Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network-猫眼课题宝

DOI：

10.48550/arxiv.2210.04349

发表时间：

2022-10

期刊：

ArXiv

影响因子：

通讯作者：

中科院分区：

其他

文献类型：

作者：

Siqi Liang;Y. Sun;F. Liang

充分降维是提取隐藏在高维数据中的核心信息的有力工具，在机器学习任务中有着潜在的重要应用。然而，现有的非线性充分降维方法往往缺乏处理大规模数据所必需的可扩展性。我们提出了一种新类型的随机神经网络下严格的概率框架，并表明它可以用于大规模数据的充分降维。建议的随机神经网络的训练使用自适应随机梯度马尔可夫链蒙特卡罗算法，其收敛性进行了严格的研究，以及在文件中。通过对真实世界的分类和回归问题的大量实验，我们表明，所提出的方法与现有的最先进的充分降维方法相比毫不逊色，并且对于大规模数据计算效率更高。

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient dimension reduction methods often lack the scalability necessary for dealing with large-scale data. We propose a new type of stochastic neural network under a rigorous probabilistic framework and show that it can be used for sufficient dimension reduction for large-scale data. The proposed stochastic neural network is trained using an adaptive stochastic gradient Markov chain Monte Carlo algorithm, whose convergence is rigorously studied in the paper as well. Through extensive experiments on real-world classification and regression problems, we show that the proposed method compares favorably with the existing state-of-the-art sufficient dimension reduction methods and is computationally more efficient for large-scale data.

Nonlinear Sufficient Dimension Reduction with a Stochastic Neural Network

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