The autumn school "Success in decision Analysis" was held
On October 28-30, the International Center for Analysis and Decision Selection of the Higher School of Economics hosted the Autumn School "Advances in Decision Analysis" with the participation of well-known leading foreign specialists Michel Grabisch (University of Paris 1 Pantheon Sorbonne), Ahmet Alkan (Sabanci University, Turkey), Arunava Sen (Indian Statistical Institute, New Delhi), Vladimir Makarenkov (University of Quebec, Montreal), Eric Maskin (Harvard University, HSE), Mario Guarracino (Cassino University, HSE), domestic leading specialists Dzhangir Dzhangirov, Andrey Vashevnik (BEAC, Russia), as well as the staff of the center.
The following performances took place within the framework of the school:
October 28th (Monday)
Arunava Sen (Indian Statistical Institute, New Dehli)
Theme: Teacher Redistribution in Public Schools
Annotation: The Right to Free and Compulsory Education Act (2009) (RTE) of the Government of India prescribes teacher-student ratios for state-run schools. One method advocated by the Act to achieve its goals is the redeployment of teachers from surplus to deficit schools. We consider a model where teachers can either remain in their initially assigned schools or be transferred to a deficit school in their acceptable set. Transfers cannot turn a surplus school into a deficit school and a deficit school cannot be made a surplus school. The planner's objective is specified in terms of the post-transfer deficit vector that can be achieved. We formulate the problem as a network-flow problem. We show that there exists a transfer policy that generates a post-transfer deficit vector that Lorenz dominates all achievable post-transfer deficit vectors. We also show that the Lorenz-dominant post-transfer deficit vector can be achieved as the outcome of a strategy-proof mechanism.
Ahmet Alkan (Sabanci University, Turkey)
Theme:The Revealed Preference Lattice and The Lattice of Stable Matches
Annotation: In economic theory, agents in a market are often described by preference orders. This is also the case in stable many-to-many matching theory where agents are additionally described by choice functions compatible with their preference orderings. In fact the theory can be worked out entirely if agents are described by choice functions alone and use is made of the revealed preference relation associated with a choice function. First, we consider an individual described by a choice function C on a universal set U. The collection of all chosen sets is the consumption set Z of the individual. Given any two S,S’ in Z, we say S is revealed better than S’ if C chooses S from the union of S and S’. We will show that the revealed preference relation so defined is a lattice if C is path independent. Next, we consider the standard many-to-many matching market, say with firms F and workers W. Each firm is described by a choice function on W and each worker by a choice function on F. It is easily seen by the Deferred Acceptance Procedure that stable matchings exist if the choice functions are path independent. A stable matching M is said to be group-revealed-preferred to another stable matching M’ if every firm revealed-prefers its set of workers in M to its set of workers in M’. We will show that stable matchings form a natural lattice under this group-revealed-preference relation provided the choice functions are path independent and “size monotone”. Further, this lattice is distributive and has other nice properties. We will conclude with some remarks on the rationalizability literature where the aim is to characterize path independent (and size monotone) choice functions with utility functions over Z or U having certain properties.
Mario Guarracino (University of Cassino and Souther Lazio (Italy), HSE University (Russia))
Theme: A Short Journey through Whole Graph Embedding Techniques
Annotation: Networks provide suitable models in many applications, ranging from social to life sciences. Such representations are able to capture interactions and dependencies among variables or observations, and can be extended to consider ensembles of networks, thus providing simple and powerful modeling of phenomena. Whole graph embedding involves the projection of ensembles of graphs into a vector space, while retaining their structural properties. In recent years, several embedding techniques using graph kernels, matrix factorization, and deep learning architectures have been developed to learn low dimensional graph representations. These embeddings can then be used for feature extraction, graph clustering or for building classification models. In these lectures, we survey embedding techniques which jointly embed whole graphs for classification tasks. We compare them and evaluate their performance on undirected synthetic and real world network datasets on different learning tasks.
Eric Maskin (Harvard University (USA), HSE University (Russia))
Theme: An Election System Resistant to Strategic Voting
Annotation: No reasonable voting system is always immune from strategic voting. However, we will present evidence that, in political elections, voters’ preferences are approximately single-peaked. For this case, we demonstrate that there is a (unique) voting rule that is strategy-resistant. It elects the Condorcet winner.
October 29th (Tuesday)
Alexey Myachin (HSE, Russia)
Theme: Theoretical Aspects and Practical Applications of Pattern Analysis
Annotation: The study focuses on specific methods of pattern analysis based on pairwise comparison of parameters. A review of classical methods for identifying patterns in data is presented. The computational complexity and distinct properties of the proposed methods are discussed. The potential for pattern detection using interval estimations is explored. Additionally, the methodology for dimensionality reduction in the search for patterns within high-dimensional data is considered. Selected examples of practical applications of various pattern analysis methods are provided.
Michel Grabisch (Universite Paris 1 Pantheon Sorbonne, France)
Theme: Random generation of capacities
Annotation: Capacities are monotone set functions widely used in decision making. For machine learning purpose, it is important to be able to generate randomly capacities. The uniform generation of capacities is a problem solved theoretically by Stanley, but infeasible in practice as soon as the universe has 5 elements. Therefore, approximations have to be found. In this talk, we will make a survey of available methods for the uniform generation of capacities. In a second part, we see how to incorporate constraints in the random generation, in the aim of representing preferences of the decision maker. We show how this can be used for eliciting models in multicriteria decision making.
Vladimir Makarenkov (University of Quebec in Montreal, Canada)
Theme: Bioinformatics and its practical applications
Annotation: During this lecture, I will first recall the key concepts and main goals of bioinformatics. I will then present some work in this area carried out in our bioinformatics laboratory at the Université du Québec à Montréal. In particular, I will demonstrate our new methods for reconstructing, comparing, and visualizing evolutionary (or phylogenetic) trees and networks. Network methods include algorithms for identifying genetic recombination and horizontal gene transfer events. We will see how these methods can be applied to identify gene transfers in the context of species evolution and language borrowings in the context of biolinguistics. Next, I will present our new software for studying genetic sequence similarity and recombination detection. We will see how our program can be used to detect recombination in coronavirus genomes, including that of SARS-CoV-2. Finally, I will present our new data clustering methods and discuss their applications in biology and biomedicine.
October 30th (Wednesday)
Boris Mirkin (HSE, Russia)
Theme: Versions of k-means clustering for interval data using the least-squares criterion and abnormal clustering approach
Annotation: Recently, k-means clustering has been extended to the so-called interval data. In contrast to conventional data case, the interval data feature values are intervals rather than single reals. This paper further explores the least-squares criterion for k-means clustering to tackle the issue of initialization, that is, finding a proper set of initial cluster centers at interval data clustering. Specifically, we extend, for the interval data, a Pythagorean decomposition of the data scatter in the sum of two items, one being a genuine k-means least-squares criterion, the other, a complementary criterion, requiring the clusters to be numerous and anomalous. Therefore we propose a method for one-byone obtaining anomalous clusters. After a run of the method, we start k-means iterations from the centers of the most numerous of the found anomalous clusters. We test and validate our proposed BIKM algorithm at versions of two newly introduced interval datasets.
Dzhangir Dzhangirov, Andrey Vashevnik (Beac, Russia)
Theme: Risk Assessment of LLMs in Financial Applications
Annotation: In this overview we will investigate quality and model risks of using large language models (LLMs) in financial applications, focusing on challenges like model bias, regulatory compliance, and decision-making problems. It develops a risk assessment framework that identifies vulnerabilities such as susceptibility to adversarial attacks, toxic behavioral, misinformation and underlearning. To assess risks we propose to use approaches based on automatic metrics, modern benchmarks and human evaluation. The study also emphasizes the need for ongoing monitoring and regular updates to maintain LLMs' effectiveness and reliability in dynamic financial environments.