A PRELIMINARY REPORT ON A GENERAL THEORY OF INDUCTIVE INFERENCE
A PRELIMINARY REPORT ON A GENERAL THEORY OF INDUCTIVE INFERENCE
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归纳推理一般理论初步报告
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
R. Solomonoff
中科院分区：
文献类型：
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作者：
R. Solomonoff
对归纳推理的一个非常一般的新理论做了一些初步的工作。通过计算各种符号序列的先验概率来实现对有序符号序列的外推。通过考虑输出为所述序列的通用图灵机，得到了序列的先验概率。先验概率的近似值由机器的最短输入给出，该机器将给出期望的输出。给出了一个更精确的公式，并使所获得的外推概率在很大程度上将与所使用的通用图灵机无关，前提是要外推的序列中有足够的信息量。通过算例说明了该方法在具体问题中的应用。对该方法在曲线拟合等连续问题中的应用进行了一定程度的探讨。提出了一些可供选择的归纳推理理论，它们的有效性似乎是所描述的第一种方法有效性的推论。
Some preliminary work is presented on a very general new theory of inductive inference. The extrapolation of an ordered sequence of symbols is implemented by computing the a priori probabilities of various sequences of symbols. The a priori probability of a sequence is obtained by considering a universal Turing machine whose output is the sequence in question. An approximation to the a priori probability is given by the shortest input to the machine that will give the desired output. A more exact formulation is given, and it is made somewhat plausible that extrapolation probabilities obtained will be largely independent of just which universal Turing machine was used, providing that the sequence to be extrapolated has an adequate amount of information in it. Some examples are worked out to show the application of the method to specific problems. Applications of the method to curve fitting and other continuous problems are discussed to some extent. Some alternative theories of inductive inference are presented whose validities appear to be corollaries of the validity of the first method described.