论文标题
钢琴：用于多项式和稀疏多项式逻辑回归的快速平行迭代算法
PIANO: A Fast Parallel Iterative Algorithm for Multinomial and Sparse Multinomial Logistic Regression
论文作者
论文摘要
多项式逻辑回归是一个良好的分类工具，已被广泛用于图像处理，计算机视觉和生物信息学等领域。在监督的分类方案下，多项式逻辑回归模型通过优化可能的可能性目标来学习重量向量，以区分任何两个类别。随着大数据的出现，数据的淹没导致了较大的维度矢量，并且还引起了大量类，这使得经典方法适用于模型估计，而不是计算上的可行性。为了解决这个问题，我们在这里提出了一种平行的迭代算法：用于多项式逻辑回归（钢琴）的并行迭代算法，该算法基于大型化最小化过程，并且可以平行更新权重向量的每个元素。此外，我们还表明，钢琴可以轻松扩展以解决稀疏的多项式逻辑回归问题 - 这是一个广泛研究的问题，因为它具有吸引人的特征选择属性。特别是，我们可以解决钢琴的扩展，以解决L1和L0正则化的稀疏多项式逻辑回归问题。我们还证明钢琴会收敛到多项式和稀疏的多项式逻辑回归问题的固定点。进行了模拟以将钢琴与现有方法进行比较，发现所提出的算法在收敛速度方面的性能优于现有方法。
Multinomial Logistic Regression is a well-studied tool for classification and has been widely used in fields like image processing, computer vision and, bioinformatics, to name a few. Under a supervised classification scenario, a Multinomial Logistic Regression model learns a weight vector to differentiate between any two classes by optimizing over the likelihood objective. With the advent of big data, the inundation of data has resulted in large dimensional weight vector and has also given rise to a huge number of classes, which makes the classical methods applicable for model estimation not computationally viable. To handle this issue, we here propose a parallel iterative algorithm: Parallel Iterative Algorithm for MultiNomial LOgistic Regression (PIANO) which is based on the Majorization Minimization procedure, and can parallely update each element of the weight vectors. Further, we also show that PIANO can be easily extended to solve the Sparse Multinomial Logistic Regression problem - an extensively studied problem because of its attractive feature selection property. In particular, we work out the extension of PIANO to solve the Sparse Multinomial Logistic Regression problem with l1 and l0 regularizations. We also prove that PIANO converges to a stationary point of the Multinomial and the Sparse Multinomial Logistic Regression problems. Simulations were conducted to compare PIANO with the existing methods, and it was found that the proposed algorithm performs better than the existing methods in terms of speed of convergence.
