For deep nets we examine contraction properties of complexity for each layer of the network. For any ReLU network there is, without loss of generality, a representation in which the sum of the absolute values of the weights into each node is exactly 1, and the input layer variables are multiplied by a value V coinciding with the total variation ...
Creator:
Barron, Andrew (Yale University)
Created:
2019-09-17
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In the 1920's the geneticist Sewall Wright introduced a class ofGaussian statistical models represented by graphs containing directedand bi-directed edges, known as path diagrams. These models have beenused extensively in psychometrics and econometrics where they arecalled structural equation models.I will first describe the subclass of bow-free...
Creator:
Richardson, Thomas S. (University of Washington)
Created:
2007-03-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Intrinsic volumes of convex sets are natural geometric quantities that also play important roles in applications. In particular, the discrete probability distribution ${cal L}(V_C)$ given by the sequence $v_0,ldots,v_d$ of conic intrinsic volumes of a closed convex cone $C$ in $mathbb{R}^d$ summarizes key information about the success of convex ...
Creator:
Goldstein, Larry
Created:
2015-04-14
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We review applications and algorithmic challenges of Gaussian Process (GP) modeling. GP is a powerful and flexible uncertainty quantification and data analysis technique that enables the construction of complex models without the need to specify algebraic relationships between variables. This is done by working directly in the space of the kerne...
Creator:
Zavala, Victor M. (Argonne National Laboratory)
Created:
2013-06-12
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The Gauss-Manin system of a function is a direct image in the category of D-modules. For the case of isolated singularities there are two Singular libraries to compute it: gmssing.lib for (local) isolated hypersurface singularities, gmspoly.lib for (global) tame polynomial functions. In both cases the Gauss-Manin system carries a rich structure:...
Creator:
Schulze, Mathias (Oklahoma State University)
Created:
2006-10-27
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.