Discrimination and its sensitivity in probabilistic networks (original) (raw)

Analysing sensitivity data from probabilistic networks

With the advance of efficient algorithms for sen sitivity analysis of probabilistic networks, study ing the sensitivities revealed by real-life net works is becoming feasible. As the amount of data yielded by an analysis of even a moderately sized network is already overwhelming, effective methods for extracting relevant information from these data are called for. One such method is to study the derivatives of the sensitivity func tions yielded, to identify the parameters that upon variation are expected to have a large effect on a probability of interest. We further propose to build upon the concept of admissible deviation, which captures the extent to which a parameter can be varied without inducing a change in the most likely outcome. We illustrate these con cepts by means of a sensitivity analysis of a real life probabilistic network in the field of oncology.

Sensitivity Analysis of Probabilistic Networks

Studies in Fuzziness and Soft Computing, 2007

Sensitivity analysis is a general technique for investigating the robustness of the output of a mathematical model and is performed for various different purposes. The practicability of conducting such an analysis of a probabilistic network has recently been studied extensively, resulting in a variety of new insights and effective methods, ranging from properties of the mathematical relation between a parameter and an output probability of interest, to methods for establishing the effects of parameter variation on decisions based on the output distribution computed from a network. In this paper, we present a survey of some of these research results and explain their significance.

On the Sensitivity of Probabilistic Networks to Reliability Characteristics

Modern Information Processing, 2006

Diagnostic reasoning in essence amounts to reasoning about an unobservable condition, based on indirect observations from diagnostic tests. Probabilistic networks that are developed for diagnostic reasoning, typically take the reliability characteristics of the tests employed into consideration to avoid misdiagnosis. In this paper, we demonstrate the effects of inaccuracies in these characteristics by means of a sensitivity analysis of a real-life network in the medical domain.

Sensitivity analysis for probability assessments in Bayesian networks

Systems, Man and Cybernetics, IEEE Transactions …, 1995

When eliciting probability models from experts, knowledge engineers may compare the results of the model with expert judgment on test scenarios, then adjust model parameters to bring the behavior of the model more in line with the expert's intuition. This paper presents a methodology for analytic computation of sensitivity values to measure the impact of small changes in a network parameter on a target probability value or distribution.

Sensitivity analysis in discrete Bayesian networks

IEEE Transactions on Systems, Man, and Cybernetics, 1997

The paper presents an efficient computational method for performing sensitivity analysis in discrete Bayesian networks. The method exploits the structure of conditional probabilities of a target node given the evidence. First, the set of parameters which are relevant to the calculation of the conditional probabilities of the target node is identified. Next, this set is reduced by removing those combinations of the parameters which either contradict the available evidence or are incompatible. Finally, using the canonical components associated with the resulting subset of parameters, the desired conditional probabilities are obtained. In this way, an important saving in the calculations is achieved. The proposed method can also be used to compute exact upper and lower bounds for the conditional probabilities, hence a sensitivity analysis can be easily performed. Examples are used to illustrate the proposed methodology.

Sensitivity Analysis in Bayesian Networks: From Single to Multiple Parameters

Cornell University - arXiv, 2012

Previous work on sensitivity analysis in Bayesian networks has focused on single parameters, where the goal is to understand the sensitivity of queries to single parameter changes, and to identify single parameter changes that would enforce a certain query constraint. In this paper, we expand the work to multiple parameters which may be in the CPT of a single variable, or the CPTs of multiple variables. Not only do we identify the solution space of multiple parameter changes that would be needed to enforce a query constraint, but we also show how to find the optimal solution, that is, the one which disturbs the current probability distribution the least (with respect to a specific measure of disturbance). We characterize the computational complexity of our new techniques and discuss their applications to developing and debugging Bayesian networks, and to the problem of reasoning about the value (reliability) of new information.

Sensitivity of Gaussian Bayesian networks to inaccuracies in their parameters

To determine the effect of a set of inaccurate parameters in Gaussian Bayesian networks, it is necessary to study the sensitivity of the model. With this aim we propose a sensitivity analysis based on comparing two different models: the original model with the initial parameters assigned to the Gaussian Bayesian network and the perturbed model obtained after perturbing a set of inaccurate parameters with specific characteristics.

Sensitivity Analysis in Gaussian Bayesian Networks Using a Divergence Measure

Communications in Statistics-theory and Methods, 2007

Bayesian network. The measure presented is based on the Kullback-Leibler divergence and is useful to evaluate the impact of prior changes over the posterior marginal density of the target variable in the network. We find that some changes do not disturb the posterior marginal density of interest. Finally, we describe a method to compare different sensitivity measures obtained depending on where the inaccuracy was. An example is used to illustrate the concepts and methods presented.

Sensitivity analysis of Bayesian networks to parameters of the conditional probability model using a Beta regression approach

Expert Systems with Applications, 2020

Ensuring the validity and credibility of Bayesian Belief Network (BBN) as a modelling tool for expert systems requires appropriate methods for sensitivity analysis (SA), in order to test the robustness of the BBN diagnostic and prognostic with respect to the parameterisation of the conditional probability model (CPM). Yet, the most widely used techniques (based on sensitivity functions for discrete BBNs) only provide a local insight on the CPM influence, i.e. by varying only one CPM parameter at a time (or a few of them) while keeping the other ones unchanged. To overcome this limitation, the present study proposes an approach for global SA relying on Beta Regression using gradient boosting (potentially combined with stability selection analysis): it presents the benefit of keeping the presentation intuitive through a graphbased approach, while being applicable to a large number of CPM parameters. The implementation of this approach is investigated for three cases, which cover a large spectrum of situations: (1) a small discrete BBN, used to capture medical knowledge, demonstrates the proposed approach; (2) a linear Gaussian BBN, used to assess the damage of reinforced concrete structures, exemplifies a case where the number of parameters is too large to be easily processed and interpreted (>40 parameters); (3) a discrete BBN, used for reliability analysis of nuclear power plant, exemplifies a case where analytical solutions for sensitivity can hardly be 2 derived. Finally, provided that the validity of the BBR model is carefully checked, we show that the proposed approach can provide richer information than traditional SA methods at different levels: (i) it selects the most influential parameters; (ii) it provides the functional relation between the CPM parameter and the result of the probabilistic query; and (iii) it identifies how the CPM parameters can lead to situations of high probability, while quantifying the confidence in the occurrence of these situations.

Sensitivity to evidence in Gaussian Bayesian networks using mutual information

Information Sciences, 2014

We introduce a methodology for sensitivity analysis of evidence variables in Gaussian Bayesian networks. Knowledge of the posterior probability distribution of the target variable in a Bayesian network, given a set of evidence, is desirable. However, this evidence is not always determined; in fact, additional information might be requested to improve the solution in terms of reducing uncertainty. In this study we develop a procedure, based on Shannon entropy and information theory measures, that allows us to prioritize information according to its utility in yielding a better result. Some examples illustrate the concepts and methods introduced.