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Introduction

## Publications

Publications (215)

The computerization of many everyday tasks generates vast amounts of data, and this has lead to the development of machine-learning methods which are capable of extracting useful information from the data so that the data can be used in future decision-making processes. For a long time now, a number of fields, such as medicine (and all healthcare-r...

Kullback–Leibler divergence KL(p,q) is the standard measure of error when we have a true probability distribution p which is approximate with probability distribution q. Its efficient computation is essential in many tasks, as in approximate computation or as a measure of error when learning a probability. In high dimensional probabilities, as the...

Given a set of uncertain discrete variables with a joint probability distribution and a set of observations for some of them, the most probable explanation is a set or configuration of values for non-observed variables maximizing the conditional probability of these variables given the observations. This is a hard problem which can be solved by a d...

This paper considers the problem of learning a generalized credal network (a set of Bayesian networks) from a dataset. It is based on using the BDEu score and computes all the networks with score above a predetermined factor of the optimal one. To avoid the problem of determining the equivalent sample size (ESS), the approach also considers the pos...

In many situations, classifiers predict a set of states of a class variable because there is no information enough to point only one state. In the data mining area, this task is known as Imprecise Classification. Decision Trees that use imprecise probabilities, also known as Credal Decision Trees (CDTs), have been adapted to this field. The adaptat...

This paper proposes a model for estimating probabilities in the presence of abrupt concept drift. This proposal is based on a dynamic Bayesian network. As the exact estimation of the parameters is unfeasible we propose an approximate procedure based on discretizing both the possible probability values and the parameter representing the probability...

Gene Regulatory Networks (GRNs) are known as the most adequate instrument to provide a clear insight and understanding of the cellular systems. One of the most successful techniques to reconstruct GRNs using gene expression data is Bayesian networks (BN) which have proven to be an ideal approach for heterogeneous data integration in the learning pr...

In this paper it is considered the problem of discounting a credal set of probability distributions by a factor α representing a degree of unreliability of the information source providing the imprecise probabilistic information. An axiomatic approach is followed by giving a set of properties that this operator should satisfy. It is shown that disc...

Estimating probabilities of a multinomial variable conditioned to a large set of variables is an important problem due to the fact that the number of parameters increases in an exponential way with the number of conditional variables. Some models, such as noisy-or gates make assumptions about the relationships between the variables that assume that...

This book constitutes the refereed proceedings of the 11th International Conference on Scalable Uncertainty Management, SUM 2017, which was held in Granada, Spain, in October 2017.
The 24 full and 6 short papers presented in this volume were carefully reviewed and selected from 35 submissions. The book also contains 3 invited papers.
Managing unce...

La deserción estudiantil en las universidades es un problema que debe ser investigado y tratado con prioridad ya que se ha constituido como un indicador de eﬁciencia dentro de las instituciones de educación superior.
Lo expuesto anteriormente nos lleva a proponer métodos que nos ayuden a identiﬁcar a tiempo los estudiantes con riesgo de deserción e...

The use of graphical probabilistic models in the field of education has been considered for this research. First, classical learning algorithms, as PC or K2 are reviewed. But the problem with these general learning procedures comes from the presence of a high number of variables that measure different aspects of the same concept, as it can be the c...

Situational awareness (SA) and its related metrics are often used to rate the performance of flight crews, especially for flight safety purposes. In the context of a Ph.D. thesis on data mining, this paper presents the principles followed to model and measure SA using Bayesian networks, focusing on the work performed to validate different data disc...

In this work we applied Variable Mesh Optimization population metaheuristc (VMO) for Bayesian network (BN) structure learning as score-and-search method. Our idea was to represent each node of the Mesh as a Bayesian network through a set of arcs. Then new BNs are created using among sets (union and difference) operations. For this process, three ty...

Expression quantitative trait loci are used as a tool to identify genetic causes of natural variation in gene expression. Only in a few cases the expression of a gene is controlled by a variant on a single genetic marker. There is a plethora of different complexity levels of interaction effects within markers, within genes and between marker and ge...

In the context of a PhD thesis on data mining, we have implemented a simulation environment that collects data for measurements of certain aspects of the Situational Awareness (SA) of a pilot using Bayesian networks (BN). The tool is based on a web application that emulates an Electronic Flight Bag (EFB) and is connected to a flight simulator, prov...

The paper by Denœux justifies the use of a consonant belief function to represent the information provided by a likelihood function and proposes some extensions to low-quality data. In my comments I consider the point of view of imprecise probabilities for the representation of likelihood information and the relationships with the proposal in the p...

This paper considers the problem of learning multinomial distributions from a sample of independent observations. The Bayesian approach usually assumes a prior Dirichlet distribution about the probabilities of the different possible values. However, there is no consensus on the parameters of this Dirichlet distribution. Here, it will be shown that...

I discuss some aspects of the distinction between ontic and epistemic views of sets as representation of imprecise or incomplete information. In particular, I consider its implications on imprecise probability representations: credal sets and sets of desirable gambles. It is emphasized that the interpretation of the same mathematical object can be...

This paper proposes a flexible framework to work with probabilistic potentials in Probabilistic Graphical Models. The so-called Extended Probability Trees allow the representation of multiplicative and additive factorisations within the structure, along with context-specific independencies, with the aim of providing a way of representing and managi...

Classification is the problem of predicting the class of a given instance, on the basis of some attributes of it. This chapter presents the traditional naive Bayes classifier (NBC), shows how it has been extended to imprecise probability for yielding the naive credal classifier (NCC). It reviews how NCC has been evolved yielding more sophisticated...

Probability trees are a powerful data structure for representing probabilistic potentials. However, their complexity can become intractable if they represent a probability distribution
over a large set of variables. In this paper, we study the problem of decomposing a
probability tree as a product of smaller trees, with the aim of being able to han...

Using domain/expert knowledge when learning Bayesian networks from data has been considered a promising idea since the very beginning of the field. However, in most of the previously proposed approaches, human experts do not play an active role in the learning process. Once their knowledge is elicited, they do not participate any more. The interact...

Recursive Probability Trees offer a flexible framework for representing the probabilistic information in Probabilistic Graphical Models. This structure is able to provide a detailed representation of the distribution it encodes, by specifying most of the types of independencies that can be found in a probability distribution. Learning this structur...

Recursive probability trees (RPTs) are a data structure for representing several types of potentials involved in probabilistic graphical models. The RPT structure improves the modeling capabilities of previous structures (like probability trees or conditional probability tables). These capabilities can be exploited to gain savings in memory space a...

This is the Proceedings of the Fourteenth Conference on Uncertainty in
Artificial Intelligence, which was held in Madison, WI, July 24-26, 1998

It is already known that power in multimarker transmission/disequilibrium tests may improve with the number of markers as some associations may require several markers to be captured. However, a mechanism such as haplotype grouping must be used to avoid incremental complexity with the number of markers. 2G, a state-of-the-art transmission/disequili...

In this paper, we consider several types of information and methods of combination associated with incomplete probabilistic systems. We discriminate between 'a priori' and evidential information. The former one is a description of the whole population, the latest is a restriction based on observations for a particular case. Then, we propose differe...

In Moral, Campos (1991) and Cano, Moral, Verdegay-Lopez (1991) a new method of conditioning convex sets of probabilities has been proposed. The result of it is a convex set of non-necessarily normalized probability distributions. The normalizing factor of each probability distribution is interpreted as the possibility assigned to it by the conditio...

This paper presents a procedure to determine a complete belief function from
the known values of belief for some of the subsets of the frame of discerment.
The method is based on the principle of minimum commitment and a new principle
called the focusing principle. This additional principle is based on the idea
that belief is specified for the most...

In this paper we study different concepts of independence for convex sets of
probabilities. There will be two basic ideas for independence. The first is
irrelevance. Two variables are independent when a change on the knowledge about
one variable does not affect the other. The second one is factorization. Two
variables are independent when the joint...

Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of the most informative valuations or as supremum of the least informative ones. It is studied how to carry out com...

Automatically learning the graph structure of a single Bayesian network (BN) which accurately represents the underlying multivariate probability distribution of a collection of random variables is a challenging task. But obtaining a Bayesian solution to this problem based on computing the posterior probability of the presence of any edge or any dir...

A Recursive Probability Tree (RPT) is a data structure for representing the potentials involved in Probabilistic Graphical Models (PGMs). This structure is developed with the aim of capturing some types of independencies that cannot be represented with previous structures. This capability leads to improvements in memory space and computation time d...

The discovery of the Markov Boundary (MB) of a target variable using observational data plays a central role in feature selection and local causal structure inference. Most existing methods previously employed for this task rely on statistical independence tests and, in consequence, do not take into account the partial evidence that a finite data s...

In the analysis of data, the discovery of dependence relations can play a very important role. Our principal aim in this paper is to present a new score to determine when two categorical variables are independent. It can be resumed as an interval-valued score that is based on the Heckerman, Geiger, and Chickering's score, which can be used in super...

The marginal likelihood of the data computed using Bayesian score metrics is at the core of score+search methods when learning Bayesian networks from data. However, common formulations of those Bayesian score metrics rely on free parameters which are hard to assess. Recent theoretical and experimental works have also shown that the commonly employe...

This paper distinguishes between objective probability—or chance—and subjective probability. Most statistical methods in machine learning are based on the hypothesis that there is a random experiment from which we get a set of observations. This random experiment could be identified with a chance or objective probability, but these probabilities de...

When using Bayesian networks in real applications it is often the case that the empirical evidence or observations we employ for making inferences are corrupt and contain noise: Failure in a sensor, outliers, human errors, etc. Although many methods have been pro-posed in the literature for data cleaning (i.e. detect and correct noisy data values),...

The enormous amount of genetic data that is currently being produced with the explosion of genome-wide association studies is yielding an important effort in the construction of genetic-based predictive models for individual susceptibility to complex diseases. However, a constant pattern of low accuracy is observed in most of them. We hypothesize t...

We study probability intervals as an interesting tool to represent uncertain information. A number of basic operations necessary to develop a calculus with probability intervals, such as combination, marginalization, conditioning and integration are studied in detail. Moreover, probability intervals are compared with other uncertainty theories, suc...

In this work, we study the application of Bayesian networks classifiers for gene expression data in three ways: first, we made an exhaustive state-of-art of Bayesian classifiers and Bayesian classifiers induced from microarray data. Second, we propose a preprocessing scheme for gene expression data, to induce Bayesian classifiers. Third, we evaluat...

The theory of sets of desirable gambles is a very general model which covers most of the existing theories for imprecise probability as special cases; it has a clear and simple axiomatic justification; and mathematical definitions are natural and intuitive. However, much work remains to be done until the theory of desirable gambles can be considere...

The marginal likelihood of the data computed using Bayesian score metrics is at the core of score+search methods when learning Bayesian networks from data. However, common formulations of those Bayesian score metrics depend of
free parameters which are hard to asses. Recent theoretical and experimental works have also shown as the commonly employed...

Automatic learning of Bayesian networks from data is a challenging task, particularly when the data are scarce and the problem domain contains a high number of random variables. The introduction of expert knowledge is recognized as an excellent solution for reducing the inherent uncertainty of the models retrieved by automatic learning methods. Pre...

In this paper, we review the role of probabilistic graphical models in artificial intelligence. We start by giving an account of the early years when there was important controversy about the suitability of probability for intelligent systems. We then discuss the main milestones for the foundations of graphical models starting with Pearl’s pioneeri...

The present paper introduces a new kind of representation for the potentials in a Bayesian network: Binary Probability Trees. They enable the representation of context-specific independences in more detail than probability trees. This enhanced capability leads to more efficient inference algorithms for some types of Bayesian networks. This paper ex...

Previous analysis of learning data can help us to discover hidden relations among features. We can use this knowledge to select the most suitable learning methods and to achieve further improvements in the performance of classification systems. For the known Naive Bayes classifier, several studies have been conducted in an attempt to reconstruct th...

This paper proposes the use of Binary Probability Trees in the propagation of credal networks. Standard and binary probability trees are suitable data structures for representing potentials because they allow to control the accuracy of inference algorithms by means of a threshold parameter. The choice of this threshold is a trade-off between accura...

The problem of aggregating two or more sources of information containing knowledge about a common domain is considered. We propose an aggregation framework for the case where the available information is modelled by coherent lower previsions, corresponding ...

We study three conditions of independence within Ev-idence Theory framework. First condition refers to the selection of pairs of focal sets. The remaining two are related to the choice of a pair of elements, once a pair of focal sets has been selected. These three concepts allow us to formalize the ideas of lack of in-teraction between variables an...

A recursive probability tree (RPT) is an incipient data structure for representing the dis-tributions in a probabilistic graphical model. RPTs capture most of the types of indepen-dencies found in a probability distribution. The explicit representation of these features using RPTs simplifies computations during inference. This paper describes a lea...

The introduction of expert knowledge when learning Bayesian Networks from data is known to be an excellent approach to boost
the performance of automatic learning methods, specially when the data is scarce. Previous approaches for this problem based
on Bayesian statistics introduce the expert knowledge modifying the prior probability distributions....

This paper proposes a new data structure for representing potentials. Recursive probability trees are a generalization of
probability trees. Both structures are able to represent context-specific independencies, but the new one is also able to
hold a potential in a factorized way. This new structure can represent some kinds of potentials in a more...

Random forest models [1] consist of an ensemble of randomized decision trees. It is one of the best performing classification
models. With this idea in mind, in this section we introduced a random split operator based on a Bayesian approach for building
a random forest. The convenience of this split method for constructing ensembles of classificati...

The present paper introduces a new kind of representation for the potentials in a Bayesian network: Binary Probability Trees.
They allow to represent finer grain context-specific independences than those which can be encoded with probability trees.
This enhanced capability leads to more efficient inference algorithms in some types of Bayesian netwo...

Sets of desirable gambles were proposed by Walley [7] as a general theory of imprecise probability. The main reasons for this are: it is a very general model, including as particular cases most of the existing theories for imprecise probability; it has a deep and simple axiomatic justification; and mathematical definitions are natural and intuitive...

Classiflcation or decision trees are one of the most efiective methods for supervised clas- siflcation. In this work, we present a Bayesian approach to induce classiflcation trees based on a Bayesian score splitting criterion and a new Bayesian method to estimate the probability of class membership based on Bayesian model averaging over the rules o...

This chapter presents a new approach to the problem of obtaining the most probable explanations given a set of observations
in a Bayesian network. The method provides a set of possibilities ranked by their probabilities. The main novelties are that
the level of detail of each one of the explanations is not uniform (with the idea of being as simple...

In this paper, we extend the set of" properties required for total uncertainty measures in the Dempster-Shafer theory of evidence (DST). For this purpose, we take into account properties and behaviors considered for these type of measures which have appeared in the literature. We analyze the differences between the main total uncertainty measures p...

The result of applying the PC learning algorithm can depend of the order in which in- dependence tests are carried out. Even if these tests are ordered by increasing size of conditional sets, the PC algorithm does not take into account which edges are weaker in order to be considered to be removed before the stronger edges. This paper proposes a ne...

This paper proposes two new algorithms for inference in credal networks. These algorithms enable probability intervals to be obtained for the states of a given query variable. The first algorithm is approximate and uses the hill-climbing technique in the Shenoy–Shafer architecture to propagate in join trees; the second is exact and is a modificatio...

The propagation of probabilities in credal networks when probabilities are estimated with a global impre- cise Dirichlet model is an important open problem. Only Zaffalon (21) has proposed an algorithm for the Naive classifier. The main difficulty is that, in gen- eral, computing upper and lower probability intervals implies the resolution of an op...

Although influence diagrams are powerful tools for representing and solving complex decision-making problems, their evaluation may require an enormous computational effort and this is a primary issue when processing real-world models. We shall propose an approximate inference algorithm to deal with very large models. For such models, it may be unfe...

We study probability intervals as a interesting tool to represent uncertain information. Basic concepts for the management of uncertain information, as combination, marginalization, conditioning and integration are considered for probability intervals. Moreover, the relationships of this theory with some others, as lower and upper probabilities and...

In this paper, a new language for convex sets of probabilities operators is presented. Its main advantage is that it allows a more direct representation of initial pieces of information without transforming them in more complex representations. The language includes logical operators and numerical values. It will allow, in some cases, a reduction o...

The upper entropy of a credal set is the maximum of the entropies of the probabilities belonging to it. Although there are algorithms for computing the upper entropy for the particular cases of credal sets associated to belief functions and probability intervals, there is none for a more general model. In this paper, we shall present an algorithm t...

The MTE (Mixture of Truncated Exponentials) model allows to deal with Bayesian networks containing discrete and continuous
variables simultaneously. This model offers an alternative to discretisation, since standard algorithms to compute the posterior
probabilities in the network, in principle designed for discrete variables, can be directly applie...

We present a new approach to measure uncertainty/information applicable to theories based on convex sets of probability distributions, also called credal sets. A definition of a total disaggregated uncertainty measure on credal sets is proposed in this paper motivated by recent outcomes. This definition is based on the upper and lower values of Sha...

We shall present a first explorative study of the variation of the parameter s of the imprecise Dirichlet model when it is used to build classification trees. In the method to build classification trees
we use uncertainty measures on closed and convex sets of probability distributions, otherwise known as credal sets. We will
use the imprecise Diric...

Taking as an inspiration the so-called Explanation Tree for abductive inference in Bayesian networks, we have developed a new clustering approach. It is based on exploiting the variable independencies with the aim of building a tree structure such that in each leaf all the variables are independent. In this work we produce a structure called Indepe...

This paper proposes some possible modications on the PC basic learning algorithm and makes some experiments to study their behaviour. The variations are: to determine minimum size cut sets between two nodes to study the deletion of a link, to make statistical decisions taking into account a Bayesian score instead of a classical Chi-square test, to...

This paper studies graphoid properties for epistemic irrelevance in sets of desirable gambles. For that aim, the basic operations
of conditioning and marginalization are expressed in terms of variables. Then, it is shown that epistemic irrelevance is an
asymmetric graphoid. The intersection property is verified in probability theory when the global...

Gert de Cooman has presented a sound and deep approach to vague probability, providing a behavioural interpretation for it. He proposes natural extension as the basic inference procedure, a simple and a general method from which very diverse inference rules can be deduced. This paper discusses some aspects of de Cooman's approach. First, I consider...

The turbulent flow consists of coherent time- and space-organized vortical structures with a particular formation and instability cycle. Research has already shown that some dynamic systems and experimental models still cannot provide a good nonlinear ...

Bayesian networks are efficient tools for probabilistic reasoning over large sets of variables, due to the fact that the joint
distribution factorises according to the structure of the network, which captures conditional independence relations among
the variables. Beyond conditional independence, the concept of asymmetric (or context specific) inde...

This talk will review the basic notions of imprecise probability following Walley’s theory [1] and its application to graphical
models which usually have considered precise Bayesian probabilities [2]. First approaches to imprecision were robustness studies:
analysis of the sensibility of the outputs to variations of network parameters [3,4]. Howeve...