Same-decision probability: A confidence measure for threshold-based decisions

Authors:
Arthur Choi;Yexiang Xue;Adnan Darwiche
Affiliations:
Computer Science Department, University of California, Los Angeles, USA;Department of Computer Science, Cornell University, USA;Computer Science Department, University of California, Los Angeles, USA
Venue:
International Journal of Approximate Reasoning
Year:
2012

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Abstract

We consider in this paper the robustness of decisions based on probabilistic thresholds. To this effect, we propose the same-decision probability as a query that can be used as a confidence measure for threshold-based decisions. More specifically, the same-decision probability is the probability that we would have made the same threshold-based decision, had we known the state of some hidden variables pertaining to our decision. We study a number of properties about the same-decision probability. First, we analyze its computational complexity. We then derive a bound on its value, which we can compute using a variable elimination algorithm that we propose. Finally, we consider decisions based on noisy sensors in particular, showing through examples that the same-decision probability can be used to reason about threshold-based decisions in a more refined way.