Related papers: Monotone Curve Estimation via Convex Duality
A graph with convex quadratic stability number is a graph for which the stability number is determined by solving a convex quadratic program. Since the very beginning, where a convex quadratic programming upper bound on the stability number…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…
Currently, knowledge discovery in databases is an essential step to identify valid, novel and useful patterns for decision making. There are many real-world scenarios, such as bankruptcy prediction, option pricing or medical diagnosis,…
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to…
In this paper we consider convex subsets of locally-convex topological vector spaces. Given a fixed point in such a convex subset, we show that there exists a curve completely contained in the convex subset and leaving the point in a given…
Accurate and reliable prediction has profound implications to a wide range of applications. In this study, we focus on an instance of spatio-temporal learning problem--traffic prediction--to demonstrate an advanced deep learning model…
Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…
We study continuous-time portfolio choice with nonlinear payoffs under smooth ambiguity and Bayesian learning. We develop a general framework for dynamic, non-concave asset allocation that accommodates nonlinear payoffs, broad utility…
Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…
In this paper, we consider variants of Newton-MR algorithm for solving unconstrained, smooth, but non-convex optimization problems. Unlike the overwhelming majority of Newton-type methods, which rely on conjugate gradient algorithm as the…
We present an efficient, parallel, constrained optimization technique for approximating CAD curves with super-convergent rates. The optimization function is a disparity measure in terms of a piece-wise polynomial approximation and a curve…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
We propose a framework of principal manifolds to model high-dimensional data. This framework is based on Sobolev spaces and designed to model data of any intrinsic dimension. It includes principal component analysis and principal curve…
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…
Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
Several large scale networks, such as the backbone of the Internet, have been observed to behave like convex Riemannian manifolds of negative curvature. In particular, this paradigm explains the observed existence, for networks of this…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…