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Predictability, complexity, and learning.   总被引:7,自引:0,他引:7  
We define predictive information I(pred)(T) as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times T:I(pred)(T) can remain finite, grow logarithmically, or grow as a fractional power law. If the time series allows us to learn a model with a finite number of parameters, then I(pred)(T) grows logarithmically with a coefficient that counts the dimensionality of the model space. In contrast, power-law growth is associated, for example, with the learning of infinite parameter (or nonparametric) models such as continuous functions with smoothness constraints. There are connections between the predictive information and measures of complexity that have been defined both in learning theory and the analysis of physical systems through statistical mechanics and dynamical systems theory. Furthermore, in the same way that entropy provides the unique measure of available information consistent with some simple and plausible conditions, we argue that the divergent part of I(pred)(T) provides the unique measure for the complexity of dynamics underlying a time series. Finally, we discuss how these ideas may be useful in problems in physics, statistics, and biology.  相似文献   

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A distinctive concern in the US military for computer security dates from the emergence of time-sharing systems in the 1960s. This paper traces the subsequent development of the idea of a “security kernel” and of the mathematical modeling of security, focusing in particular on the paradigmatic Bell-LaPadula model. The paper examines the connections between computer security and formal, deductive verification of the properties of computer systems. It goes on to discuss differences between the cultures of communications security and computer security, the bureaucratic turf war over security, and the emergence and impact of the Department of Defense's Trusted Computer System Evaluation Criteria (the so-called Orange Book), which effectively took its final form in 1983. The paper ends by outlining the fragmentation of computer security since the Orange Book was written  相似文献   

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