Learning gradients : predictive models that infer geometry and dependence
Learning gradients : predictive models that infer geometry and dependence
复制标题
学习梯度：推断几何和依赖性的预测模型
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
S. Mukherjee
中科院分区：
文献类型：
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作者：
Q. Wu;J. Guinney;M. Maggioni;S. Mukherjee
本文开发并讨论了一种称为学习梯度的建模框架，该框架允许预测模型同时推断与预测相关的输入空间的几何和统计依赖性。本文讨论的几何关系适用于欧几里得空间以及流形设置。该框架中的中心量是回归或分类函数的梯度估计，它是通过判别性方法计算的。我们将梯度与逆回归问题联系起来，在机器学习社区中，逆回归问题通常通过生成模型来解决。这种关系的结果是对统计文献中的各种同步回归和降维方法进行简单而精确的比较。梯度估计应用于机器学习的各种核心问题：变量选择、线性和非线性降维，以及与预测相关的输入变量的依赖关系的图形模型的推断。
This paper develops and discusses a modeling framework called learning gradients that allows for predictive models that simultaneously infer the geometry and statistical dependencies of the input space relevant for prediction. The geometric relations addressed in this paper hold for Euclidean spaces as well as the manifold setting. The central quantity in this framework is an estimate of the gradient of a regression or classification function, which is computed by a discriminative approach. We relate the gradient to the problem of inverse regression which in the machine learning community is typically addressed by generative models. A result of this relation is a simple and precise comparison of a variety of simultaneous regression and dimensionality reduction methods from the statistics literature. The gradient estimate is applied to a variety of problems central to machine learning: variable selection, linear and nonlinear dimension reduction, and the inference of a graphical model of the dependencies of the input variables that are relevant to prediction.
DOI：
10.1073/pnas.0500334102
发表时间：
2005-05-24
影响因子：
11.1
作者：
Coifman, RR;Lafon, S;Zucker, SW
通讯作者：
Zucker, SW