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Optimal representation in average using Kolmogorov complexity

E. Rivals, J.P. Delahaye
1998 Theoretical Computer Science  
In this work, we sketch a theory of average optimal representation that formalizes natural ideas and operates where intuition does not suffice.  ...  First, we formulate a definition of K-optimality on average for a pattern, then demonstrate results that corroborate intuitive ideas, and give worthy insights into the best compression in more complex  ...  Let us examine the Kolmogorov complexity concept.  ... 
doi:10.1016/s0304-3975(97)00275-2 fatcat:qkv6ktedxbh3fa7liiel27wmcu

Page 2060 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
(F-LILL-FI; Villeneuve d’Ascq) Optimal representation in average using Kolmogorov complexity. (English summary) Theoret. Comput. Sci. 200 (1998), no. 1-2, 261-287.  ...  The paper contains a sketch of a new theory of average optimal representation based on a structural hypothesis.  ... 

Computational Complexity, Genetic Programming, and Implications [chapter]

Bart Rylander, Terry Soule, James Foster
2001 Lecture Notes in Computer Science  
this result does not hold if the random number generator used in the evolution is a true random source; and 3) an optimization problem being solved with a GP will have a complexity that can be bounded  ...  below by the growth rate of the minimum length problem representation used for the implementation.  ...  Acknowledgments This research was funded in part by NSF EPS0080935, NIH F33GM20122-01, and NSA MDA 904-98-C-A894.  ... 
doi:10.1007/3-540-45355-5_28 fatcat:2233yj4vfnbvpmq53vtpewcdei

Algorithmic statistics

P. Gacs, J.T. Tromp, P.M.B. Vitanyi
2001 IEEE Transactions on Information Theory  
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample  ...  Index Terms-Algorithmic information theory, description format (explicit, implicit), foundations of statistics, Kolmogorov complexity, minimal sufficient statistic (algorithmic), mutual information (algorithmic  ...  Kolmogorov [11] introduced the complexity proper. The prefix-version of Kolmogorov complexity used in this paper was introduced in [14] and also treated later in [3] .  ... 
doi:10.1109/18.945257 fatcat:qe7s4mib4vff5eawevwxdrgwyu

Algorithmic complexity of multiplex networks [article]

A. Santoro, V. Nicosia
2019 arXiv   pre-print
Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social  ...  We propose an intuitive way to encode a multilayer network into a bit string, and we define the complexity of a multilayer network as the ratio of the Kolmogorov complexity of the bit strings associated  ...  Indeed, the optimal aggregations found by using C(M) often offer a substantial reduction in the number of layers needed to represent the system while still retaining most of the structural complexity of  ... 
arXiv:1903.08049v2 fatcat:qnyprx73w5fclbmuru6c6jfunm

Towards an Algorithmic Statistics [chapter]

Peter Gács, John Tromp, Paul Vitányi
2000 Lecture Notes in Computer Science  
While Kolmogorov complexity is the accepted absolute measure of information content of an individual nite object, a similarly absolute notion is needed for the relation between an individual data sample  ...  and an individual model summarizing the information in the data, for example, a nite set where the data sample typically came from.  ...  Kolmogorov formulated this task rigorously in terms of Kolmogorov complexity (according to 14, 2] ).  ... 
doi:10.1007/3-540-40992-0_4 fatcat:673bcuz4vvcrliz73oqnt3h2mq

Optimal Coding Theorems in Time-Bounded Kolmogorov Complexity [article]

Zhenjian Lu, Igor C. Oliveira, Marius Zimand
2022 arXiv   pre-print
≥ 0.99, a probabilistic representation of x that certifies this rKt complexity bound.  ...  The classical coding theorem in Kolmogorov complexity states that if an n-bit string x is sampled with probability δ by an algorithm with prefix-free domain then K(x) ≤log(1/δ) + O(1).  ...  We are grateful to Bruno Bauwens for discussions and useful insights. M. Zimand was supported in part by the National Science Foundation through grant CCF 1811729. Z. Lu and I.C.  ... 
arXiv:2204.08312v1 fatcat:g5y7win7wndgdguem6t5xxzqrq

Image Similarity Using Sparse Representation and Compression Distance

Tanaya Guha, Rabab K. Ward
2014 IEEE transactions on multimedia  
This paper proposes a sparse representation-based approach to encode the information content of an image using information from the other image, and uses the compactness (sparsity) of the representation  ...  The existing compression-based similarity methods, although successful in the discrete one dimensional domain, do not work well in the context of images.  ...  Nevertheless, the present work is not closed and we hope that this will stimulate interest in the areas of compression or Kolmogorov complexity-based similarity measurement using sparse representation.  ... 
doi:10.1109/tmm.2014.2306175 fatcat:c5veb6f7kbbcxkv7yalu5z3ymm

Image Similarity Using Sparse Representation and Compression Distance [article]

Tanaya Guha, Rabab K. Ward
2013 arXiv   pre-print
This paper proposes a sparse representation-based approach to encode the information content of an image using information from the other image, and uses the compactness (sparsity) of the representation  ...  The existing compression-based similarity methods, although successful in the discrete one dimensional domain, do not work well in the context of images.  ...  Nevertheless, the present work is not closed and we hope that this will stimulate interest in the areas of compression or Kolmogorov complexity-based similarity measurement using sparse representation.  ... 
arXiv:1206.2627v2 fatcat:566nlgvdtvgljopz6hf3sbvr7m

Complexity distortion theory

D.M. Sow, A. Eleftheriadis
2003 IEEE Transactions on Information Theory  
by Kolmogorov in Kolmogorov complexity theory and its extension to lossy source coding, CDT.  ...  Using this model, the mathematical framework for examining the efficiency of coding schemes is the algorithmic or Kolmogorov complexity.  ...  There exist many variants of the Kolmogorov complexity in the literature. Throughout this paper, we will use the prefix Kolmogorov complexity introduced by Levin and Gacs. We denote it by .  ... 
doi:10.1109/tit.2002.808135 fatcat:lvwiax43x5as5mjna5vifsd2ny

Face Representations via Tensorfaces of Various Complexities

Sidney R. Lehky, Anh Huy Phan, Andrzej Cichocki, Keiji Tanaka
2019 Neural Computation  
Given the computational load imposed in creating high-complexity face cells (in the form of algorithmic information and logical depth) and in the absence of a compelling advantage to using high-complexity  ...  In this theoretical study, we explore the effects of complexity, defined as algorithmic information (Kolmogorov complexity) and logical depth, on possible ways that face cells may be organized.  ...  Kolmogorov complexity was averaged over those 1000 tensorfaces. The same set of tensorfaces was used in calculations of logical depth, power spectra, and globality described below.  ... 
doi:10.1162/neco_a_01258 pmid:31835006 fatcat:efaxje45jjccjl5caxshs2pble

Algorithmic Statistics [article]

Peter Gacs, Paul Vitanyi (CWI, University of Amsterdam)
2001 arXiv   pre-print
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample  ...  We give characterizations of algorithmic (Kolmogorov) minimal sufficient statistic for all data samples for both description modes--in the explicit mode under some constraints.  ...  Kolmogorov [11] introduced the complexity proper. The prefix-version of Kolmogorov complexity used in this paper was introduced in [14] and also treated later in [3] .  ... 
arXiv:math/0006233v3 fatcat:x4ve4ecswzf63jcx7wuwshw3ai

An optimal approximation of discrete random variables with respect to the Kolmogorov distance [article]

Liat Cohen, Dror Fried, Gera Weiss
2018 arXiv   pre-print
In addition to a formal theoretical analysis of the correctness and of the computational complexity of the algorithm, we present a detailed empirical evaluation that shows how the proposed approach performs  ...  in practice in different applications and domains.  ...  The curves in the figure show the average error of OptTrim and Trim operators with comparison to the average error of the optimal approximation provided by KolmogorovApprox as a function of m.  ... 
arXiv:1805.07535v1 fatcat:u22fmvi7crdppf5aqs47qtm35q

A Novel Hyperparameter-free Approach to Decision Tree Construction that Avoids Overfitting by Design [article]

Rafael Garcia Leiva, Antonio Fernandez Anta, Vincenzo Mancuso, Paolo Casari
2019 arXiv   pre-print
A distinctive feature of our algorithm is that it requires neither the optimization of any hyperparameters, nor the use of regularization techniques, thus significantly reducing the decision tree training  ...  Unfortunately, overfitting in decision trees still remains an open issue that sometimes prevents achieving good performance.  ...  For the representation of a tree as a string we use the following template: Where [attrs] is the list of attributes used, and only those used in the model, 5 [attr] is a single attribute represented  ... 
arXiv:1906.01246v1 fatcat:fcnmcptmavd4tjcmuyl3ea5pba

The Generalized Universal Law of Generalization [article]

Nick Chater
2001 arXiv   pre-print
We show that, nonetheless, the Universal Law of Generalization can be derived in the more complex setting of arbitrary stimuli, using a much more universal measure of distance.  ...  In experimental contexts, distance is typically defined in terms of a multidimensional Euclidean space-but this assumption seems unlikely to hold for complex stimuli.  ...  The Kolmogorov complexity of an object is a form of absolute information of the individual object, in contrast to standard (probabilistic) information theory [9] which is only concerned with the average  ... 
arXiv:cs/0101036v1 fatcat:pvamwtnizfbetmt6u56au5ayqy
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