Análisis de la tasa de abandono de primer año del Grado en Estadística Aplicada. Evolución y proyección

Fac. de Estudios EstadísticosFALSEsubmitte

Auctions: A New Method for Selling Objects with Bimodal Density Functions

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

Multiple bipolar fuzzy measures: an application to community detection problems for networks with additional information

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.Depto. de Estadística y Ciencia de los DatosFac. de Estudios EstadísticosTRUEpu

Fuzzy measures: a solution to deal with community detection problems for networks with additional information

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.Government of Spain, Grant Plan Nacional de I+D+iDepto. de Estadística y Ciencia de los DatosFac. de Estudios EstadísticosTRUEpu

From fuzzy information to community detection: an approach to social networks analysis with soft information

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.Depto. de Estadística y Ciencia de los DatosFac. de Estudios EstadísticosTRUEpu

Elaboración y diseño de estructura modular para la formación en Técnicas estadísticas básicas y para la investigación

Depto. de Estadística y Ciencia de los DatosFac. de Estudios EstadísticosFALSEsubmitte

Explanation of machine learning classification models with fuzzy measures: an approach to individual classification

Lecture Notes in Networks and Systems. Volume 505 LNNSAbstract: In the field of Machine Learning, there is a common point in almost all methodologies about measuring the importance of features in a model: estimating the value of a collection of them in several situations where different information sources (features) are available. To establish the value of the response feature, these techniques need to know the predictive ability of some features over others. We can distinguish two ways of performing this allocation. The first does not pay attention to the available information of known characteristics, assigning a random allocation value. The other option is to assume that the feasible values for the unknown features have to be any of the values observed in the sample (in the known part of the database), assuming that the values of the known features are correct. Despite its interest, there is a serious problem of overfitting in this approach, in situations in which there is a continuous feature: the values of a continuous feature are not likely to occur in any other, so there is a large loss of randomization (there will surely be an insignificant number of records for each possible value). In this scenario, it is probably unrealistic to assume a perfect estimation. Then, in this paper we propose a new methodology based on fuzzy measures which allows the analysis and consideration of the available information in known features, avoiding the problem of overfitting in the presence of continuous features. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AGSecretaría de Estado de Investigacion, Desarrollo e InnovacionDepto. de Estadística y Ciencia de los DatosFac. de Estudios EstadísticosTRUEpu

On measuring features importance in Machine Learning models in a two-dimensional representation scenario

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.Depto. de Estadística y Ciencia de los DatosFac. de Estudios EstadísticosTRUEpu