Data-driven applications are growing. Machine learning and data analysis now finds both scientific and industrial application in biology, chemistry, geology, medicine, and physics. These applications rely on large quantities of data gathered from automated sensors and user input. Furthermore, the dimensionality of many datasets is extreme: more details are being gathered about single user inter...

The approximate nearest neighbor problem ( -ANN) in Euclidean settings is a fundamental question, which has been addressed by two main approaches: Data-dependent space partitioning techniques perform well when the dimension is relatively low, but are affected by the curse of dimensionality. On the other hand, locality sensitive hashing has polynomial dependence in the dimension, sublinear query...

We improve on the lower bounds for the optimal density of sphere packings. In all sufficiently large dimensions the improvement is by a factor of at least 10, 000; along a sparse sequence of dimensions ni we improve the density by roughly log log ni.

B y far the bulk of our planet is hidden from view, within the earth, under high pressures and temperatures. The behavior of this material dictates the formation, evolution, and present state of the solid earth. Recent geophysical and geochemical studies of the planet present us with a rich array of large-scale processes and phenomena that are not fully understood. These range from the fate of ...

We consider the performance of the bootstrap in high-dimensions for the setting of linear regression, where p < n but p/n is not close to zero. We consider ordinary least-squares as well as robust regression methods and adopt a minimalist performance requirement: can the bootstrap give us good confidence intervals for a single coordinate of ? (where is the true regression vector). We show throu...