Abduction as Incomplete Parameter Estimation

  • Moto Kamiura
Keywords: Autoregressive model, Parameter Estimation, Observation, Cauchy distribution, Power law


Abduction is a kind of logical inference, and has been studied in computer science and artificial intelligence (Fin- lay and Dix 1996). Recently, Sawa and Gunji (2010) introduced a diagram to represent three types of inference: i.e. deduc- tion, induction, and abduction, which are articulated by C.S.Peirce. Sawa-Gunji’s representation provides a new approach to a numerical aspect of abduction. In the present paper, we show that Sawa-Gunji's representation of abduction is consistent with Finlay-Dix's one, and integrate the two representations. Both parameter estimation and abduction occupy a similar position on the integrated representation, although they are not completely corresponding. We present "incomplete" pa- rameter estimation as a sort of "simulated abduction", which is a numerical aspect of abduction. It is applied to a first-order autoregressive (AR(1)) model. As a result of numerical analyses on AR(1), the incompletely estimated parameter (IEP) follows a Cauchy distribution, which has a power law of the slope -2 in the tail, although conventionally estimated parameter is normally distributed. It is shown that the Cauchy distribution of the IEP is based on structure of ratio distribution of normal random variables generated from the AR(1). This research suggests that the distribution of the IEP is not based on a mech- anism of system itself, but on relationship between data structure on the given system (i.e. the given AR(1) process) and one on the system observer (i.e. the estimator of the AR(1) parameter).

Author Biography

Moto Kamiura
March 2007: Doctor of Science on Physics, Kobe University June 2007 - March 2008 Technical Assistant in Kobe University April 2008 - Present: Assistant Professor in Faculty of Science and Technology, Tokyo University of Science April 2010 - Present: Cooperative Researcher in Research Institute of Electrical Communication, Tohoku University
Special Issue: Towards a New Science of Information