58,006 research outputs found
Inductive inference of recursive functions: complexity bounds
This survey includes principal results on complexity
of inductive inference for recursively enumerable classes of total
recursive functions. Inductive inference is a process to find an
algorithm from sample computations. In the case when the given class
of functions is recursively enumerable it is easy to define a
natural complexity measure for the inductive inference, namely, the
worst-case mindchange number for the first n functions in the given
class. Surely, the complexity depends not only on the class, but
also on the numbering, i.e. which function is the first, which one
is the second, etc. It turns out that, if the result of inference is
Goedel number, then complexity of inference may vary between
log n+o(log2n ) and an arbitrarily slow recursive function. If the
result of the inference is an index in the numbering of the
recursively enumerable class, then the complexity may go up to
const-n. Additionally, effects previously found in the Kolmogorov
complexity theory are discovered in the complexity of inductive
inference as well
Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis
Even with impressive advances in automated formal methods, certain problems
in system verification and synthesis remain challenging. Examples include the
verification of quantitative properties of software involving constraints on
timing and energy consumption, and the automatic synthesis of systems from
specifications. The major challenges include environment modeling,
incompleteness in specifications, and the complexity of underlying decision
problems.
This position paper proposes sciduction, an approach to tackle these
challenges by integrating inductive inference, deductive reasoning, and
structure hypotheses. Deductive reasoning, which leads from general rules or
concepts to conclusions about specific problem instances, includes techniques
such as logical inference and constraint solving. Inductive inference, which
generalizes from specific instances to yield a concept, includes algorithmic
learning from examples. Structure hypotheses are used to define the class of
artifacts, such as invariants or program fragments, generated during
verification or synthesis. Sciduction constrains inductive and deductive
reasoning using structure hypotheses, and actively combines inductive and
deductive reasoning: for instance, deductive techniques generate examples for
learning, and inductive reasoning is used to guide the deductive engines.
We illustrate this approach with three applications: (i) timing analysis of
software; (ii) synthesis of loop-free programs, and (iii) controller synthesis
for hybrid systems. Some future applications are also discussed
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
Descriptive Complexity Approaches to Inductive Inference
We present a critical review of descriptive complexity approaches to inductive inference. Inductive inference is defined as any process by which a model of the world is formed from observations. The descriptive complexity approach is a formalization of Occam\u27s razor: choose the simplest model consistent with the data. Descriptive complexity as defined by Kolmogorov, Chaitin and Solomonoff is presented as a generalization of Shannon\u27s entropy. We discuss its relationship with randomness and present examples. However, a major result of the theory is negative: descriptive complexity is uncomputable.
Rissanen\u27s minimum description length (MDL) principle is presented as a restricted form of the descriptive complexity which avoids the uncomputability problem. We demonstrate the effectiveness of MDL through its application to AR processes. Lastly, we present and discuss LeClerc\u27s application of MDL to the problem of image segmentation
Towards a Statistical Geometrodynamics
Can the spatial distance between two identical particles be explained in
terms of the extent that one can be distinguished from the other? Is the
geometry of space a macroscopic manifestation of an underlying microscopic
statistical structure? Is geometrodynamics derivable from general principles of
inductive inference? Tentative answers are suggested by a model of
geometrodynamics based on the statistical concepts of entropy, information
geometry, and entropic dynamics.Comment: Invited talk at the Decoherence, Information, Entropy, and Complexity
Workshop, DICE02, September 2000, Piombino, Ital
A graph regularization based approach to transductive class-membership prediction
Considering the increasing availability of structured machine processable knowledge in the context of the Semantic Web, only relying on purely deductive inference may be limiting. This work proposes a new method for similarity-based class-membership prediction in Description Logic knowledge bases. The underlying idea is based on the concept of propagating class-membership information among similar individuals; it is non-parametric in nature and characterised by interesting complexity properties, making it a potential candidate for large-scale transductive inference. We also evaluate its effectiveness with respect to other approaches based on inductive inference in SW literature
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