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Optimal representation in average using Kolmogorov complexity

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. ...

##
###
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]

2001
*
Lecture Notes in Computer Science
*

this result does not hold if the random number generator

doi:10.1007/3-540-45355-5_28
fatcat:2233yj4vfnbvpmq53vtpewcdei
*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. ...##
###
Algorithmic statistics

2001
*
IEEE Transactions on Information Theory
*

While

doi:10.1109/18.945257
fatcat:qe7s4mib4vff5eawevwxdrgwyu
*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] . ...##
###
Algorithmic complexity of multiplex networks
[article]

2019
*
arXiv
*
pre-print

Multilayer networks preserve full information about the different interactions among the constituents of a

arXiv:1903.08049v2
fatcat:qnyprx73w5fclbmuru6c6jfunm
*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 ...##
###
Towards an Algorithmic Statistics
[chapter]

2000
*
Lecture Notes in Computer Science
*

While

doi:10.1007/3-540-40992-0_4
fatcat:673bcuz4vvcrliz73oqnt3h2mq
*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] ). ...##
###
Optimal Coding Theorems in Time-Bounded Kolmogorov Complexity
[article]

2022
*
arXiv
*
pre-print

≥ 0.99, a probabilistic

arXiv:2204.08312v1
fatcat:g5y7win7wndgdguem6t5xxzqrq
*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. ...##
###
Image Similarity Using Sparse Representation and Compression Distance

2014
*
IEEE transactions on multimedia
*

This paper proposes a sparse

doi:10.1109/tmm.2014.2306175
fatcat:c5veb6f7kbbcxkv7yalu5z3ymm
*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*. ...##
###
Image Similarity Using Sparse Representation and Compression Distance
[article]

2013
*
arXiv
*
pre-print

This paper proposes a sparse

arXiv:1206.2627v2
fatcat:566nlgvdtvgljopz6hf3sbvr7m
*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*. ...##
###
Complexity distortion theory

2003
*
IEEE Transactions on Information Theory
*

by

doi:10.1109/tit.2002.808135
fatcat:lvwiax43x5as5mjna5vifsd2ny
*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 . ...##
###
Face Representations via Tensorfaces of Various Complexities

2019
*
Neural Computation
*

Given the computational load imposed

doi:10.1162/neco_a_01258
pmid:31835006
fatcat:efaxje45jjccjl5caxshs2pble
*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. ...##
###
Algorithmic Statistics
[article]

2001
*
arXiv
*
pre-print

While

arXiv:math/0006233v3
fatcat:x4ve4ecswzf63jcx7wuwshw3ai
*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] . ...##
###
An optimal approximation of discrete random variables with respect to the Kolmogorov distance
[article]

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. ...

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

2019
*
arXiv
*
pre-print

A distinctive feature of our algorithm is that it requires neither the

arXiv:1906.01246v1
fatcat:fcnmcptmavd4tjcmuyl3ea5pba
*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 ...##
###
The Generalized Universal Law of Generalization
[article]

2001
*
arXiv
*
pre-print

We show that, nonetheless, the Universal Law of Generalization can be derived

arXiv:cs/0101036v1
fatcat:pvamwtnizfbetmt6u56au5ayqy
*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*...
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