Linear Time Feature Selection for Regularized Least-Squares

We propose a novel algorithm for greedy forward feature selection for regularized least-squares (RLS) regression and classification, also known as the least-squares support vector machine or ridge regression. The algorithm, which we call greedy RLS, starts from the empty feature set, and on each iteration adds the feature whose addition provides the best leave-one-out cross-validation performance. Our method is considerably faster than the previously proposed ones, since its time complexity is linear in the number of training examples, the number of features in the original data set, and the desired size of the set of selected features. Therefore, as a side effect we obtain a new training algorithm for learning sparse linear RLS predictors which can be used for large scale learning. This speed is possible due to matrix calculus based short-cuts for leave-one-out and feature addition. We experimentally demonstrate the scalability of our algorithm and its ability to find good quality feature sets.Comment: 17 pages, 15 figure

The general circulation of the atmosphere

Theories of how Earth's surface climate may change in the future, of how it may have been in the past, and of how it is related to climates of other planets must build upon a theory of the general circulation of the atmosphere. The view of the atmospheric general circulation presented here focuses not on Earth's general circulation as such but on a continuum of idealized circulations with axisymmetric flow statistics. Analyses of observational data for Earth's atmosphere, simulations with idealized general circulation models, and theoretical considerations suggest how characteristics of the tropical Hadley circulation, of the extratropical circulation, and of atmospheric macroturbulence may depend on parameters such as the planet radius and rotation rate and the strength of the differential heating at the surface

Vortex Mass in a Superfluid

We consider the inertial mass of a vortex in a superfluid. We obtain a vortex mass that is well defined and is determined microscopically and self-consistently by the elementary excitation energy of the kelvon quasiparticle localised within the vortex core. The obtained result for the vortex mass is found to be consistent with experimental observations on superfluid quantum gases and vortex rings in water. We propose a method to measure the inertial rest mass and Berry phase of a vortex in superfluid Bose and Fermi gases.Comment: 12 pages, 1 figur

Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm

We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincar\'e inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class of convex functionals that a local Poincar\'e inequality is implied by the weak displacement convexity of the functional.Comment: 25 pages, 1 figur