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20
Building probabilistic networks: where do the numbers come from?  a guide to the literature
 IEEE Transactions on Knowledge and Data Engineering
, 2000
"... Probabilistic networks are now fairly well established as practical representations of knowledge for reasoning under uncertainty, as demonstrated by an increasing number of successful applications in such domains as (medical) diagnosis and prognosis, planning, vision, ..."
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Cited by 33 (3 self)
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Probabilistic networks are now fairly well established as practical representations of knowledge for reasoning under uncertainty, as demonstrated by an increasing number of successful applications in such domains as (medical) diagnosis and prognosis, planning, vision,
Sensitivity analysis in Bayesian networks: From single to multiple parameters
 In 20’th Conference on Uncertainty in Artificial Intelligence (UAI
, 2004
"... 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 wo ..."
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Cited by 18 (2 self)
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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. 1
Sensitivity Analysis and Explanations for Robust Query Evaluation in Probabilistic Databases
 In SIGMOD
, 2011
"... Probabilistic database systems have successfully established themselves as a tool for managing uncertain data. However, much of the research in this area has focused on efficient query evaluation and has largely ignored two key issues that commonly arise in uncertain data management: First, how to p ..."
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Cited by 13 (0 self)
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Probabilistic database systems have successfully established themselves as a tool for managing uncertain data. However, much of the research in this area has focused on efficient query evaluation and has largely ignored two key issues that commonly arise in uncertain data management: First, how to provide explanations for query results, e.g., “Why is this tuple in my result? ” or “Why does this output tuple have such high probability?”. Second, the problem of determining the sensitive input tuples for the given query, e.g., users are interested to know the input tuples that can substantially alter the output, when their probabilities are modified (since they may be unsure about the input probability values). Existing systems provide the lineage/provenance of each of the output tuples in addition to the output probabilities, which is a boolean formula indicating the dependence of the output tuple on the input tuples. However, lineage does not immediately provide a quantitative relationship and it is not informative when we have multiple output tuples. In this paper, we propose a unified framework that can handle both the issues mentioned above to facilitate robust query processing. We formally define the notions of influence and explanations and provide algorithms to determine the topℓ influential set of variables and the topℓ set of explanations for a variety of queries, including conjunctive queries, probabilistic threshold queries, topk queries and aggregation queries. Further, our framework naturally enables highly efficient incremental evaluation when input probabilities are modified (e.g., if uncertainty is resolved). Our preliminary experimental results demonstrate the benefits of our framework for performing robust query processing over probabilistic databases.
A distance measure for bounding probabilistic belief change
"... We propose a distance measure between two probability distributions, which allows one to bound the amount of belief change that occurs when moving from one distribution to another. We contrast the proposed measure with some well known measures, including KLdivergence, showing how they fail to be th ..."
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Cited by 13 (4 self)
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We propose a distance measure between two probability distributions, which allows one to bound the amount of belief change that occurs when moving from one distribution to another. We contrast the proposed measure with some well known measures, including KLdivergence, showing how they fail to be the basis for bounding belief change as is done using the proposed measure. We then present two practical applications of the proposed distance measure: sensitivity analysis in belief networks and probabilistic belief revision. We show how the distance measure can be easily computed in these applications, and then use it to bound global belief changes that result from either the perturbation of local conditional beliefs or the accommodation of soft evidence. Finally, we show that two well known techniques in sensitivity analysis and belief revision correspond to the minimization of our proposed distance measure and, hence, can be shown to be optimal from that viewpoint.
On the robustness of Most Probable Explanations
 In Proceedings of the Twenty Second Conference on Uncertainty in Artificial Intelligence
"... In Bayesian networks, a Most Probable Explanation (MPE) is a complete variable instantiation with the highest probability given the current evidence. In this paper, we discuss the problem of finding robustness conditions of the MPE under single parameter changes. Specifically, we ask the question: H ..."
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Cited by 7 (0 self)
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In Bayesian networks, a Most Probable Explanation (MPE) is a complete variable instantiation with the highest probability given the current evidence. In this paper, we discuss the problem of finding robustness conditions of the MPE under single parameter changes. Specifically, we ask the question: How much change in a single network parameter can we afford to apply while keeping the MPE unchanged? We will describe a procedure, which is the first of its kind, that computes this answer for all parameters in the Bayesian network in time O(n exp(w)), where n is the number of network variables and w is its treewidth. 1
An overview of advances in reliability estimation of individual predictions in machine learning. Intelligent Data Analysis (in press
"... In Machine Learning, estimation of the predictive accuracy for a given model is most commonly approached by analyzing the average accuracy of the model. In general, the predictive models do not provide accuracy estimates for their individual predictions. The reliability estimates of individual predi ..."
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Cited by 6 (1 self)
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In Machine Learning, estimation of the predictive accuracy for a given model is most commonly approached by analyzing the average accuracy of the model. In general, the predictive models do not provide accuracy estimates for their individual predictions. The reliability estimates of individual predictions require the analysis of various model and instance properties. In the paper we make an overview of the approaches for estimation of individual prediction reliability. We start by summarizing three research fields, that provided ideas and motivation for our work: (a) approaches to perturbing learning data, (b) the usage of unlabeled data in supervised learning, and (c) the sensitivity analysis. The main part of the paper presents two classes of reliability estimation approaches and summarizes the relevant terminology, which is often used in this and related research fields.
Quantifying the Uncertainty of a Belief Net Response: Bayesian ErrorBars for Belief Net Inference
"... A Bayesian belief network models a joint distribution over variables using a DAG to represent variable dependencies and network parameters to represent the conditional probability of each variable given an assignment to its immediate parents. Existing algorithms assume each network parameter is fixe ..."
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Cited by 4 (1 self)
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A Bayesian belief network models a joint distribution over variables using a DAG to represent variable dependencies and network parameters to represent the conditional probability of each variable given an assignment to its immediate parents. Existing algorithms assume each network parameter is fixed. From a Bayesian perspective, however, these network parameters can be random variables that reflect uncertainty in parameter estimates, arising because the parameters are learned from data, or as they are elicited from uncertain experts. Belief networks are commonly used to compute responses to queries — i.e., return a number for P(H = h  E = e). Parameter uncertainty induces uncertainty in query responses, which are thus themselves random variables. This paper investigates this query response distribution, and shows how to accurately model it for any query and any network structure. In particular, we prove that the query response is asymptotically Gaussian and provide its mean value and asymptotic variance. Moreover, we present an algorithm for computing these quantities that has the same worstcase complexity as inference in general, and also describe straightline code when the query includes all n variables. We provide empirical evidence that (1) our approximation of the variance is very accurate, and (2) a Beta distribution with these moments provides a very accurate model of the observed query response distribution. We also show how to use this to produce accurate error bars around these responses — i.e., to determine that the response to P(H = h  E = e) is x ± y with confidence 1 − δ.
Effect of imprecision in probabilities on Bayesian network models: An empirical study
 In Working notes of the European Conference on Artificial Intelligence in Medicine (AIME03): Qualitative and Modelbased Reasoning in Biomedicine, Protaras
, 2003
"... While most knowledge engineers believe that the quality of results obtained from Bayesian networks is not too sensitive to imprecision in probabilities, this remains a conjecture with only modest empirical support. Our work on a Bayesian network model for diagnosis of liver disorders, Hepar II, pres ..."
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Cited by 3 (2 self)
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While most knowledge engineers believe that the quality of results obtained from Bayesian networks is not too sensitive to imprecision in probabilities, this remains a conjecture with only modest empirical support. Our work on a Bayesian network model for diagnosis of liver disorders, Hepar II, presented us with an opportunity to test this conjecture in a practical setting. We present the results of an empirical study in which we systematically introduce noise in Hepar II’s probabilities and test the diagnostic accuracy of the resulting model. We replicate an experiment conducted by Pradhan et al. [13] and show that Hepar II is more sensitive to noise in parameters than the CPCS network that they examined. Our data show that the diagnostic accuracy of the model deteriorates almost linearly with noise. While our result is merely a single data point that sheds light on the hypothesis in question, we suggest that Bayesian networks are more sensitive to the quality of their numerical parameters than popularly believed. 1
The Computational Complexity of Sensitivity Analysis and Parameter Tuning
"... While known algorithms for sensitivity analysis and parameter tuning in probabilistic networks have a running time that is exponential in the size of the network, the exact computational complexity of these problems has not been established as yet. In this paper we study several variants of the tuni ..."
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While known algorithms for sensitivity analysis and parameter tuning in probabilistic networks have a running time that is exponential in the size of the network, the exact computational complexity of these problems has not been established as yet. In this paper we study several variants of the tuning problem and show that these problems are NPPPcomplete in general. We further show that the problems remain NPcomplete or PPcomplete, for a number of restricted variants. These complexity results provide insight in whether or not recent achievements in sensitivity analysis and tuning can be extended to more general, practicable methods. 1
Evidence and Scenario Sensitivities in Naive Bayesian Classifiers
, 2008
"... Empirical evidence shows that naive Bayesian classifiers perform quite well compared to more sophisticated classifiers, even in view of inaccuracies in their parameters. In this paper, we study the effects of such parameter inaccuracies by investigating the sensitivity functions of a naive Bayesian ..."
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Empirical evidence shows that naive Bayesian classifiers perform quite well compared to more sophisticated classifiers, even in view of inaccuracies in their parameters. In this paper, we study the effects of such parameter inaccuracies by investigating the sensitivity functions of a naive Bayesian network. We show that, as a consequence of the network’s independence properties, these sensitivity functions are highly constrained. We further investigate whether the patterns of sensitivity that follow from these functions support the observed robustness of naive Bayesian classifiers. In addition to standard sensitivities given available evidence, we also study the effect of parameter inaccuracies in view of scenarios of additional evidence. We show that standard sensitivity functions suffice to describe such scenario sensitivities.