Related papers: The characterization problem for one class high or…

The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…

A formal framework is given for the characterizability of a class of belief revision operators, defined using minimization over a class of partial preorders, by postulates. It is shown that for partial orders characterizability implies a…

In strategic classification, an institution (e.g., a bank) anticipates adaptation from users who change their features to increase utility in a classification task (e.g., loan repayment). Since a key challenge is the distribution shift…

Given a set of data, biclustering aims at finding simultaneous partitions in biclusters of its samples and of the features which are used for representing the samples. Consistent biclusterings allow to obtain correct classifications of the…

We establish an algorithm for a criterion of the diagonalisability of a matrix over a local field by a unitary matrix. For this sake, we define the notion of normality of a $p$-adic operator, and give several criteria for the normality. We…

Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…

Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…

Structural parameter identifiability is a property of a differential model with parameters that allows for the parameters to be determined from the model equations in the absence of noise. One of the standard approaches to assessing this…

We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed…

We construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from input-output training pairs. The primary challenge of…

We discuss the frequent pattern mining problem in a general setting. From an analysis of abstract representations, summarization and frequent pattern mining, we arrive at a generalization of the problem. Then, we show how the problem can be…

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…

Despite significant recent advances in the regularity theory for obstacle problems with integro-differential operators, some fundamental questions remained open. On the one hand, there was a lack of understanding of parabolic problems with…

Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…

Characterizing domains is essential for models analyzing dynamic environments, as it allows them to adapt to evolving conditions or to hand the task over to backup systems when facing conditions outside their operational domain. Existing…

This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…

Parameter identification problems for partial differential equations are an important subclass of inverse problems. The parameter-to-state map, which maps the parameter of interest to the respective solution of the PDE or state of the…

This article presents a mathematical study of the problem of identifying a time-dependent source term in transport processes described by a timefractional parabolic equation, based on noisy time-dependent measurements taken at an arbitrary…