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Bivariate Partial Information Decomposition: The Optimization Perspective

Abdullah Makkeh, Dirk Theis, Raul Vicente
2017 Entropy  
Bertschinger, Rauh, Olbrich, Jost, and Ay (Entropy, 2014) have proposed a definition of a decomposition of the mutual information MI(X : Y, Z) into shared, synergistic, and unique information by way of  ...  solving a convex optimization problem.  ...  [1] reveals some subtleties which makes the computation of the information decomposition challenging.  ... 
doi:10.3390/e19100530 fatcat:mcrp37z4abaixjpvvfjkcfsgve

BROJA-2PID: A Robust Estimator for Bivariate Partial Information Decomposition

Abdullah Makkeh, Dirk Theis, Raul Vicente
2018 Entropy  
Makkeh, Theis, and Vicente found that Cone Programming model is the most robust to compute the Bertschinger et al. partial information decomposition (BROJA PID) measure.  ...  In this paper, we prove the important property of strong duality for the Cone Program and prove an equivalence between the Cone Program and the original Convex problem.  ...  R.V. also thanks the financial support from ETAG through the personal research grant PUT1476.  ... 
doi:10.3390/e20040271 pmid:33265362 fatcat:rkmeasmjrnhrxjtc5nj5bjm364

Pointwise Partial Information Decomposition Using the Specificity and Ambiguity Lattices

Conor Finn, Joseph Lizier
2018 Entropy  
The redundancy lattice from the partial information decomposition of Williams and Beer provided a promising glimpse at the answer to these questions.  ...  These atoms can be recombined to yield the sought-after multivariate information decomposition.  ...  Author Contributions: C.F. and J.L. conceived the idea; C.F. designed, wrote and analyzed the computational examples; C.F. and J.L. wrote the manuscript.  ... 
doi:10.3390/e20040297 pmid:33265388 fatcat:sp66lar45bcvjjuk3x6jswwify

Partial Information Decomposition of Boolean Functions: a Fourier Analysis perspective [article]

Abdullah Makkeh, Dirk Oliver Theis, Raul Vicente
2020 arXiv   pre-print
Partial information decomposition (PID) partitions the information that a set of sources has about a target variable into synergistic, unique, and redundant contributions.  ...  This information-theoretic tool has recently attracted attention due to its potential to characterize the information processing in multivariate systems.  ...  R.V. also thanks the financial support from ETAG through the personal research grant PUT1476.  ... 
arXiv:2010.06976v1 fatcat:uo2tsf4onjghbgonm4mxkqk4ke

Decomposition methods for structural reliability analysis revisited

Sharif Rahman
2011 Probabilistic Engineering Mechanics  
However, a second-moment error analysis finds neither the RDD approximation nor the cut-HDMR approximation to be optimal, whereas the approximation derived from the analysis-of-variance dimensional decomposition  ...  from a distinct perspective, lead to identical function approximations.  ...  4 provide useful information that can be effectively exploited for decomposition-based reliability analysis.  ... 
doi:10.1016/j.probengmech.2010.09.005 fatcat:dcalfa62szgf7fp7styhciwepa

An operational information decomposition via synergistic disclosure [article]

Fernando Rosas, Pedro Mediano, Borzoo Rassouli, Adam Barrett
2020 arXiv   pre-print
Here we fill this gap by proposing a new information decomposition based on a novel operationalisation of informational synergy, which leverages recent developments in the literature of data privacy.  ...  At the heart of this disagreement lies the absence of a clear operational interpretation of what synergistic information is.  ...  P.M. is funded by the Wellcome Trust (grant no. 210920/Z/18/Z).  ... 
arXiv:2001.10387v2 fatcat:bhjmjiv7hvbqpe4n27yyivmuh4

Variance Decomposition [chapter]

Helmut Lütkepohl
2018 The New Palgrave Dictionary of Economics  
He devoted himself with assiduity to the theory of value, and wrote a book on the subject.  ...  He maintains that the law of value depends rigidly on supply and demand, supporting this theory with a geometrical illustration from the relative quantities of both; he combats the theory of cost of production  ...  The results are consistent with venture capitalists possessing inside information and with the (partial) adjustment of the market to that information.  ... 
doi:10.1057/978-1-349-95189-5_2274 fatcat:3vmh5d4advhxbc5ry75v3s47z4

Kolmogorov Superposition Theorem and Wavelet Decomposition for Image Compression [chapter]

Pierre-Emmanuel Leni, Yohan D. Fougerolle, Frédéric Truchetet
2009 Lecture Notes in Computer Science  
We propose a new algorithm to decompose images into continuous monovariate functions, and propose a compression approach: thanks to the decomposition scheme, the quantity of information taken into account  ...  Thanks to the decomposition into monovariate functions, our goal is to apply this decomposition to images and obtain image compression.  ...  Conclusion and perspectives We have dealt with multivariate function decomposition using KST.  ... 
doi:10.1007/978-3-642-04697-1_5 fatcat:njc2hemehbf3rd4dopybmjjoeu

A Novel Approach to the Partial Information Decomposition

Artemy Kolchinsky
2022 Entropy  
We consider the "partial information decomposition" (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant  ...  In the second part of this paper, we use our general framework to define a PID in terms of the well-known Blackwell order, which has a fundamental operational interpretation.  ...  We also thank the Santa Fe Institute for helping to support this research. Conflicts of Interest: The authors declare no conflict of interest. Entropy 2022, 24, 403  ... 
doi:10.3390/e24030403 pmid:35327914 pmcid:PMC8947370 fatcat:begj22xqufheppj6mpbe6jo36y

A Novel Approach to the Partial Information Decomposition [article]

Artemy Kolchinsky
2022 arXiv   pre-print
We consider the "partial information decomposition" (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant  ...  In the second part of this paper, we use our general framework to define a PID in terms of the well-known Blackwell order, which has a fundamental operational interpretation.  ...  We also thank the Santa Fe Institute for helping to support this research.  ... 
arXiv:1908.08642v4 fatcat:zidhk37xsnf5rj5md6a2lojfm4

Exact and approximate polynomial decomposition methods for signal processing applications

Sefa Demirtas, Guolong Su, Alan V. Oppenheim
2013 2013 IEEE International Conference on Acoustics, Speech and Signal Processing  
In this paper, we summarize the fundamentals of functional composition and decomposition for polynomials from the perspective of exploiting them in signal processing.  ...  Moreover, computations can be performed more efficiently and data can be represented more compactly in information systems represented in the context of a compositional structure.  ...  In this paper, we summarize the fundamentals of functional composition and decomposition for polynomials from the perspective of exploiting them in signal processing.  ... 
doi:10.1109/icassp.2013.6638689 dblp:conf/icassp/DemirtasSO13 fatcat:c63loi7nzrdrbarp7wt7wtzmm4

An operational information decomposition via synergistic disclosure

Fernando Rosas, Pedro Mediano, Borzoo Rassouli, Adam Barrett
2020 Journal of Physics A: Mathematical and Theoretical  
Here we fill this gap by proposing a new information decomposition based on a novel operationalisation of informational synergy, which leverages recent developments in the literature of data privacy.  ...  At the heart of this disagreement lies the absence of a clear operational interpretation of what synergistic information is.  ...  PM is funded by the Wellcome Trust (Grant Nos. 210920/Z/18/Z). A.B.B. was supported by the Dr.  ... 
doi:10.1088/1751-8121/abb723 fatcat:hdufdo3arva2fir3anxb4nehsq

Kolmogorov superposition theorem and its application to wavelet image decompositions

Pierre-Emmanuel Leni, Yohan D. Fougerolle, Frédéric Truchetet, Frederic Truchetet, Olivier Laligant
2009 Wavelet Applications in Industrial Processing VI  
We detail the reconstruction quality and the quantity of information contained in Igelnik's network.  ...  The second algorithm, proposed by Igelnik in Ref. 4, increases the parameters flexibility, but only approximates the monovariate functions: the number of layers is variable, a neural networks optimizes  ...  We showed that changing tile size was leading to only partial use of original image information, which can be considered as a compression process: we studied Igelnik's network size, and concluded that  ... 
doi:10.1117/12.805916 fatcat:uujp4ifwnvb3berlcnee2ugyvy

Toward automatic decomposition of monolithic software into microservices

Jakob Lohnertz, Ana-Maria Oprescu
2020 Zenodo  
However, the latter approach bears many difficulties that involve much manual work, specifically in the early stages of such a decomposition process.  ...  To do this, four dimensions of coupling are calculated out of the input software that each construct a weighted graph with the edges resembling coupling between the units of the software.  ...  This approach has the advantage that the mental models regarding the existing solution might be broken apart partially to offer new perspectives onto how the current software works, which was already remarked  ... 
doi:10.5281/zenodo.4280724 fatcat:zj4sxauwuramfdyfcbyqdwjnei

Kolmogorov Superposition Theorem and Its Application to Multivariate Function Decompositions and Image Representation

Pierre-Emmanuel Leni, Yohan D. Fougerolle, Frédéric Truchetet
2008 2008 IEEE International Conference on Signal Image Technology and Internet Based Systems  
We synthetise our observations, before presenting several research perspectives.  ...  We first present the algorithm proposed by Sprecher, then the algorithm proposed by Igelnik, and we present several results of decomposition for gray level images.  ...  Results We present the results of the decomposition applied to gray levels images, that can be seen as bivariate functions f (x, y) = I(x, y).  ... 
doi:10.1109/sitis.2008.16 dblp:conf/sitis/LeniFT08 fatcat:n5cz5xhjibel5i3jejs3klf3sa
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