Related papers: Monotone Curve Estimation via Convex Duality
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
Learning curves are a fundamental primitive in supervised learning, describing how an algorithm's performance improves with more data and providing a quantitative measure of its generalization ability. Formally, a learning curve plots the…
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…
In this paper, we investigate accelerated first-order methods for smooth convex optimization problems under inexact information on the gradient of the objective. The noise in the gradient is considered to be additive with two possibilities:…
We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
A method of modeling data with gaps by a sequence of curves has been developed. The new method is a generalization of iterative construction of singular expansion of matrices with gaps. Under discussion are three versions of the method…
ConicCurv is a new derivative-free algorithm to estimate the curvature of a plane curve from a sample of data points. It is based on a known tangent estimator method grounded on classic results of Projective Geometry and B\'ezier rational…
We study when the \emph{optimization curve} of first-order methods -- the sequence \${f(x\_n)}*{n\ge0}\$ produced by constant-stepsize iterations -- is convex, equivalently when the forward differences \$f(x\_n)-f(x*{n+1})\$ are…
The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…
We introduce principal curves in Wasserstein space, and in general compact metric spaces. Our motivation for the Wasserstein case comes from optimal-transport-based trajectory inference, where a developing population of cells traces out a…
This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…
We consider feasibility and constrained optimization problems defined over smooth and/or strongly convex sets. These notions mirror their popular function counterparts but are much less explored in the first-order optimization literature.…
We propose in this paper a unifying scheme for several algorithms from the literature dedicated to the solving of monotone inclusion problems involving compositions with linear continuous operators in infinite dimensional Hilbert spaces. We…
This paper proposes a robust adaptive algorithm for smooth graph signal recovery which is based on generalized correntropy. A proper cost function is defined for this purpose. The proposed algorithm is derived and a kernel width…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays…
This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor…