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

Paris D. L. Flood, Ramon Viñas, Pietro Liò
2021 arXiv   pre-print
A preference for predicting graphs 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.  ... 
arXiv:2006.04258v2 fatcat:3t33e3quzjbgbfe6k7vnq3ueia

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.  ... 

Kolmogorov Complexity and Model Selection [chapter]

Nikolay Vereshchagin
2009 Lecture Notes in Computer Science  
The 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.  ... 
doi:10.1007/978-3-642-03351-3_3 fatcat:mrgqoi5f6zbihawjshpqfhea5e

Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexity

Nikolai K. Vereshchagin, Paul M.B. Vitanyi
2010 IEEE Transactions on Information Theory  
We examine the structure of families of distortion balls from the perspective of 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  ... 
doi:10.1109/tit.2010.2048491 fatcat:wyjuj3cntraczi4u4flil6csk4

Generating behavioral acts of predetermined apparent complexity [article]

Andrei Olifer
2017 arXiv   pre-print
This study introduces a quantitative measure of behavioral acts -- their apparent 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.  ... 
arXiv:1711.05141v1 fatcat:kwzd5uxlnzgrtb2eod4xknvwny

Discussion on Kolmogorov Complexity and Statistical Analysis

A. Shen
1999 Computer journal  
In particular, Li and Vitányi [6], Rissanen [3], Wallace and Dowe [7] have discussed the connection between 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  ... 
doi:10.1093/comjnl/42.4.340 fatcat:r6o5ybuk35cypinugcfl3xblia

A Short Introduction to Model Selection, Kolmogorov Complexity and Minimum Description Length (MDL) [article]

Volker Nannen
2010 arXiv   pre-print
After providing some background information on information theory and 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.  ... 
arXiv:1005.2364v2 fatcat:fkk2qo2so5acvodaz4wrbibwlq

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.  ... 

A Short Introduction to Kolmogorov Complexity [article]

Volker Nannen
2010 arXiv   pre-print
This is a short introduction to 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.  ... 
arXiv:1005.2400v2 fatcat:ma7q5wca3ra3vc62k44mmreerm

On hausdorff and topological dimensions of the kolmogorov complexity of the real line

Jin-yi Cai, Juris Hartmanis
1994 Journal of computer and system sciences (Print)  
We investigate the 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).  ... 
doi:10.1016/s0022-0000(05)80073-x fatcat:vgmphpoc6nc4xhwatn3glv2qkq

Comparing Security Notions of Secret Sharing Schemes

Songsong Dai, Donghui Guo
2015 Entropy  
This paper is concerned 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.  ... 
doi:10.3390/e17031135 fatcat:ii2ydfczx5gjxak4jfi6xi5fs4

Correlation of automorphism group size and topological properties with program-size complexity evaluations of graphs and complex networks

Hector Zenil, Fernando Soler-Toscano, Kamaludin Dingle, Ard A. Louis
2014 Physica A: Statistical Mechanics and its Applications  
networks) and high 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  ... 
doi:10.1016/j.physa.2014.02.060 fatcat:gcvvh6jbinhvbdcyqwm6o5m2te

How Incomputable Is Kolmogorov Complexity?

Paul M.B. Vitányi
2020 Entropy  
We discuss the incomputability of 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.  ... 
doi:10.3390/e22040408 pmid:33286182 fatcat:imcanhdpnval5i5dj5wejyrj2m

When Worlds Collide: Derandomization, Lower Bounds, and Kolmogorov Complexity [chapter]

Eric Allender
2001 Lecture Notes in Computer Science  
-To introduce a new notion of time-bounded 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  ... 
doi:10.1007/3-540-45294-x_1 fatcat:7chu7jpdqrdidhia26ojmhgsdu

Power from Random Strings

Eric Allender, Harry Buhrman, Michal Koucký, Dieter van Melkebeek, Detlef Ronneburger
2006 SIAM journal on computing (Print)  
We consider 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  ... 
doi:10.1137/050628994 fatcat:jh7n3uvehbbcjkjs5jeicf35rq
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