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Investigating Estimated Kolmogorov Complexity as a Means of Regularization for Link Prediction
[article]

2021
*
arXiv
*
pre-print

A preference for predicting graphs

arXiv:2006.04258v2
fatcat:3t33e3quzjbgbfe6k7vnq3ueia
*with*simpler*generating*mechanisms motivates our choice of*Kolmogorov**complexity*as a regularization term. ... We investigate a flexible means of regularization for link prediction based on an approximation of the*Kolmogorov**complexity*of graphs that is differentiable and compatible*with*recent advances in link ... In this work, we investigate penalizing graphs*with*large estimated*Kolmogorov**complexity*to encourage the creation of graphs*with*simpler*generating*mechanisms. ...##
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Page 2264 of Mathematical Reviews Vol. , Issue 94d
[page]

1994
*
Mathematical Reviews
*

Book’s paper surveys the basic properties of K[log, poly], the

*set*of strings*with**small**Kolmogorov**complex*- ity. ... Book, On*sets**with**small*in- formation content (23-42); David W. Juedes and Jack H. ...##
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Kolmogorov Complexity and Model Selection
[chapter]

2009
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Lecture Notes in Computer Science
*

The

doi:10.1007/978-3-642-03351-3_3
fatcat:mrgqoi5f6zbihawjshpqfhea5e
*Kolmogorov**complexity*of a finite*set*A is defined as the*Kolmogorov**complexity*of the list of all elements of A in some fixed order, say, in the lexicographical one. ... The work was in part supported by a RFBR grant 09-01-00709. 1 Roughly speaking, the*Kolmogorov**complexity*of a string x is the length of a shortest program printing x. ... Do we finally obtain a hypothesis*with**small*randomness deficiency? More specifically, let ML x (α) stand for a*set*A that minimises |A| among all A x of*Kolmogorov**complexity*at most α. ...##
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Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexity

2010
*
IEEE Transactions on Information Theory
*

We examine the structure of families of distortion balls from the perspective of

doi:10.1109/tit.2010.2048491
fatcat:wyjuj3cntraczi4u4flil6csk4
*Kolmogorov**complexity*. ... Special attention is paid to the canonical rate-distortion function of a source word which returns the minimal*Kolmogorov**complexity*of all distortion balls containing that word subject to a bound on their ... The authors would also like to thank the referees for their constructive comments; one referee pointed out that yet another example would be the case of Euclidean balls*with*the usual Euclidean distance ...##
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Generating behavioral acts of predetermined apparent complexity
[article]

2017
*
arXiv
*
pre-print

This study introduces a quantitative measure of behavioral acts -- their apparent

arXiv:1711.05141v1
fatcat:kwzd5uxlnzgrtb2eod4xknvwny
*complexity*. The measure is based on the concept of the*Kolmogorov**complexity*. ... The article describes an algorithm of*generating*behavioral acts of predetermined apparent*complexity*. Such acts can be used to evaluate and develop learning abilities of artificial agents. ... The first one is the incomputability of the*Kolmogorov**complexity*. It means that in*general*the*Kolmogorov**complexity*cannot be calculated exactly. ...##
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Discussion on Kolmogorov Complexity and Statistical Analysis

1999
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Computer journal
*

In particular, Li and Vitányi [6], Rissanen [3], Wallace and Dowe [7] have discussed the connection between

doi:10.1093/comjnl/42.4.340
fatcat:r6o5ybuk35cypinugcfl3xblia
*Kolmogorov*(algorithmic)*complexity*and minimum description length (minimum message length) principle ... (Even the time-bounded*complexity*of p is*small*since the pseudo-random number*generator*is computationally efficient.) ... We may now think of programs consisting of two parts, where the first part describes optimally the*set*A*with*the number of bits given by the*Kolmogorov**complexity*K (A) and the second part merely describes ...##
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A Short Introduction to Model Selection, Kolmogorov Complexity and Minimum Description Length (MDL)
[article]

2010
*
arXiv
*
pre-print

After providing some background information on information theory and

arXiv:1005.2364v2
fatcat:fkk2qo2so5acvodaz4wrbibwlq
*Kolmogorov**complexity*, we provide a short explanation of Minimum Description Length and error minimization. ... The concept of overfitting in model selection is explained and demonstrated*with*an example. ...*Kolmogorov**complexity*of*sets*. The*Kolmogorov**complexity*of a*set*of strings S is the length of the shortest program that can output the members of S on the UTM and then halt. ...##
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Page 5977 of Mathematical Reviews Vol. , Issue 94j
[page]

1994
*
Mathematical Reviews
*

Chapter 2 (“Algorithmic

*complexity*”) is dedicated to the theory of the most*general*form of*Kolmogorov**complexity*, called in the book the plain*Kolmogorov**complex*- ity. ... Working in the*setting*of information-based*complexity*, the au- thors present an example of a linear problem*with*finite infor- mational*complexity*but infinite combinatory*complexity*. ...##
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A Short Introduction to Kolmogorov Complexity
[article]

2010
*
arXiv
*
pre-print

This is a short introduction to

arXiv:1005.2400v2
fatcat:ma7q5wca3ra3vc62k44mmreerm
*Kolmogorov**Complexity*. ... The interested reader is referred to the text books by Cover & Thomas as well as Li & V\'itanyi, which cover the fields of information theory and*Kolmogorov**complexity*in depth and*with*all the necessary ...*Kolmogorov**complexity*of*sets*. The*Kolmogorov**complexity*of a*set*of strings S is the length of the shortest program that can output the members of S on the UTM and then halt. ...##
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On hausdorff and topological dimensions of the kolmogorov complexity of the real line

1994
*
Journal of computer and system sciences (Print)
*

We investigate the

doi:10.1016/s0022-0000(05)80073-x
fatcat:vgmphpoc6nc4xhwatn3glv2qkq
*Kolmogorov**complexity*of real numbers. Let K be the*Kolmogorov**complexity*function; we determine the Hausdorff dimension and the topological dimension of the graph of K. ... Since these dimensions are different, the graph of the*Kolmogorov**complexity*function of the real line forms a fractal in the sense of Mandelbrot. ... Consider the subset of the Besicovitch*set*Ep consisting of only those points*with**Kolmogorov**complexity*that are equal to H(p). ...##
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Comparing Security Notions of Secret Sharing Schemes

2015
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Entropy
*

This paper is concerned

doi:10.3390/e17031135
fatcat:ii2ydfczx5gjxak4jfi6xi5fs4
*with*these security notions for secret sharing schemes defined by the variational measures, including Shannon entropy, guessing probability, min entropy and*Kolmogorov**complexity*... Different to the entropies,*Kolmogorov**complexity*was also defined and used in study the security of individual instances for secret sharing schemes. ... From above theorem, we know that a string*with*high*Kolmogorov**complexity*, or a nearly*Kolmogorov*random string, cannot be split among participants*with**small*share sizes and high security parameter. ...##
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Correlation of automorphism group size and topological properties with program-size complexity evaluations of graphs and complex networks

2014
*
Physica A: Statistical Mechanics and its Applications
*

networks) and high

doi:10.1016/j.physa.2014.02.060
fatcat:gcvvh6jbinhvbdcyqwm6o5m2te
*Kolmogorov**complexity*to (random) Erdos-Renyi graphs. ... We show that approximations of K characterise synthetic and natural networks by their*generating*mechanisms, assigning lower algorithmic randomness to*complex*network models (Watts-Strogatz and Barabasi-Albert ... The group of*complex*networks peak at different K m values,*with*Watts-Strogatz networks ranking low for p = 0.01 when the*small*world effect is produced, and then moves towards high*Kolmogorov**complexity*...##
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How Incomputable Is Kolmogorov Complexity?

2020
*
Entropy
*

We discuss the incomputability of

doi:10.3390/e22040408
pmid:33286182
fatcat:imcanhdpnval5i5dj5wejyrj2m
*Kolmogorov**complexity*, which formal loopholes this leaves us*with*, recent approaches to compute or approximate*Kolmogorov**complexity*, which approaches are problematic, ...*Kolmogorov**complexity*is the length of the ultimately compressed version of a file (i.e., anything which can be put in a computer). ... Conclusions The review shows that the*Kolmogorov**complexity*of a string is incomputable in*general*, but may be computable for some arguments. ...##
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When Worlds Collide: Derandomization, Lower Bounds, and Kolmogorov Complexity
[chapter]

2001
*
Lecture Notes in Computer Science
*

-To introduce a new notion of time-bounded

doi:10.1007/3-540-45294-x_1
fatcat:7chu7jpdqrdidhia26ojmhgsdu
*Kolmogorov**complexity*(KT), and show that it provides a useful tool for understanding advances in derandomization, and for putting various results in context. ... Random Strings The canonical dense*sets**with*large*Kolmogorov**complexity*are the*sets*containing all of the random strings. ... It says that assuming that one class of*sets*has*small**Kolmogorov**complexity*is equivalent to another class of*sets*having large*Kolmogorov**complexity*(using slightly different notions of time-bounded ...##
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Power from Random Strings

2006
*
SIAM journal on computing (Print)
*

We consider

doi:10.1137/050628994
fatcat:jh7n3uvehbbcjkjs5jeicf35rq
*sets*of strings*with*high*Kolmogorov**complexity*, mainly in resource-bounded*settings*but also in the traditional recursion-theoretic sense. ... Of greater interest is the fact that the*set*R KS of strings*with*high space-bounded*Kolmogorov**complexity*is complete for PSPACE under ZPP-Turing reductions. ... We acknowledge illuminating discussions*with*Lance Fortnow, as well as helpful conversations of the first author*with*Paul Beame, Henry Cohn, Chris Umans, and Ramarathnam Venkatesan during a visit to Microsoft ...
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