Sparse single-index model
Sparse single-index model
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DOI：
10.5555/2567709.2502589
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发表时间：
2011-01
期刊：
影响因子：
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通讯作者：
Pierre Alquier;G. Biau
中科院分区：
文献类型：
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作者：
Pierre Alquier;G. Biau
设（X，Y）是取Rp × R中值的随机对。在所谓的单指标模型中，有Y = f*（θ*TX）+W，其中f* 是未知的单变量可测函数，θ* 是Rd中的未知向量，W表示满足E[W| X] = 0。已知单索引模型提供了一种灵活的方式来建模各种高维现实世界的现象。然而，尽管它相对简单，这种降维方案面临着严重的并发症，只要潜在的维度变得大于观察的数量（“p大于n”的范例）。为了避免这个困难，我们考虑单指标模型估计问题，从稀疏的角度使用PAC贝叶斯方法。在理论方面，我们提供了一个尖锐的预言不等式，这是更强大的比最有名的预言不等式的其他常见的单索引恢复过程。所提出的方法是通过可逆跳马尔可夫链蒙特卡罗技术实现的，其性能与标准程序进行了比较。
Let (X,Y) be a random pair taking values in Rp × R. In the so-called single-index model, one has Y = f*(θ*TX)+W, where f* is an unknown univariate measurable function, θ* is an unknown vector in Rd, and W denotes a random noise satisfying E[W|X] = 0. The single-index model is known to offer a flexible way to model a variety of high-dimensional real-world phenomena. However, despite its relative simplicity, this dimension reduction scheme is faced with severe complications as soon as the underlying dimension becomes larger than the number of observations ("p larger than n" paradigm). To circumvent this difficulty, we consider the single-index model estimation problem from a sparsity perspective using a PAC-Bayesian approach. On the theoretical side, we offer a sharp oracle inequality, which is more powerful than the best known oracle inequalities for other common procedures of single-index recovery. The proposed method is implemented by means of the reversible jump Markov chain Monte Carlo technique and its performance is compared with that of standard procedures.