Related papers: Selected aspects of tractability analysis
Moral responsibility is a major concern in autonomous systems, with applications ranging from self-driving cars to kidney exchanges. Although there have been recent attempts to formalise responsibility and blame, among similar notions, the…
Interpretable machine learning tackles the important problem that humans cannot understand the behaviors of complex machine learning models and how these models arrive at a particular decision. Although many approaches have been proposed, a…
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal…
In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…
This paper provides a description of the spectrum of diagonal perturbation of weighted shift operator acting on a separable Hilbert space.
We study multivariate approximation in the average case setting with the error measured in the weighted $L_2$ norm. We consider algorithms that use standard information $\Lambda^{\rm std}$ consisting of function values or general linear…
In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the…
Integrable integral operator can be studied by means of a matrix Riemann--Hilbert problem. However, in the case of so-called integrable operators with shifts, the associated Riemann--Hilbert problem becomes operator valued and this…
Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…
This paper focuses on the stability of self-adjointness of linear relations under perturbations in Hilbert spaces. It is shown that a self-adjoint relation is still self-adjoint under bounded and relatively bounded perturbations. The…
Meta-analysis is routinely performed in many scientific disciplines. This analysis is attractive since discoveries are possible even when all the individual studies are underpowered. However, the meta-analytic discoveries may be entirely…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
The minimisation problem of a sum of unary and pairwise functions of discrete variables is a general NP-hard problem with wide applications such as computing MAP configurations in Markov Random Fields (MRF), minimising Gibbs energy, or…
The main objective of this paper is to develop a notion of joint spectrum for complex solvable Lie algebras of operators acting on a Banach space, which generalizes the Taylor joint spectrum (T.J.S.) for several commuting operators.
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
In a previous paper, we presented an Abstract Beurling's Theorem for valuation Hilbert modules over valuation algebras. In this paper, we shall apply this theorem to obtain complete descriptions of the closed invariant subspaces of a number…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
In this paper we consider integration and $L_2$-approximation for functions over $\RR^s$ from weighted Hermite spaces. The first part of the paper is devoted to a comparison of several weighted Hermite spaces that appear in literature,…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator.…