David Poole

Bahare Fatemi, Perouz Taslakian, David Vazquez et al.

Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple embedding-based model called ReAlE that performs link prediction in knowledge hypergraphs (generalized knowledge graphs) and can represent high-level abstractions in terms of relational algebra operations. We show theoretically that ReAlE is fully expressive and provide proofs and empirical evidence that it can represent a large subset of the primitive relational algebra operations, namely renaming, projection, set union, selection, and set difference. We also verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.

Matthew Dirks, David Poole

Many evaluation methods exist, each for a particular prediction task, and there are a number of prediction tasks commonly performed including classification and regression. In binarised regression, binary decisions are generated from a learned regression model (or real-valued dependent variable), which is useful when the division between instances that should be predicted positive or negative depends on the utility. For example, in mining, the boundary between a valuable rock and a waste rock depends on the market price of various metals, which varies with time. This paper proposes impact curves to evaluate binarised regression with instance-varying costs, where some instances are much worse to be classified as positive (or negative) than other instances; e.g., it is much worse to throw away a high-grade gold rock than a medium-grade copper-ore rock, even if the mine wishes to keep both because both are profitable. We show how to construct an impact curve for a variety of domains, including examples from healthcare, mining, and entertainment. Impact curves optimize binary decisions across all utilities of the chosen utility function, identify the conditions where one model may be favoured over another, and quantitatively assess improvement between competing models.

David L. Poole, Gregory M. Provan

Within diagnostic reasoning there have been a number of proposed definitions of a diagnosis, and thus of the most likely diagnosis, including most probable posterior hypothesis, most probable interpretation, most probable covering hypothesis, etc. Most of these approaches assume that the most likely diagnosis must be computed, and that a definition of what should be computed can be made a priori, independent of what the diagnosis is used for. We argue that the diagnostic problem, as currently posed, is incomplete: it does not consider how the diagnosis is to be used, or the utility associated with the treatment of the abnormalities. In this paper we analyze several well-known definitions of diagnosis, showing that the different definitions of the most likely diagnosis have different qualitative meanings, even given the same input data. We argue that the most appropriate definition of (optimal) diagnosis needs to take into account the utility of outcomes and what the diagnosis is used for.