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Tails of Lipschitz Triangular Flows [article]

Priyank Jaini, Ivan Kobyzev, Yaoliang Yu, Marcus Brubaker
<span title="2020-09-18">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We investigate the ability of popular flow based methods to capture tail-properties of a target density by studying the increasing triangular maps used in these flow methods acting on a tractable source  ...  We circumvent this problem by proposing tail-adaptive flows consisting of a source distribution that can be learned simultaneously with the triangular map to capture tail-properties of a target density  ...  ) Tails in Affine Flows We call a triangular map T affine if T j (z j ; z 1 , · · · , z j−1 ) is an affine function of z j .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1907.04481v3">arXiv:1907.04481v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eu7jsbjrejhxpmnbkbffq3mvem">fatcat:eu7jsbjrejhxpmnbkbffq3mvem</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200923001002/https://arxiv.org/pdf/1907.04481v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1907.04481v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Graphical Residual Flows [article]

Jacobie Mouton, Steve Kroon
<span title="2022-04-23">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our approach to incorporating dependency information in the flow, means that we are able to calculate the Jacobian determinant of these flows exactly.  ...  Graphical flows add further structure to normalizing flows by encoding non-trivial variable dependencies.  ...  They only consider the class of flows that enforces a triangular Jacobian matrix.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2204.11846v1">arXiv:2204.11846v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q2zyot4phjcqdm5ytgyi4h3vy4">fatcat:q2zyot4phjcqdm5ytgyi4h3vy4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220504210609/https://arxiv.org/pdf/2204.11846v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d2/51/d25133df3bb143edd0463782be6dc8af21e43eaa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2204.11846v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Representational aspects of depth and conditioning in normalizing flows [article]

Frederic Koehler, Viraj Mehta, Andrej Risteski
<span title="2021-06-25">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Finally, we show a depth lower bound for general flow architectures with few neurons per layer and bounded Lipschitz constant.  ...  Normalizing flows are among the most popular paradigms in generative modeling, especially for images, primarily because we can efficiently evaluate the likelihood of a data point.  ...  The discrepancy between the two KL divergences comes from the fact that the functions g, f θ may have different Lipschitz constants, hence the tails of g #N and f #N behave differently.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.01155v2">arXiv:2010.01155v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/keadvxstnnfpxkrmsfgwefzbgy">fatcat:keadvxstnnfpxkrmsfgwefzbgy</a> </span>
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Understanding and Mitigating Exploding Inverses in Invertible Neural Networks [article]

Jens Behrmann, Paul Vicol, Kuan-Chieh Wang, Roger Grosse, Jörn-Henrik Jacobsen
<span title="2021-12-24">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We further derive bi-Lipschitz properties of atomic building blocks of common architectures. These insights into the stability of INNs then provide ways forward to remedy these failures.  ...  For problems where global invertibility is necessary, such as applying normalizing flows on OOD data, we show the importance of designing stable INN building blocks.  ...  Acknowledgements Resources used in preparing this research were provided, in part, by the Province of Ontario, the Government of Canada through CIFAR, and companies sponsoring the Vector Institute www.vectorinstitute  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.09347v2">arXiv:2006.09347v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lbbmkelbanfzfgxwpvg56zqthu">fatcat:lbbmkelbanfzfgxwpvg56zqthu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220105102611/https://arxiv.org/pdf/2006.09347v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8c/0b/8c0b75099f577cc009065e985cae6986cf755d4d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.09347v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Stochastic Neural Network with Kronecker Flow [article]

Chin-Wei Huang, Ahmed Touati, Pascal Vincent, Gintare Karolina Dziugaite, Alexandre Lacoste, Aaron Courville
<span title="2020-02-13">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work, we address this need and present the Kronecker Flow, a generalization of the Kronecker product to invertible mappings designed for stochastic neural networks.  ...  Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks  ...  Acknowledgement CWH would like to thank Kris Sankaran for pointing to the TIS inequality for Gaussian concentration, which is a key component in deriving the tail bound on Lipschitz flows.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1906.04282v2">arXiv:1906.04282v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/44e5rr6zarhb3dzddqiycgpyzq">fatcat:44e5rr6zarhb3dzddqiycgpyzq</a> </span>
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The Expressive Power of a Class of Normalizing Flow Models [article]

Zhifeng Kong, Kamalika Chaudhuri
<span title="2020-05-31">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
While a wide variety of flow models have been proposed, there is little formal understanding of the representation power of these models.  ...  Normalizing flows have received a great deal of recent attention as they allow flexible generative modeling as well as easy likelihood computation.  ...  on non-triangular flows.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.00392v1">arXiv:2006.00392v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oifufrbwljfpvmg424hqylpabe">fatcat:oifufrbwljfpvmg424hqylpabe</a> </span>
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A Tutorial on Solution Properties of State Space Models of Dynamical Systems [article]

Bassam Bamieh
<span title="2022-04-24">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This property is an asymptotic version of the nilpotence property of a strictly-lower-triangular matrix.  ...  The convergence of the series and iterations is a consequence of the key property of asymptotic nilpotence of the Volterra operator.  ...  Note that any linear mapping x → Ax on R n is Lipschitz, with Lipschitz constant being the matrix norm of A induced by the chosen vector norm on x.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2204.06104v3">arXiv:2204.06104v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r2tp7kbvfjfydgpr2zwew4sebq">fatcat:r2tp7kbvfjfydgpr2zwew4sebq</a> </span>
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Normalizing Flows: An Introduction and Review of Current Methods [article]

Ivan Kobyzev and Simon J.D. Prince and Marcus A. Brubaker
<span title="2020-04-28">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The goal of this survey article is to give a coherent and comprehensive review of the literature around the construction and use of Normalizing Flows for distribution learning.  ...  Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact.  ...  Form of diffeomorphisms The majority of the flows explored are triangular flows (either coupling or autoregressive architectures).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1908.09257v3">arXiv:1908.09257v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ycncgjmxojdercls7vdecci5mq">fatcat:ycncgjmxojdercls7vdecci5mq</a> </span>
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Percolation since Saint-Flour [article]

Geoffrey R. Grimmett, Harry Kesten
<span title="2012-07-02">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This is a short survey of work on percolation and first-passage percolation since the publication (in 1996 and 1984, respectively) of the two authors' Saint-Flour notes on these topics.  ...  Acknowledgements We thank Raphaël Cerf, Michael Damron, Christophe Garban, and Chuck Newman for their comments on a draft of this article.  ...  They consider the general situation of maximal flows in a scaling limit of n −1 Z d as n → ∞.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1207.0373v1">arXiv:1207.0373v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qkilkcc4zre6bjrbjr67aq36au">fatcat:qkilkcc4zre6bjrbjr67aq36au</a> </span>
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The tail process and tail measure of continuous time regularly varying stochastic processes [article]

Philippe Soulier
<span title="2021-03-30">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure  ...  , in the framework of continuous time stochastic processes with paths in the space 𝒟 of càdlàg functions indexed by ℝ, endowed with Skorohod's J_1 topology.  ...  As a consequence of metrizability and the characterization of vague convergence by Lipschitz functions, we obtain the following triangular argument.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.00325v3">arXiv:2004.00325v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nn47vatmxzacvmpdkjnmmlo32a">fatcat:nn47vatmxzacvmpdkjnmmlo32a</a> </span>
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On Robustness of Equilibria in Dynamical Transportation Networks

Rasmus Stalberg, Gustav Nilsson, Giacomo Como
<span title="">2019</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ogb7bnzpdjan7gjun477b3ydvy" style="color: black;">2019 18th European Control Conference (ECC)</a> </i> &nbsp;
of the Lighthill-Whitham-Richards traffic flow model [3], [4] .  ...  More specifically, if and when the equilibrium of the perturbed dynamics is still in free flow.  ...  i l coincides with the tail node of i 1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.23919/ecc.2019.8796234">doi:10.23919/ecc.2019.8796234</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/eucc/StalbergNC19.html">dblp:conf/eucc/StalbergNC19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qlo22rmmfvcufe6fjf2ese3s5u">fatcat:qlo22rmmfvcufe6fjf2ese3s5u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200506052128/https://portal.research.lu.se/ws/files/66756431/RobustnessEquilibria.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f3/d0/f3d0079b9d60591bd7a3cf616cfcb8e116e32418.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.23919/ecc.2019.8796234"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

An adaptive transport framework for joint and conditional density estimation [article]

Ricardo Baptista, Olivier Zahm, Youssef Marzouk
<span title="2020-09-22">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Transport maps or "flows" deterministically couple two distributions via an expressive monotone transformation.  ...  We demonstrate how this framework can learn densities with stable generalization performance across a wide range of sample sizes on real-world datasets.  ...  RB and YM are also grateful for the support from the AFOSR Computational Mathematics program (MURI award FA9550-15-1-0038) and the US Department of Energy AEOLUS project.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2009.10303v1">arXiv:2009.10303v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rgr4rsw5rnf5hhk5p5bplfk5a4">fatcat:rgr4rsw5rnf5hhk5p5bplfk5a4</a> </span>
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Symmetric Monotone Embedding of Traffic Flow Networks with First-In-First-Out Dynamics

Samuel Coogan, Murat Arcak
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4oklsgzkjvbihhegxblzc6b7re" style="color: black;">IFAC-PapersOnLine</a> </i> &nbsp;
Standard approaches which rely on monotonicity of the flow dynamics do not immediately apply to such first-in-first-out models. The network model nonetheless exhibits a mixed monotonicity property.  ...  We study a flow network model for vehicular traffic that captures congestion effects at diverging junctions.  ...  Let σ( ) and τ ( ) denote the head and tail junction of link ∈ L, respectively, where we assume σ( ) = τ ( ), i.e., no self-loops. Traffic flows from τ ( ) to σ( ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ifacol.2016.10.238">doi:10.1016/j.ifacol.2016.10.238</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yluusassuzhqzno2u4g6xgnom4">fatcat:yluusassuzhqzno2u4g6xgnom4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160909225929/http://seas.ucla.edu:80/~scoogan/papers/pdf/coogan2016nolcos.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fd/b7/fdb7fa65f76037a2eaa472e8568dbbf929bc5ac7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ifacol.2016.10.238"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Non-asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso [article]

Shengchun Kong, Bin Nan
<span title="2012-04-09">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
arguments to tackle the difficulty caused by the lack of iid and Lipschitz property.  ...  Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed  ...  the Cox model due to the lack of Lipschitz property.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1204.1992v1">arXiv:1204.1992v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hzgdq5aptrdr7nwbigk4omq4li">fatcat:hzgdq5aptrdr7nwbigk4omq4li</a> </span>
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Stability of traffic flow networks with a polytree topology

Samuel Coogan, Murat Arcak
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e5pgtxytlra45muqmfmoj6kvte" style="color: black;">Automatica</a> </i> &nbsp;
We consider global stability of a flow network model for vehicular traffic.  ...  Standard approaches which rely on monotonicity of flow networks for stability analysis do not immediately apply to traffic networks with diverging junctions.  ...  Let σ( ) and τ ( ) denote the head and tail junction of link ∈ L, respectively, where we assume σ( ) = τ ( ), i.e., no selfloops. Traffic flows from τ ( ) to σ( ).  ... 
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