61,866 research outputs found
Complexity Characterization in a Probabilistic Approach to Dynamical Systems Through Information Geometry and Inductive Inference
Information geometric techniques and inductive inference methods hold great
promise for solving computational problems of interest in classical and quantum
physics, especially with regard to complexity characterization of dynamical
systems in terms of their probabilistic description on curved statistical
manifolds. In this article, we investigate the possibility of describing the
macroscopic behavior of complex systems in terms of the underlying statistical
structure of their microscopic degrees of freedom by use of statistical
inductive inference and information geometry. We review the Maximum Relative
Entropy (MrE) formalism and the theoretical structure of the information
geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special
focus is devoted to the description of the roles played by the sectional
curvature, the Jacobi field intensity and the information geometrodynamical
entropy (IGE). These quantities serve as powerful information geometric
complexity measures of information-constrained dynamics associated with
arbitrary chaotic and regular systems defined on the statistical manifold.
Finally, the application of such information geometric techniques to several
theoretical models are presented.Comment: 29 page
There are no universal rules for induction
In a material theory of induction, inductive inferences are warranted by facts that prevail locally. This approach, it is urged, is preferable to formal theories of induction in which the good inductive inferences are delineated as those conforming to universal schemas. An inductive inference problem concerning indeterministic, nonprobabilistic systems in physics is posed, and it is argued that Bayesians cannot responsibly analyze it, thereby demonstrating that the probability calculus is not the universal logic of induction. Copyright 2010 by the Philosophy of Science Association.All right reserved
Induction without Probabilities
A simple indeterministic system is displayed and it is urged that we cannot responsibly infer inductively over it if we presume that the probability calculus is the appropriate logic of induction. The example illustrates the general thesis of a material theory of induction, that the logic appropriate to a particular domain is determined by the facts that prevail there
On the role of explanatory and systematic power in scientific reasoning
The paper investigates measures of explanatory power and how to define the inference schema “Inference to the Best Explanation”. It argues that these measures can also be used to quantify the systematic power of a hypothesis and the inference schema “Inference to the Best Systematization” is defined. It demonstrates that systematic power is a fruitful criterion for theory choice and IBS is truth-conducive. It also shows that even radical Bayesians must admit that systemic power is an integral component of Bayesian reasoning. Finally, the paper puts the achieved results in perspective with van Fraassen’s famous criticism of IB
An Ordinal View of Independence with Application to Plausible Reasoning
An ordinal view of independence is studied in the framework of possibility
theory. We investigate three possible definitions of dependence, of increasing
strength. One of them is the counterpart to the multiplication law in
probability theory, and the two others are based on the notion of conditional
possibility. These two have enough expressive power to support the whole
possibility theory, and a complete axiomatization is provided for the strongest
one. Moreover we show that weak independence is well-suited to the problems of
belief change and plausible reasoning, especially to address the problem of
blocking of property inheritance in exception-tolerant taxonomic reasoning.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in
Artificial Intelligence (UAI1994
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