Related papers: Chaining, Interpolation, and Convexity II: The con…

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be…

The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from…

Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the…

We present a numerically efficient and accurate Multiple Scattering formalism, which is a generalization of the Multiple Scattering method with a truncated basis set [X. -G. Zhang and W. H. Butler, Phys. Rev. B 46,7433 (1992)]. Compared to…

This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…

This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…

Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…

Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…

Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…

The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…

In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at…

In this article, we consider linearly convex complex cones in complex Banach spaces and we define a new projective metric on these cones. Compared to the hyperbolic gauge of Rugh, it has the advantage of being explicit, and easier to…

We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…

We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…

Given a set of snapshots from a temporal network we develop, analyze, and experimentally validate a so-called network interpolation scheme. Our method allows us to build a plausible, albeit random, sequence of graphs that transition between…

The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…

In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making…