Person:
Gutiérrez García-Pardo, Inmaculada

First Name

Inmaculada

Last Name

Gutiérrez García-Pardo

URI

https://hdl.handle.net/20.500.14352/86240

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Estudios estadísticos

Department

Estadística y Ciencia de los Datos

Identifiers

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Now showing 1 - 8 of 8

On measuring features importance in Machine Learning models in a two-dimensional representation scenario
(2022) Gutiérrez García-Pardo, Inmaculada; Santos, Daniel; Castro Cantalejo, Javier; Gómez González, Daniel; Espínola Vílchez, María Rosario; Guevara Gil, Juan Antonio
Abstract: There is a wide range of papers in the literature about the explanation of machine learning models in which Shapley value is considered to measure the importance of the features in these models. We can distinguish between these which set their basis on the cooperative game theory principles, and these focused on fuzzy measures. It is important to mention that all of these approaches only provide a crisp value (or a fix point) to measure the importance of a feature in a specific model. The reason is that an aggregation process of the different marginal contributions produces a single output for each variable. Nevertheless, and because of the relations between features, we cannot distinguish the case in which we do not know all the features. To this aim, we propose a disaggregated model which allows the analysis of the importance of the features, regarding the available information. This new proposal can be viewed as a generalization of all previous measures found in literature providing a two dimensional graph which, in a very intuitive and visual way, provides this rich disaggregated information. This information may be aggregated with several aggregation functions with which obtain new measures to establish the importance of the features. Specifically, the aggregation by the sum results in the Shapley value. We also explain the characteristics of those graphics in different scenarios of the relations among features, to raise this useful information at a glance.
Multiple bipolar fuzzy measures: an application to community detection problems for networks with additional information
(International Journal of Computational Intelligence Systems, 2020) Gutiérrez García-Pardo, Inmaculada; Gómez González, Daniel; Castro Cantalejo, Javier; Espínola Vílchez, María Rosario
In this paper we introduce the concept of multiple bipolar fuzzy measures as a generalization of a bipolar fuzzy measure. We also propose a new definition of a group, which is based on the multidimensional bipolar fuzzy relations of its elements. Taking into account this information, we provide a novel procedure (based on the well-known Louvain algorithm) to deal with community detection problems. This new method considers the multidimensional bipolar information provided by multiple bipolar fuzzy measures, as well as the information provided by a graph. We also give some detailed computational tests, obtained from the application of this algorithm in several benchmark models.
A new edge betweenness measure using a game theoretical approach: an application to hierarchical community cetection
(Mathematics, 2021) Espínola Vílchez, María Rosario; Gómez González, Daniel; Castro Cantalejo, Javier; Gutiérrez García-Pardo, Inmaculada; Jiménez-Losada, Andrés; Goubko, Mikhail
In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.
From fuzzy information to community detection: an approach to social networks analysis with soft information
(Mathematics, 2022) Gutiérrez García-Pardo, Inmaculada; Gómez González, Daniel; Castro Cantalejo, Javier; Espínola Vílchez, María Rosario; Wierzchoń, Sławomir T.
On the basis of network analysis, and within the context of modeling imprecision or vague information with fuzzy sets, we propose an innovative way to analyze, aggregate and apply this uncertain knowledge into community detection of real-life problems. This work is set on the existence of one (or multiple) soft information sources, independent of the network considered, assuming this extra knowledge is modeled by a vector of fuzzy sets (or a family of vectors). This information may represent, for example, how much some people agree with a specific law, or their position against several politicians. We emphasize the importance of being able to manage the vagueness which usually appears in real life because of the common use of linguistic terms. Then, we propose a constructive method to build fuzzy measures from fuzzy sets. These measures are the basis of a new representation model which combines the information of a network with that of fuzzy sets, specifically when it comes to linguistic terms. We propose a specific application of that model in terms of finding communities in a network with additional soft information. To do so, we propose an efficient algorithm and measure its performance by means of a benchmarking process, obtaining high-quality results.
Fuzzy measures: a solution to deal with community detection problems for networks with additional information
(Journal of Intelligent & Fuzzy Systems, 2020) Gutiérrez García-Pardo, Inmaculada; Gómez González, Daniel; Castro Cantalejo, Javier; Espínola Vílchez, María Rosario; Kahraman, Cengiz
In this work we introduce the notion of the weighted graph associated with a fuzzy measure. Having a finite set of elements between which there exists an affinity fuzzy relation, we propose the definition of a group based on that affinity fuzzy relation between the individuals. Then, we propose an algorithm based on the Louvain’s method to deal with community detection problems with additional information independent of the graph. We also provide a particular method to solve community detection problems over extended fuzzy graphs. Finally, we test the performance of our proposal by means of some detailed computational tests calculated in several benchmark models.
A new approach to polarization modeling using Markov chains
(2022) Guevara Gil, Juan Antonio; Gómez González, Daniel; Castro Cantalejo, Javier; Gutiérrez García-Pardo, Inmaculada; Robles Morales, José Manuel; Ciucci, Davide; Couso, Inés; Medina, Jesús; Ślęzak, Dominik; Petturiti, Davide; Bouchon-Meunier, Bernadette; Yager, Ronald R.
Abstract: In this study, we approach the problem of polarization modeling with Markov Chains (PMMC). We propose a probabilistic model that provides an interesting approach to knowing what the probability for a specific attitudinal distribution is to get to an i.e. social, political, or affective Polarization. It also quantifies how many steps are needed to reach Polarization for that distribution. In this way, we can know how risky an attitudinal distribution is for reaching polarization in the near future. To do so, we establish some premises over which our model fits reality. Furthermore, we compare this probability with the polarization measure proposed by Esteban and Ray and the fuzzy polarization measure by Guevara et al. In this way, PMMC provides the opportunity to study in deep what is the performance of these polarization measures in specific conditions. We find that our model presents evidence that in fact, some distributions will presumably show higher risk than others even when the entire population holds the same attitude. In this sense, according to our model, we find that moderate/indecisive attitudes present a higher risk for polarization than extreme attitudes and should not be considered the same scenario despite the fact that the entire population maintains the same attitude.
Auctions: A New Method for Selling Objects with Bimodal Density Functions
(Computational Economics, 2022) Castro Cantalejo, Javier; Espínola Vílchez, María Rosario; Gutiérrez García-Pardo, Inmaculada; Gómez González, Daniel
In this paper we define a new auction, called the Draw auction. It is based on the implementation of a draw when a minimum price of sale is not reached. We find that a Bayesian Nash equilibrium is reached in the Draw auction when each player bids his true personal valuation of the object. Furthermore, we show that the expected profit for the seller in the Draw auction is greater than in second-price auctions, with or without minimum price of sale. We make this affirmation for objects whose valuation can be modeled as a bimodal density function in which the first mode is much greater than the second one. Regarding the Myerson auction, we show that the expected profit for the seller in the Draw auction is nearly as good as the expected profit in the optimal auction, with the difference that our method is much more simple to implement than Myerson’s one. All these results are shown by computational tests, for whose development we have defined an algorithm to calculate Myerson auction.
Community detection problem based on polarization measures: an application to Twitter: the COVID-19 case in Spain
(Mathematics, 2021) Gutiérrez García-Pardo, Inmaculada; Gómez González, Daniel; Castro Cantalejo, Javier; Guevara Gil, Juan Antonio; Espínola Vílchez, María Rosario; Nescolarde Selva, Josue Antonio
In this paper, we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the risk of polarization. Particularly, we are interested in dealing with the problem of taking into account the polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more likely to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem.