Papers by Georgios Domazakis
Markov chain lumpability and applications to credit risk modelling in compliance with the International Financial Reporting Standard 9 framework
Eur. J. Oper. Res., 2021
The aim of this paper is threefold. Firstly, we define the necessary quantities associated to the... more The aim of this paper is threefold. Firstly, we define the necessary quantities associated to the lumpability of a Markov chain and study their fundamental properties. Secondly, we examine the case of approximate lumpability of a non-lumpable Markov and an efficient method of minimizing the error in the approximation. Finally, we introduce a family of general minimization problems that can be approached using this method and examine applications in credit risk modelling, particularly under recent regulatory changes related to loan classification and provision calculations under IFRS 9.
ArXiv, 2019
In this work, learning schemes for measure-valued data are proposed, i.e. data that their structu... more In this work, learning schemes for measure-valued data are proposed, i.e. data that their structure can be more efficiently represented as probability measures instead of points on R, employing the concept of probability barycenters as defined with respect to the Wasserstein metric. Such type of learning approaches are highly appreciated in many fields where the observational/experimental error is significant (e.g. astronomy, biology, remote sensing, etc.) or the data nature is more complex and the traditional learning algorithms are not applicable or effective to treat them (e.g. network data, interval data, high frequency records, matrix data, etc.). Under this perspective, each observation is identified by an appropriate probability measure and the proposed statistical learning schemes rely on discrimination criteria that utilize the geometric structure of the space of probability measures through core techniques from the optimal transport theory. The discussed approaches are imp...
Journal of Linear and Topological Algebra, 2019
In this paper we consider the minimization of a positive semidefinite quadratic form, having a si... more In this paper we consider the minimization of a positive semidefinite quadratic form, having a singular corresponding matrix H. We state the dual formulation of the original problem and treat both problems only using the vectors x ∈ N (H)⊥ instead of the classical approach of convex optimization techniques such as the null space method. Given this approach and based on the strong duality principle, we provide a closed formula for the calculation of the Lagrange multipliers λ in the cases when (i) the constraint equation is consistent and (ii) the constraint equation is inconsistent, using the general normal equation. In both cases the Moore-Penrose inverse will be used to determine a unique solution of the problems. In addition, in the case of a consistent constraint equation, we also give sufficient conditions for our solution to exist using the well known KKT conditions. c ⃝ 2019 IAUCTB. All rights reserved.
On clustering uncertain and structured data with Wasserstein barycenters and a geodesic criterion for the number of clusters
Clustering schemes for uncertain and structured data are considered relying on the notion of Wass... more Clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space. Such type of clustering approaches are highly appreciated in many fields where the observational/experimental error is significant or the data nature is more complex and the traditional learning algorithms are not applicable or effective to treat. Under this perspective, each observation is identified by an appropriate probability measure and the proposed clustering schemes rely on discrimination criteria that utilize the geometric structure of the space of probability measures through core techniques from the optimal transport theory. The advantages and capabilities of the proposed approach and the geodesic criterion performance are illustrated through a simulation study and the implementation in two different applications: (a) clustering eurozone countries’ bond ...
Sustainability
In this paper, we provide a critical overview of the current migration policies of the EU as fram... more In this paper, we provide a critical overview of the current migration policies of the EU as framed by the recent amendments of the EU migration policies since 2015. We highlight that the construction of the migration policy is a constitutive element of the spatial process of reorganization of territorial policies through the combination and diffusion of state, regional and global. We show that the perception of permanent and static migration pressure, and countries’ specialization in migration are the basis for diffusion of asylum and migration policies to a number of different countries imposing similar migration systems and establishing a global governance of migration regime. The paper highlights a geographic and political change in migration and border management, through the patterns of EU Member States cooperation, and in particular their reluctance to establish a common asylum system based on solidarity and the focus on substituting the lack of a common asylum system by bila...
Clustering measure-valued data with Wasserstein barycenters
arXiv: Machine Learning, 2019
In this work, learning schemes for measure-valued data are proposed, i.e. data that their structu... more In this work, learning schemes for measure-valued data are proposed, i.e. data that their structure can be more efficiently represented as probability measures instead of points on $\R^d$, employing the concept of probability barycenters as defined with respect to the Wasserstein metric. Such type of learning approaches are highly appreciated in many fields where the observational/experimental error is significant (e.g. astronomy, biology, remote sensing, etc.) or the data nature is more complex and the traditional learning algorithms are not applicable or effective to treat them (e.g. network data, interval data, high frequency records, matrix data, etc.). Under this perspective, each observation is identified by an appropriate probability measure and the proposed statistical learning schemes rely on discrimination criteria that utilize the geometric structure of the space of probability measures through core techniques from the optimal transport theory. The discussed approaches ar...
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Papers by Georgios Domazakis