ON THE CONNECTION BETWEEN THE COMPLEXITY AND CREDIBILITY OF INFERRED MODELS
- 1 January 1978
- journal article
- research article
- Published by Taylor & Francis in International Journal of General Systems
- Vol. 4 (4) , 255-264
- https://doi.org/10.1080/03081077808960690
Abstract
The connection between the simplicity of scientific theories and the credence attributed to their predictions seems to permeate the practice of scientific discovery. When a scientist succeeds in explaining a set of nobservations using a model Mof complexity c then it is generally believed that the likelihood of finding another explanatory model with similar complexity but leading to opposite predictions decreases with increasing nand decreasing c. This paper derives formal relationships between n, c and the probability of ambiguous predictions by examining three modeling languages under binary classification tasks: perceptrons, Boolean formulae, and Boolean networks. Bounds are also derived for the probability of error associated with the policy of accepting only models of complexity not exceeding c. Human tendency to regard the simpler as the more trustworthy is given a qualified justification.Keywords
This publication has 5 references indexed in Scilit:
- A distribution-free performance bound in error estimation (Corresp.)IEEE Transactions on Information Theory, 1976
- On the Uniform Convergence of Relative Frequencies of Events to Their ProbabilitiesTheory of Probability and Its Applications, 1971
- Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern RecognitionIEEE Transactions on Electronic Computers, 1965
- On simple theories of a complex worldSynthese, 1963
- Experience and prediction: An analysis of the foundations and the structure of knowledge.Published by American Psychological Association (APA) ,1952