Positive dependence in qualitative probabilistic networks

Qualitative probabilistic networks (QPNs) combine the conditional independence assumptions of Bayesian networks with the qualitative properties of positive and negative dependence. They formalise various intuitive properties of positive dependence to allow inferences over a large network of variables. However, we will demonstrate in this paper that, due to an incorrect symmetry property, many inferences obtained in non-binary QPNs are not mathematically true. We will provide examples of such incorrect inferences and briefly discuss possible resolutions.Comment: 10 pages, 3 figure

Explaining inference on a population of independent agents using Bayesian networks

The main goal of this research is to design, implement, and evaluate a novel explanation method, the hierarchical explanation method (HEM), for explaining Bayesian network (BN) inference when the network is modeling a population of conditionally independent agents, each of which is modeled as a subnetwork. For example, consider disease-outbreak detection in which the agents are patients who are modeled as independent, conditioned on the factors that cause disease spread. Given evidence about these patients, such as their symptoms, suppose that the BN system infers that a respiratory anthrax outbreak is highly likely. A public-health official who received such a report would generally want to know why anthrax is being given a high posterior probability. The HEM explains such inferences. The explanation approach is applicable in general to inference on BNs that model conditionally independent agents; it complements previous approaches for explaining inference on BNs that model a single agent (e.g., for explaining the diagnostic inference for a single patient using a BN that models just that patient). The hypotheses that were tested are: (1) the proposed explanation method provides information that helps a user to understand how and why the inference results have been obtained, (2) the proposed explanation method helps to improve the quality of the inferences that users draw from evidence

New Techniques for Learning Parameters in Bayesian Networks.

PhDOne of the hardest challenges in building a realistic Bayesian network (BN) model is to construct the node probability tables (NPTs). Even with a fixed predefined model structure and very large amounts of relevant data, machine learning methods do not consistently achieve great accuracy compared to the ground truth when learning the NPT entries (parameters). Hence, it is widely believed that incorporating expert judgment or related domain knowledge can improve the parameter learning accuracy. This is especially true in the sparse data situation. Expert judgments come in many forms. In this thesis we focus on expert judgment that specifies inequality or equality relationships among variables. Related domain knowledge is data that comes from a different but related problem. By exploiting expert judgment and related knowledge, this thesis makes novel contributions to improve the BN parameter learning performance, including: • The multinomial parameter learning model with interior constraints (MPL-C) and exterior constraints (MPL-EC). This model itself is an auxiliary BN, which encodes the multinomial parameter learning process and constraints elicited from the expert judgments. • The BN parameter transfer learning (BNPTL) algorithm. Given some potentially related (source) BNs, this algorithm automatically explores the most relevant source BN and BN fragments, and fuses the selected source and target parameters in a robust way. • A generic BN parameter learning framework. This framework uses both expert judgments and transferred knowledge to improve the learning accuracy. This framework transfers the mined data statistics from the source network as the parameter priors of the target network. Experiments based on the BNs from a well-known repository as well as two realworld case studies using different data sample sizes demonstrate that the proposed new approaches can achieve much greater learning accuracy compared to other state-of-theart methods with relatively sparse data.China Scholarship Counci

Qualitative approaches to quantifying probabilistic networks

A probabilistic network consists of a graphical representation (a directed graph) of the important variables in a domain of application, and the relationships between them, together with a joint probability distribution over the variables. A probabilistic network allows for computing any probability of interest. The joint probability distribution factorises into conditional probability distributions such that for each variable represented in the graph a distribution is specified conditional on all possible combinations of the variable's parents in the graph. Even for a moderate sized probabilistic network, thousands of probabilities need to be specified. Often the only source of probabilistic information is the knowledge and experience of experts. People, even experts, are known not be very good at assessing probabilities, and often dislike expressing their estimates as numbers. To overcome this problem, we propose two qualitative approaches to quantifying probabilistic networks. The first approach is abstracting away from probabilities by using qualitative probabilistic networks. The second approach is to allow the use of verbal expressions of probability during elicitation. In qualitative probabilistic networks, the arcs of the directed graph are augmented with signs: `+',`-', `0', and `?', indicating the direction of shift in probability for the variable at one end of the arc, given a shift in values of the variable at the other end of the arc. For example, a positive influence of variable A on variable B indicates that higher values for B become more likely given higher values for A. Qualitative probabilistic networks allow for reasoning with probabilistic networks in a qualitative way, thereby enabling us to check the robustness of the network's structure before probabilities are assessed. In addition, the qualitative signs provide constraints on the probabilities to be elicited. Qualitative networks are, however, not very expressive and therefore easily result in uninformative answers (`?'s) during reasoning. We will suggest several refinements of the formalism of qualitative probabilistic networks that enhance their expressiveness and applicability. To make probability elicitation easier on experts, we allow them to state verbal probability expressions, such as "probable" and "impossible", as well as numbers. To this end, we have augmented a vertical probability elicitation scale with verbal expressions. These expressions, and their position on the scale, are the result of several studies we conducted. The scale, together with other ingredients such as text-fragments describing the probability to be assessed and grouping of the probabilities that should sum to 1, is used in a newly designed probability elicitation method. The method provides for the elicitation of initial rough assessments. Assessments for which the outcome of the network is very sensitive can be refined using additional experts and/or the more conventional elicitation methods. Our method has been used with two experts in oncology in the construction of a probabilistic network for oesophageal carcinoma and allows us to elicit a large number of probabilities in little time. The experts felt comfortable with the method and evaluations of the resulting network have shown that it performs quite well with the rough assessments

Enhancing QPNs for Trade-off Resolution

Qualitative probabilistic networks have been introduced as qualitative abstractions of Bayesian belief networks. One of the major drawbacks of these qualitative networks is their coarse level of detail, which may lead to unresolved trade-offs during inference. We present an enhanced formalism for qualitative networks with a finer level of detail. An enhanced qualitative probabilistic network differs from a regular qualitative network in that it distinguishes between strong and weak influences. Enhanced qualitative probabilistic networks are purely qualitative in nature, as regular qualitative networks are, yet allow for efficiently resolving trade-offs during inference