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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)
We searched for the −− (1860) pentaquark in the photoproduction process off the deuteron in the − π −-decay channel using CLAS. The invariant-mass spectrum of the − π − system does not indicate any statistically significant enhancement near the reported mass M = 1.860 GeV. The statistical analysis of the sideband-subtracted mass spectrum yields a(More)
The proposed measurements are twofold. First, we propose to measure the multiplicities for several hadron species (π + , π − , π 0 , K + , K − , K 0 s) using both hydrogen and deuterium targets. The goal of these measurements is the control of the fragmentation functions used in the extraction of the individual quark and antiquark contributions to the(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)
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. In this lecture, we will introduce the concept of hyperbolic polynomials, a generalization of real stable polynomials. We will also introduce the concept of hyperbolicity cones, which are the set of directions along which a polynomial is always(More)
Consider a population consisting of n individuals, each of whom has one of d types (e.g. their blood type, in which case d = 4). We are allowed to query this database by specifying a subset of the population, and in response we observe a noiseless histogram (a d-dimensional vector of counts) of types of the pooled individuals. This measurement model arises(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)