > 0$ 和 $\delta > 0$ 对所有在 $\mathcal{X}$ 上的分布 $D$,以及对所有的目标概念 $c \in C$,当...
对于简单的问题(如Learning axis-aligned rectangles)可以直接使用PAC理论证明其是可学习的,但对于大多数问题,只能给出定性的分析。 概率上界 PAC理论指出学习的关键是 PS∼DN[R^S(h)≤ϵ]≥1−δ⇔R(h)≈0 实际泛化误差R(h)无法直接获得,但根据大数定律,当样本量N足够大时,经验误差和泛化误差趋于相等...
PAC-Bayesian Machine Learning: Learning by Optimizing a Performance GuaranteeMario Marchand
PAC 学习 (PAC learning )若存在算法 A\mathcal{A}A 与多项式函数 poly(⋅,⋅,⋅,⋅)poly(\cdot,\cdot,\cdot,\cdot)poly(⋅,⋅,⋅,⋅), 使得任意 ε>0\varepsilon>0ε>0 与δ>0\delta>0δ>0 , 对任意 XXX 上的分布 DDD与 任意目标概念c∈Cc\in Cc∈C 下述不等式成立, 对任何...
One of the most basic lower bounds in machine learning is that in nearly any nontrivial setting, it takes at least 1/ϵ samples to learn to error ϵ (and more, if the classifier being learned is complex). However, suppose that data points are agents who have the ability to improve ...
It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the existence of a test or criterion for deciding the feasibility of attempting to learn. We investigate the existence of such a criterion in the setting of PAC-learning, ...
Zeugmann, T. (2016). PAC Learning. In: Sammut, C., Webb, G. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7502-7_631-1 Download citation .RIS .ENW .BIB
Foundations of Machine Learning: The PAC Learning Framework(2)(一)假设集有限在一致性下的学习界。 在上一篇文章中我们介绍了PAC-learnable的定义,以及证明了一个例子是PAC-learnable。 这一节我们介绍当hypothe
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