论文标题
迭代性考奇阈值：正规化与先验
Iterative Cauchy Thresholding: Regularisation with a heavy-tailed prior
论文作者
论文摘要
在机器学习时代，由于其对学习模型的好处，稀疏性继续引起重大兴趣。旨在优化\（\ ell_0 \） - 和\（\ ell_1 \）的算法是实现稀疏性的常见选择。在这项工作中，提出了一种替代算法，该算法是根据表征稀疏域中系数的cauchy分布的假设得出的。已知Cauchy分布能够在数据中捕获与稀疏过程有关的重尾。我们首先推导cauchy近端运营商，然后提出一种算法，以优化包括库奇罚款项的成本函数。我们将我们的贡献作为迭代的Cauchy阈值（ICT）。结果表明，在稀疏的编码方法下，使用ICT与固定的过度完整离散余弦词典结合使用，可以实现稀疏的溶液。
In the machine learning era, sparsity continues to attract significant interest due to the benefits it provides to learning models. Algorithms aiming to optimise the \(\ell_0\)- and \(\ell_1\)-norm are the common choices to achieve sparsity. In this work, an alternative algorithm is proposed, which is derived based on the assumption of a Cauchy distribution characterising the coefficients in sparse domains. The Cauchy distribution is known to be able to capture heavy-tails in the data, which are linked to sparse processes. We begin by deriving the Cauchy proximal operator and subsequently propose an algorithm for optimising a cost function which includes a Cauchy penalty term. We have coined our contribution as Iterative Cauchy Thresholding (ICT). Results indicate that sparser solutions can be achieved using ICT in conjunction with a fixed over-complete discrete cosine transform dictionary under a sparse coding methodology.
