×

zbMATH — the first resource for mathematics

Probability and plurality for aggregations of learning machines. (English) Zbl 0646.68096
A new notion of probabilistic team inductive inference is introduced and compared with both probabilistic inference and team inference. In many cases, but not all, probabilism can be traded for pluralism, and vice versa. Necessary and sufficient conditions are given describing when a team of deterministic or probabilistic learning machines can be coalesced into a single learning machine. A subtle difference between probabilism and pluralism is revealed.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Angluin, D.; Smith, C.H., Inductive inference: theory and methods, Comput. surveys, 15, 237-269, (1983)
[2] Angluin, D.; Smith, C.H., Inductive inference, (), 409-418
[3] Barzdin, J., Two theorems on the limiting synthesis of functions, (), 82-88
[4] Blum, L.; Blum, M., Toward a mathematical theory of inductive inference, Inform. and control, 28, 125-155, (1975) · Zbl 0375.02028
[5] Case, J.; Smith, C., Comparison of identification criteria for machine inductive inference, Theoret. comput. sci., 25, 193-220, (1983) · Zbl 0524.03025
[6] Daley, R., On the error correcting power of pluralism in BC-type inductive inference, Theoret. comput. sci., 24, 95-104, (1983) · Zbl 0582.68020
[7] Feldman, J., Some decidability results on grammatical inference of best programs, Inform. and control, 20, 244-262, (1972) · Zbl 0242.68053
[8] Freivalds, R.V., Functions computable in the limit by probabilistic machines, (), 77-87
[9] Freivalds, R.V., Finite identification of general recursive functions by probabilistic strategies, (), 138-145
[10] Freivalds, R.V., On the principle capabilities of probabilistic algorithms in inductive inference, Semiotika inform., 12, 137-140, (1979)
[11] Gold, E.M., Language identification in the limit, Inform. and control, 10, 447-474, (1967) · Zbl 0259.68032
[12] Machtey, M.; Young, P., ()
[13] Osherson, D.; Stob, M.; Weinstein, S., ()
[14] Osherson, D.N.; Stob, M.; Weinstein, S., Aggregating inductive expertise, Inform. and control, 70, 69-95, (1986) · Zbl 0612.68077
[15] Pitt, L., A characterization of probabilistic inference, (), 485-494, to appear
[16] Podnieks, K.M., Probabilistic synthesis of enumerated classes of functions, Soviet math. dokl., 16, 1042-1045, (1975) · Zbl 0341.02028
[17] Podnieks, K.M., Probabilistic program synthesis, (), 57-88 · Zbl 0377.68008
[18] Smith, C.H., The power of pluralism for automatic program synthesis, J. assoc. comput. Mach., 29, 1144-1165, (1982) · Zbl 0496.68065
[19] Valiant, L.G., A theory of the learnable, Comm. ACM, 27, 1134-1142, (1984) · Zbl 0587.68077
[20] Wiehagen, R.; Freivalds, R.; Kinber, E.K., On the power of probabilistic strategies in inductive inference, Theoret. comput. sci., 28, 111-133, (1984) · Zbl 0555.68014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.