论文标题
具有非线性傅立叶功能的稀疏恢复
Sparse Recovery With Non-Linear Fourier Features
论文作者
论文摘要
在广泛的回归和分类应用中，随机非线性傅立叶特征最近显示出了出色的性能。在这一成功的动机上，本文着重于稀疏的非线性傅立叶功能（NFF）模型。我们提供了足够数量的数据点的表征，以确保具有高概率的未知参数的完美恢复。特别是，我们展示了足够数量的数据点取决于与输入数据的概率分布函数相关的内核矩阵。我们将结果与有界正交系统的可恢复性界限进行了比较，并提供了示例，以说明NFF模型下的稀疏恢复。
Random non-linear Fourier features have recently shown remarkable performance in a wide-range of regression and classification applications. Motivated by this success, this article focuses on a sparse non-linear Fourier feature (NFF) model. We provide a characterization of the sufficient number of data points that guarantee perfect recovery of the unknown parameters with high-probability. In particular, we show how the sufficient number of data points depends on the kernel matrix associated with the probability distribution function of the input data. We compare our results with the recoverability bounds for the bounded orthonormal systems and provide examples that illustrate sparse recovery under the NFF model.
