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Domain Sparsification of Discrete Distributions using Entropic Independence [article]

Nima Anari, Michał Dereziński, Thuy-Duong Vuong, Elizabeth Yang
2021 arXiv   pre-print
Here, 1/α∈ [1, k] is the parameter of entropic independence for μ.  ...  This phenomenon, which we dub domain sparsification, allows us to pay a one-time cost of estimating the marginals of μ, and in return reduce the amortized cost needed to produce many samples from the distribution  ...  This preprocessing step may be of independent interest for other discrete sampling problems outside of entropically independent and fractionally log-concave distributions.  ... 
arXiv:2109.06442v2 fatcat:bpblgidim5brrebiyqmd6iktpm

Image matching using alpha-entropy measures and entropic graphs

Huzefa Neemuchwala, Alfred Hero, Paul Carson
2005 Signal Processing  
We compare our technique to previous entropy matching methods for a variety of continuous and discrete features sets including: single pixel gray levels; tag sub-image features; and independent component  ...  In this paper we present a general method based on matching high dimensional image features, using entropic similarity measures that can be empirically estimated using entropic graphs such as the minimal  ...  Acknowledgments We thank Sun Chung PhD, QMCS Department, University of St. Thomas for the valuable suggestions on acceleration of the MST algorithm.  ... 
doi:10.1016/j.sigpro.2004.10.002 fatcat:rwu3ooq7xvf3vghalz54gytr5u

Entropic Graphs for Registration [chapter]

Huzefa Neemuchwala, Alfred Hero
2005 Signal Processing and Communications  
Higher dimensional features used for this work include basis functions like multidimensional wavelets and independent component analysis (ICA).  ...  Recently a new class of entropic-graph similarity measures was introduced for image registration, feature clustering and classification.  ...  The independent successes of relative entropy methods, e.g., MI image registration, and the use of high dimensional features, e.g., SVM's for handwriting recognition, suggest that an extension of entropic  ... 
doi:10.1201/9781420026986.ch6 fatcat:z6ib7bttzfdetbtxcuubemm6iq

Competitive spiking and indirect entropy minimization of rate code: Efficient search for hidden components

Botond Szatmáry, Barnabás Póczos, András Lőrincz
2004 Journal of Physiology - Paris  
Memory components are modified in order to directly minimize the reconstruction error and to indirectly minimize the entropy of the spike rate distribution, via a combination of a stochastic gradient search  ...  This tuning dynamically changes the learning rate: the higher the entropy of the spike rate, the higher the learning rate of the gradient search in the subnetworks.  ...  We are most grateful to Csaba Szepesvári for his notes on the formal treatment of our approximations. This work was partially supported by Hungarian National Science Foundation (Grant No. OTKA 32487).  ... 
doi:10.1016/j.jphysparis.2005.09.007 pmid:16289549 fatcat:rvj5tiifqnctdkvpdnlelnpm2e

Evaluating systemic risk using bank default probabilities in financial networks

Sergio Rubens Stancato de Souza, Thiago Christiano Silva, Benjamin Miranda Tabak, Solange Maria Guerra
2016 Journal of Economic Dynamics and Control  
Although these Working Papers often represent preliminary work, citation of source is required when used or reproduced.  ...  Finally, our results provide insights and guidelines that can be useful for policymaking.  ...  Thus, he proposes using the Kullback (1959) 's cross-entropy minimization procedure to recover the distribution that is most consistent with the banks' DP and DB constraints, while minimizing the entropic  ... 
doi:10.1016/j.jedc.2016.03.003 fatcat:6gc57ruxwfgkndyrdcv3libnre

An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems

Hector Zenil, Narsis A. Kiani, Francesco Marabita, Yue Deng, Szabolcs Elias, Angelika Schmidt, Gordon Ball, Jesper Tegnér
2019 iScience  
We demonstrate the method by reconstructing the phase space and their generative rules of some discrete dynamical systems (cellular automata) serving as controlled case studies.  ...  Next, the model-based interventional or causal calculus is evaluated and validated using (1) a huge large set of small graphs, (2) a number of larger networks with different topologies, and finally (3)  ...  AUTHOR CONTRIBUTIONS DECLARATION OF INTERESTS The authors declare no competing interests.  ... 
doi:10.1016/j.isci.2019.07.043 pmid:31541920 pmcid:PMC6831824 fatcat:xpeyzezusretlka6vnxecqloru

HEMP: High-order Entropy Minimization for neural network comPression

Enzo Tartaglione, Stephane Lathuiliere, Attilio Fiandrotti, Marco Cagnazzo, Marco Grangetto
2021 Neurocomputing  
Our approach compares favorably over similar methods, enjoying the benefits of higher order entropy estimate, showing flexibility towards non-uniform quantization (we use Lloyd-max quantization), scalability  ...  towards any entropy order to be minimized and efficiency in terms of compression.  ...  The quantizer generates the discrete-valued representation W of the network parameters at training time.  ... 
doi:10.1016/j.neucom.2021.07.022 fatcat:s34zl2f4fvehfjxpv4sgivipsy

HexaShrink, an exact scalable framework for hexahedral meshes with attributes and discontinuities: multiresolution rendering and storage of geoscience models

Jean-Luc Peyrot, Laurent Duval, Frédéric Payan, Lauriane Bouard, Lénaïc Chizat, Sébastien Schneider, Marc Antonini
2019 Computational Geosciences  
They emphasize the consistency of the proposed representation, in terms of visualization, attribute downsampling and distribution at different resolutions.  ...  The latter are used for instance in biomedical engineering, materials science, or geosciences. HexaShrink provides a comprehensive framework allowing efficient mesh visualization and storage.  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http:// creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution  ... 
doi:10.1007/s10596-019-9816-2 fatcat:gltpzzoyvfe3bbez5snwtcjayq

Two-Stage Focused Inference for Resource-Constrained Collision-Free Navigation

Beipeng Mu, Ali-akbar Agha-mohammadi, Liam Paull, Matthew Graham, Jonathan How, John Leonard
2015 Robotics: Science and Systems XI  
The question then arises of how to choose which data is most useful to keep to achieve the task at hand.  ...  First, a subset of the variables (focused variables) is selected that are most useful for a particular task.  ...  as a Gaussian distribution using the Laplacian approximation [28] .  ... 
doi:10.15607/rss.2015.xi.004 dblp:conf/rss/MuAPGHL15 fatcat:64brp5wmwzchlovctkv7w7fexm

Near-Optimal Discrete Optimization for Experimental Design: A Regret Minimization Approach [article]

Zeyuan Allen-Zhu and Yuanzhi Li and Aarti Singh and Yining Wang
2017 arXiv   pre-print
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected  ...  In contrast, to the best of our knowledge, before our work, no polynomial-time algorithm achieves (1+ε) approximations for D/E/G-optimality, and the best poly-time algorithm achieving (1+ε)-approximation  ...  Acknowledgements We thank Adams Wei Yu for helpful discussions regarding the implementation of the entropic mirror descent solver for the continuous (convex) relaxation problem, thank Aleksandar Nikolov  ... 
arXiv:1711.05174v1 fatcat:cks4fzg5cng33czh3o3bbgv7re

Learning to compress and search visual data in large-scale systems [article]

Sohrab Ferdowsi
2019 arXiv   pre-print
Finally, the proposed algorithms are used to solve ill-posed inverse problems. In particular, the problems of image denoising and compressive sensing are addressed with promising results.  ...  The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective.  ...  This means that independent of the decoding algorithm, searching in a less entropic space is faster.  ... 
arXiv:1901.08437v1 fatcat:bqtixilyt5c7pb2uphjkkw5ivm

Hypercontractivity on High Dimensional Expanders: a Local-to-Global Approach for Higher Moments [article]

Mitali Bafna, Max Hopkins, Tali Kaufman, Shachar Lovett
2021 arXiv   pre-print
We handle these barriers with the introduction of two new tools of independent interest: a new explicit combinatorial Fourier basis for HDX that behaves well under restriction, and a new local-to-global  ...  Originally studied over the discrete hypercube, recent years have seen increasing interest in extensions to settings like the p-biased cube, slice, or Grassmannian, where variants of hypercontractivity  ...  These works offered a general theory of hypercontractivity for such domains, but their strength depended on the underlying distributions in the product space.  ... 
arXiv:2111.09444v2 fatcat:glm7cfkvgrbn7ck7knabem7fgq

High dimension and symmetries in quantum information theory [article]

Cécilia Lancien
2016 arXiv   pre-print
This time though, the strategy is to make use of the symmetries inherent to each particular situation we are looking at in order to derive a problem-dependent simplification.  ...  Oppositely, the second part of this manuscript is specifically dedicated to the analysis of high dimensional quantum systems and some of their typical features.  ...  It is not obvious how to adapt these constructions to obtain sparsifications of the uniform POVM using few or no randomness. 6.5.4 Sparsification of any POVM Theorem 6.5.2 initiated intensive research  ... 
arXiv:1607.06843v1 fatcat:zs6j2vcztvgnhocptjmoisl6km

Matrix-free Brownian dynamics simulation technique for semidilute polymeric solutions

Amir Saadat, Bamin Khomami
2015 Physical Review E  
of macromolecules) and in turn computation of Brownian displacements in the box.  ...  The fidelity and computational efficiency of the algorithm is demonstrated by evaluating the asymptotic value of center of mass diffusivity of polymer molecules at very low concentrations and their radius  ...  This research was also supported in part by an allocation of advanced computational resources provided by the National Science Foundation.  ... 
doi:10.1103/physreve.92.033307 pmid:26465586 fatcat:kfwmsas4enh3fdkofhxwhya7mi

Scalable Loss-calibrated Bayesian Decision Theory and Preference Learning [article]

Ehsan Abbasnejad, University, The Australian National, University, The Australian National
2017
The application of Bayesian decision theory in practice is often limited by two problems: (1) in application domains such as recommendation, the true utility function of a user is a priori unknown and  ...  In our first contribution, we exploit community structure prevalent in collective user preferences using a Dirichlet Process mixture of Gaussian Processes (GPs).  ...  Nevertheless, the IVM's purely entropic sparsification criterion fails at addressing the varying loss functions that may be of interest to the final decision-theoretic task -especially those tasks that  ... 
doi:10.25911/5d6fa168ef44b fatcat:kmefcgxu2rerhh7u4zs3j4wizm
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