A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
Optimal representation in average using Kolmogorov complexity
1998
Theoretical Computer Science
Preserved Fulltext
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
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
(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
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
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
2001
IEEE Transactions on Information Theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2006; you can also visit the original URL.
The file type is application/pdf.
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]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
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]
2000
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
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]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
≥ 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
2014
IEEE transactions on multimedia
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
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]
2013
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
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
2003
IEEE Transactions on Information Theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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
2019
Neural Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
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]
2001
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
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]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
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]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
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]
2001
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
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
« Previous
Showing results 1 — 15 out of 21,799 results