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One approach to improving the running time of kernel-based machine learning methods is to build a small sketch of the input and use it in lieu of the full kernel matrix in the machine learning task of interest. Here, we describe a version of this approach that comes with running time guarantees as well as improved guarantees on its statistical performance.… (More)

One approach to improving the running time of kernel-based methods is to build a small sketch of the kernel matrix and use it in lieu of the full matrix in the machine learning task of interest. Here, we describe a version of this approach that comes with running time guarantees as well as improved guarantees on its statistical performance. By extending the… (More)

We present new algorithms for computing the log-determinant of symmetric , diagonally dominant matrices. Existing algorithms run with cubic complexity with respect to the size of the matrix in the worst case. Our algorithm computes an approximation of the log-determinant in time near-linear with respect to the number of non-zero entries and with high… (More)

Given a weighted graph with N vertices, consider a real-valued regression problem in a semi-supervised setting, where one observes n labeled vertices, and the task is to label the remaining ones. We present a theoretical study of ℓ p-based Laplacian regularization under a d-dimensional geometric random graph model. We provide a variational characterization… (More)

Given a weighted graph with N vertices, consider a real-valued regression problem in a semi-supervised setting, where one observes n labeled vertices, and the task is to label the remaining ones. We present a theoretical study of p-based Laplacian regularization under a d-dimensional geometric random graph model. We provide a variational characterization of… (More)

- Ahmed El Alaoui
- 2015

Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. In this lecture we introduce the concept of interlacing for polynomials. This concept provide a convenient way of reasoning about orderings of the roots of real-rooted polynomials. Specifically, it provides a way of tying the roots of the average… (More)

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