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Large margin transformation learning.

机译：大幅度转型学习。

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摘要

With the current explosion of data coming from many scientific fields and industry, machine learning algorithms are more important than ever to help make sense of this data in an automated manner. Support vector machine (SVMs) have been a very successful learning algorithm for many applied settings. However, the support vector machine only finds linear classifiers so data often needs to be preprocessed with appropriately chosen nonlinear mappings in order to find a model with good predictive properties. These mappings can either take the form of an explicit transformation or be defined implicitly with a kernel function.;Automatically choosing these mappings has been studied raider the name of kernel learning. These methods typically optimize a cost function to find a kernel made up of a combination of base kernels thus implicitly learning mappings. This dissertation investigates methods for choosing explicit transformations automatically. This setting differs from the kernel learning framework by learning a combination of base transformations rather than base kernels. This allows prior knowledge to be exploited in the functional form of the transformations which may not be easily encoded as kernels such as when learning monotonic transformations. Additionally, kernel based SVMs are often hard to interpret because they lead to complex decision boundaries which are only linear in the implicitly defined space. However, by working with explicit mappings, models with an intuitive meaning can be learned. The learned transformations can be visualized to lend insight into the problem, and the hyperplane weights indicate the importance of transformed features.;The two basic models that will be studied are the a mixture of transformations phi( x) = sumimi&phis;i( x) and the matrix mixture of transformations which defines kernels of the form k(x, x') = sum i,jmimj&phis;i(x) T&phis;j(x'). The matrix mixture reduces to mixture of transformation learning when M is rank 1 and mixture of kernel learning when M is a diagonal matrix. First, greedy algorithms are proposed to simultaneously learn a mixture of transformations and a large margin hyperplane classifier. Then, a convex semidefinite algorithm is derived to find a matrix mixture of transformations and large margin hyperplane. More efficient algorithms based on the extragradient method are introduced to solve larger problems and extend the basic framework to a multitask setting. Another cost function based on kernel alignment is explored to learn matrix mixture of transformations. Maximizing the alignment with a cardinality constraint on the mixture weights gives rise to approximation algorithms with constant factor approximations similar to the Max-Cut problem. These methods are then applied to the task of learning monotonic transformations which are built from a mixture of truncated ramp functions. Experimental results for synthetic data, image histogram classification, text classification and gender recognition demonstrate the utility of these learned transformations.
机译：随着来自许多科学领域和行业的数据的爆炸式增长，机器学习算法比以往任何时候都更重要，它有助于以自动化的方式理解这些数据。支持向量机（SVM）对于许多应用设置来说是一种非常成功的学习算法。但是，支持向量机只能找到线性分类器，因此通常需要使用适当选择的非线性映射对数据进行预处理，以找到具有良好预测特性的模型。这些映射可以采用显式转换的形式，也可以通过内核函数隐式定义。;已经研究了自动选择这些映射的方法，以内核学习为名。这些方法通常优化成本函数以查找由基本内核的组合组成的内核，从而隐式地学习映射。本文研究了自动选择显式变换的方法。此设置与内核学习框架的不同之处在于，它学习基本转换而不是基本内核的组合。这允许以变换的功能形式来利用先验知识，例如当学习单调变换时，其可能不容易被编码为内核。此外，基于内核的SVM通常难以解释，因为它们会导致复杂的决策边界，这些边界仅在隐式定义的空间内呈线性。但是，通过使用显式映射，可以学习具有直观含义的模型。可以将学习的变换可视化以深入了解问题，超平面权重表明变换特征的重要性。将要研究的两个基本模型是变换的混合phi（x）= sumimi＆phis; i（x）以及定义矩阵形式为k（x，x'）= sum i，jmimjji（x）T Tphi（j'x'）的转换矩阵混合。当M为等级1时，矩阵混合减少为变换学习的混合；当M为对角矩阵时，矩阵混合减少为核学习的混合。首先，提出了贪婪算法以同时学习变换和大余量超平面分类器的混合。然后，导出凸半定算法，以找到变换和大余量超平面的矩阵混合。引入了基于超梯度方法的更有效算法来解决更大的问题，并将基本框架扩展到多任务设置。探索了基于核对齐的另一个成本函数，以学习变换的矩阵混合。在混合权重上使用基数约束最大程度地实现对齐，从而产生具有类似于Max-Cut问题的常数因子近似的近似算法。然后将这些方法应用于学习由截断的斜坡函数的混合建立的单​​调变换的任务。综合数据，图像直方图分类，文本分类和性别识别的实验结果证明了这些学习的转换的实用性。

著录项

  • 作者

    Howard, Andrew G.;

  • 作者单位

    Columbia University.;

  • 授予单位 Columbia University.;
  • 学科 Artificial Intelligence.;Computer Science.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 90 p.
  • 总页数 90
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

  • 入库时间 2022-08-17 11:38:24

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