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We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…

Machine Learning · Computer Science 2017-07-31 Carlo Ciliberto , Alessandro Rudi , Lorenzo Rosasco

Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler…

Category Theory · Mathematics 2023-11-27 Namita Behera , Avisek Bist , Volker Mehrmann

We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for controlled paths which is interesting in its own right.

Classical Analysis and ODEs · Mathematics 2015-02-16 Horatio Boedihardjo , Danyu Yang , Terry Lyons

We propose regularization methods for linear models based on the $L_q$-likelihood, which is a generalization of the log-likelihood using a power function. Some heavy-tailed distributions are known as $q$-normal distributions. We find that…

Methodology · Statistics 2020-10-28 Yoshihiro Hirose

In this paper we study the semilinear partial differential equations in the plane the linear part of which is written in a divergence form. The main result is given as a factorization theorem. This theorem states that every weak solution of…

Complex Variables · Mathematics 2017-11-02 Vladimir Gutlyanskii , Olga Nesmelova , Vladimir Ryazanov

We generalize recent matrix-based factorization theorems for Lambert series generating functions generating the coefficients $(f \ast 1)(n)$ for some arithmetic function $f$. Our new factorization theorems provide analogs to these…

Number Theory · Mathematics 2019-09-23 Hamed Mousavi , Maxie D. Schmidt

We here first study the state space realization of a tensor-product of a pair of rational functions. At the expense of "inflating" the dimensions, we recover the classical expressions for realization of a regular product of rational…

Optimization and Control · Mathematics 2018-12-05 Daniel Alpay , Izchak Lewkowicz

In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…

Methodology · Statistics 2023-03-01 Shan Wang , Hanxiang Peng

In this note, we concentrate on the backward error of the equality constrained indefinite least squares problem. For the normwise backward error of the equality constrained indefinite least square problem, we adopt the linearization method…

Numerical Analysis · Mathematics 2018-01-30 Huai-An Diao , Tong-Yu Zhou

A novel method of asymptotic factorization of $n \times n$ matrix functions is proposed. Considered class of matrices is motivated by certain problems originated in the elasticity theory. An example is constructed to illustrate…

Complex Variables · Mathematics 2015-06-18 Gennady Mishuris , Sergei Rogosin

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

Statistics Theory · Mathematics 2023-03-17 Anna Scampicchio , Elena Arcari , Melanie N. Zeilinger

We prove L^p estimates for a class of two-dimensional multilinear forms that naturally generalize (dyadic variants of) both classical paraproducts and the twisted paraproduct introduced in [5] and studied in [1] and [6]. The method we use…

Classical Analysis and ODEs · Mathematics 2012-07-24 Vjekoslav Kovač

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…

Classical Analysis and ODEs · Mathematics 2012-07-12 Imdat Iscan

In many longitudinal settings, economic theory does not guide practitioners on the type of restrictions that must be imposed to solve the rotational indeterminacy of factor-augmented linear models. We study this problem and offer several…

Econometrics · Economics 2022-03-08 Matthew Harding , Carlos Lamarche , Chris Muris

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

Classical Analysis and ODEs · Mathematics 2017-10-20 Victor A. Pessers , Tom H. Koornwinder

The product of any finite number of factorial Schur functions can be expanded as a $Z[y]$-linear combination of Schur functions. We give a rule for computing the coefficients in such an expansion which generalizes a specialization of the…

Combinatorics · Mathematics 2008-03-04 V. Kreiman

We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and…

High Energy Physics - Theory · Physics 2014-12-04 Matthias Berwein

The main purpose of this paper is to give characterization theorems on derivations as well as on linear functions. Among others the following problem will be investigated: Let $n\in\mathbb{Z}$, $f, g\colon\mathbb{R}\to\mathbb{R}$ be…

Classical Analysis and ODEs · Mathematics 2013-07-03 Eszter Gselmann

Linear representations for a subclass of boolean symmetric functions selected by a parity condition are shown to constitute a generalization of the linear constraints on probabilities introduced by Boole. These linear constraints are…

Artificial Intelligence · Computer Science 2013-04-12 Silvio Ursic

The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…

Analysis of PDEs · Mathematics 2025-07-24 Michal Bathory