Imprecise probability models for inference in exponential families

When considering sampling models described by a distribution from an exponential family, it is possible to create two types of imprecise probability models. One is based on the corresponding conjugate distribution and the other on the corresponding predictive distribution. In this paper, we show how these types of models can be constructed for any (regular, linear, canonical) exponential family, such as the centered normal distribution. To illustrate the possible use of such models, we take a look at credal classification. We show that they are very natural and potentially promising candidates for describing the attributes of a credal classifier, also in the case of continuous attributes

Epistemic irrelevance in credal networks : the case of imprecise Markov trees

We replace strong independence in credal networks with the weaker notion of epistemic irrelevance. Focusing on directed trees, we show how to combine local credal sets into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is essentially linear in the number of nodes, is formulated entirely in terms of coherent lower previsions. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of our model for prediction

Completing an uncertainty criterion of classification

We present a variation of a method of classification based in uncertainty on credal set. Similarly to its origin it use the imprecise Dirichlet model to create the credal set and the same uncertainty measures. It take into account sets of two variables to reduce the uncertainty and to seek the direct relations between the variables in the data base and the variable to be classified. The success are equivalent to the success of the first method except in those where there are a direct relations between some variables that decide the value of the variable to be classified where we have a notable improvement

Reliable Uncertain Evidence Modeling in Bayesian Networks by Credal Networks

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.Comment: 19 page

Binary credal classification under sparsity constraints.

Binary classification is a well known problem in statistics. Besides classical methods, several techniques such as the naive credal classifier (for categorical data) and imprecise logistic regression (for continuous data) have been proposed to handle sparse data. However, a convincing approach to the classification problem in high dimensional problems (i.e., when the number of attributes is larger than the number of observations) is yet to be explored in the context of imprecise probability. In this article, we propose a sensitivity analysis based on penalised logistic regression scheme that works as binary classifier for high dimensional cases. We use an approach based on a set of likelihood functions (i.e. an imprecise likelihood, if you like), that assigns a set of weights to the attributes, to ensure a robust selection of the important attributes, whilst training the model at the same time, all in one fell swoop. We do a sensitivity analysis on the weights of the penalty term resulting in a set of sparse constraints which helps to identify imprecision in the dataset

Dynamic classifier selection based on imprecise probabilities : a case study for the naive Bayes classifier

Dynamic classifier selection is a classification technique that, for every new instance to be classified, selects and uses the most competent classifier among a set of available ones. In this way, a new classifier is obtained, whose accuracy often outperforms that of the individual classifiers it is based on. We here present a version of this technique where, for a given instance, the competency of a classifier is based on the robustness of its prediction: the extent to which the classifier can be altered without changing its prediction. In order to define and compute this robustness, we adopt methods from the theory of imprecise probabilities. As a proof of concept, we here apply this idea to the simple case of naive Bayes classifiers. Based on our preliminary experiments, we find that the resulting classifier outperforms the individual classifiers it is based on

Epistemic irrelevance in credal nets: the case of imprecise Markov trees

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.Comment: 29 pages, 5 figures, 1 tabl

Robust dynamic classifier selection for remote sensing image classification

Dynamic classifier selection (DCS) is a classification technique that, for each new sample to be classified, selects and uses the most competent classifier among a set of available ones. We here propose a novel DCS model (R-DCS) based on the robustness of its prediction: the extent to which the classifier can be altered without changing its prediction. In order to define and compute this robustness, we adopt methods from the theory of imprecise probabilities. Additionally, two selection strategies for R-DCS model are presented and are applied on remote sensing images. The experiment results demonstrate that our model successfully incorporates uncertainty with respect to the model parameters without losing the performance

Using extreme prior probabilities on the Naive Credal Classifier

The Naive Credal Classifier (NCC) was the first method proposed for Imprecise Classification. It starts from the known Naive Bayes algorithm (NB), which assumes that the attributes are independent given the class variable. Despite this unrealistic assumption, NB and NCC have been successfully used in practical applications. In this work, we propose a new version of NCC, called Extreme Prior Naive Credal Classifier (EP-NCC). Unlike NCC, EP-NCC takes into consideration the lower and upper prior probabilities of the class variable in the estimation of the lower and upper conditional probabilities. We demonstrate that, with our proposed EP-NCC, the predictions are more informative than with NCC without increasing the risk of making erroneous predictions. An experimental analysis carried out in this work shows that EP-NCC significantly outperforms NCC and obtains statistically equivalent results to the algorithm proposed so far for Imprecise Classification based on decision trees, even though EP-NCC is computationally simpler. Therefore, EP-NCC is more suitable to be applied to large datasets for Imprecise Classification than the methods proposed so far in this field. This is an important issue in favor of our proposal due to the increasing amount of data in every area.This work has been supported by UGR-FEDER funds under Project A-TIC-344-UGR20, by the “FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades ” under Project P20_00159, and by research scholarship FPU17/02685