اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدInformation Distance
137
0
0.0
(
0
)
تأليف
Charles H. Bennett
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two pictures. We give several natural definitions of a universal information metric, based on length of shortest programs for either ordinary computations or reversible (dissipationless) computations. It turns out that these definitions are equivalent up to an additive logarithmic term. We show that the information distance is a universal cognitive similarity distance. We investigate the maximal correlation of the shortest programs involved, the maximal uncorrelation of programs (a generalization of the Slepian-Wolf theorem of classical information theory), and the density properties of the discrete metric spaces induced by the information distances. A related distance measures the amount of nonreversibility of a computation. Using the physical theory of reversible computation, we give an appropriate (universal, anti-symmetric, and transitive) measure of the thermodynamic work required to transform one object in another object by the most efficient process. Information distance between individual objects is needed in pattern recognition where one wants to express effective notions of pattern similarity or cognitive similarity between individual objects and in thermodynamics of computation where one wants to analyse the energy dissipation of a computation from a particular input to a particular output.
قيم البحث
اقرأ أيضاً
For a certain moment, the information volume represented in a probability space can be accurately measured by Shannon entropy. But in real life, the results of things usually change over time, and the prediction of the information volume contained in
the future is still an open question. Deng entropy proposed by Deng in recent years is widely applied on measuring the uncertainty, but its physical explanation is controversial. In this paper, we give Deng entropy a new explanation based on the fractal idea, and proposed its generalization called time fractal-based (TFB) entropy. The TFB entropy is recognized as predicting the uncertainty over a period of time by splitting times, and its maximum value, called higher order information volume of mass function (HOIVMF), can express more uncertain information than all of existing methods.
Given a probability measure $mu$ over ${mathbb R}^n$, it is often useful to approximate it by the convex combination of a small number of probability measures, such that each component is close to a product measure. Recently, Ronen Eldan used a stoch
astic localization argument to prove a general decomposition result of this type. In Eldans theorem, the `number of components is characterized by the entropy of the mixture, and `closeness to product is characterized by the covariance matrix of each component. We present an elementary proof of Eldans theorem which makes use of an information theory (or estimation theory) interpretation. The proof is analogous to the one of an earlier decomposition result known as the `pinning lemma.
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas f
or quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive noninteger real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, $n$, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over $n$ dimensions, as needed in the direct calculation of the desired moment.
In this paper we apply different techniques of information distortion on a set of classical books written in English. We study the impact that these distortions have upon the Kolmogorov complexity and the clustering by compression technique (the latt
er based on Normalized Compression Distance, NCD). We show how to decrease the complexity of the considered books introducing several modifications in them. We measure how the information contained in each book is maintained using a clustering error measure. We find experimentally that the best way to keep the clustering error is by means of modifications in the most frequent words. We explain the details of these information distortions and we compare with other kinds of modifications like random word distortions and unfrequent word distortions. Finally, some phenomenological explanations from the different empirical results that have been carried out are presented.
A finite form of de Finettis representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $ngeq k$ is close to a mixture of product d
istributions. Closeness is measured in terms of the relative entropy and an explicit bound is provided.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
