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Maximum Entropy Flow Networks

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Gabriel Loaiza-Ganem, Yuanjun Gao, John P. Cunningham

Methodology · Submitted 12 Jan 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Simulation results demonstrate the effectiveness of our method, and applications to finance and computer vision show the flexibility and accuracy of using maximum entropy flow networks.

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arXiv ID1701.03504 (version 2)
Pith IDU3CSKN5J, Pith's permanent record of this paper and its review
CitationGabriel Loaiza-Ganem, John P. Cunningham, Yuanjun Gao. "Maximum Entropy Flow Networks." arXiv:1701.03504 (2017). https://pith.science/paper/U3CSKN5J
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arXiv listing abstract v2. Results and the main claim are underlined; .

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired maximum entropy distribution. Doing so is nontrivial in that the objective being maximized (entropy) is a function of the density itself. By exploiting recent developments in normalizing flow networks, we cast the maximum entropy problem into a finite-dimensional constrained optimization, and solve the problem by combining stochastic optimization with the augmented Lagrangian method. Simulation results demonstrate the effectiveness of our method, and applications to finance and computer vision show the flexibility and accuracy of using maximum entropy flow networks.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. background 1.00 0.04 0.02 asserted 1.00
s1 In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired maximum entropy distribution. method 0.61 0.93 0.11 asserted 0.99
s2 Doing so is nontrivial in that the objective being maximized (entropy) is a function of the density itself. background 0.51 0.27 0.03 asserted 1.00
s3 By exploiting recent developments in normalizing flow networks, we cast the maximum entropy problem into a finite-dimensional constrained optimization, and solve the problem by combining stochastic optimization with the augmented Lagrangian method. method 0.97 0.91 0.12 asserted 1.00
s4 Simulation results demonstrate the effectiveness of our method, and applications to finance and computer vision show the flexibility and accuracy of using maximum entropy flow networks. result 0.98 0.95 0.78 asserted 1.00

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired maximum entropy distribution. Doing so is nontrivial in that the objective being maximized (entropy) is a function of the density itself. By exploiting recent developments in normalizing flow networks, we cast the maximum entropy problem into a finite-dimensional constrained optimization, and solve the problem by combining stochastic optimization with the augmented Lagrangian method. Simulation results demonstrate the effectiveness of our method, and applications to finance and computer vision show the flexibility and accuracy of using maximum entropy flow networks.

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5 arXiv papers cite this in 6 sentences

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Cites it as background 2 papers

What it cites · 12 sentences without a confident label

Uses the method or tool of 4 papers
  • For the transformation family $ℱ$ we use the real NVP network structure proposed in [ref] (we adapted <https://github.com/taesung89/real-nvp>).

    Density estimation using Real NVP · Modeling images of textures · 1.00

  • We follow [ref] (we adapted <https://github.com/ProofByConstruction/texture-networks>) to create a texture loss measure $T(): [0,1]^d →ℝ$,

    Texture Networks: Feed-forward Synthesis of Textures and Stylized Images · Modeling images of textures · 1.00

  • Augmented Lagrangian iteration $k = 1,...,k_max$ SGD iteration $i = 1,...,i_max$ Sample $^(1),...,^(n) ∼p_0$, get transformed variables $^(i)_ϕ= f_ϕ(^(i)), i = 1,...,n$ Update $ϕ$ by descending its stochastic gradient (using e.g. ADADELTA [ref] ): [equation] Sample $^(1),...,^(ñ) ∼p_0$, get transformed variables $^(i)_ϕ= f_ϕ(^(i)), i = 1,...,ñ$ Update $λ_k+1 = λ_k + c_k 1/ñ ∑_i=1^ñ T( ^(i)_ϕ)$ Update $c_k+1≥c_k$ (see text for detail)

    ADADELTA: An Adaptive Learning Rate Method · Algorithm · 1.00

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