Functional Classification with Margin Conditions
Functional Classification with Margin Conditions
复制标题
具有裕度条件的功能分类
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Christine Tuleau
中科院分区：
文献类型：
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作者：
M. Fromont;Christine Tuleau
设（X，Y）是一个$\mathcal{X}$× 0，1值的随机对，考虑一个样本（X1，Y1），.，(Xn，Yn）的分布。我们的目标是从这个样本构建一个分类器，它是一个函数，可以从X的观察值预测Y的值。$\mathcal{X}$是函数空间的特殊情况由于所谓的维数灾难而特别有趣。在最近的一篇论文中，Biau等人。[1]建议在傅立叶基中过滤Xi，并将经典的k-近邻规则应用于展开式的第一个d系数。k和d的选择都是通过惩罚标准自动进行的。我们扩展了这项研究，并注意到在这里使用的惩罚Biau等人。当我们考虑极大极小的观点下，一些保证金类型的假设是太重了。我们证明，使用较小的顺序或等于零的罚款是更可取的理论和实践。我们的实验研究还表明，引入一个小的顺序惩罚稳定的选择过程，同时保持相当好的性能。
Let (X,Y) be a $\mathcal{X}$× 0,1 valued random pair and consider a sample (X1,Y1),...,(Xn,Yn) drawn from the distribution of (X,Y). We aim at constructing from this sample a classifier that is a function which would predict the value of Y from the observation of X. The special case where $\mathcal{X}$is a functional space is of particular interest due to the so called curse of dimensionality. In a recent paper, Biau et al. [1] propose to filter the Xi’s in the Fourier basis and to apply the classical k–Nearest Neighbor rule to the first d coefficients of the expansion. The selection of both k and d is made automatically via a penalized criterion. We extend this study, and note here the penalty used by Biau et al. is too heavy when we consider the minimax point of view under some margin type assumptions. We prove that using a penalty of smaller order or equal to zero is preferable both in theory and practice. Our experimental study furthermore shows that the introduction of a small-order penalty stabilizes the selection process, while preserving rather good performances.