DENSITY ESTIMATION BY DUAL ASCENT OF THE LOG-LIKELIHOOD ∗

By Esteban G. Tabak, Eric Vanden-Eijnden. 2010

432 citations recorded by the source corpus.

Subfields: Finance, Ocean Engineering, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Stochastic Normalizing Flows (2020, background): “Normalizing flows (NFs) [41, 40, 5, 35, 6, 33] combined with importance sampling methods are an alternative approach that enjoys growing interest in molecular and material sciences and nuclear physics [28, 25, 32, 22, 1, 30].”
Variational Inference with Normalizing Flows (2015, background): “One path towards this ideal is based on the principle of normalizing ﬂows (Tabak & Turner, 2013; Tabak & Vanden-Eijnden, 2010).”
Deep Kalman Filters (2015, background): “| | An interesting question is whether using the idea of the universality of normalizing ﬂows (Tabak et al. , 2010; Rezende & Mohamed, 2015) one can transform q φ ( z x ) to be equal (or arbitrarily close) to p θ ( z x ) and thus attain equality in the lower bound.”
Equivariant Hamiltonian Flows (2019, background): “Normal-izing ﬂows [26, 11, 5, 18, 4, 24, 16] provide a simple mechanism to build expressive density estimators in problems without much domain knowledge.”
Normalizing Flows for Probabilistic Modeling and Inference (2019, background): “Tabak and Vanden-Eijnden (2010) approached Gaussianization from the perspective of diffusion processes, making connections to statistical mechanics—specifically, using Liouville’s equation to characterize the flow.”
Sylvester Normalizing Flows for Variational Inference (2018, neutral): “The resulting transformed density after one such transformation f is as follows (Tabak and Turner, 2013; Tabak and Vanden-Eijnden, 2010):”
Improving Variational Auto-Encoders using Householder Flow (2016, methodology): “In general, any full-covariance matrix Σ can be represented by the eigenvalue decomposition using eigenvectors and eigenvalues: where U is an orthogonal matrix with eigenvectors in columns, D is a diagonal matrix with eigenvalues.”
LIA: Latently Invertible Autoencoder with Adversarial Learning (2019, background): “Overall, generative models fall into four categories: autoencoder and its most important variant of Variational Auto-Encoder (VAE) [21], auto-regressive models [42, 41], Generative Adversarial Network (GAN) [10], and normalizing flows (NF) [38, 37, 32].”
Latent Normalizing Flows for Discrete Sequences (2019, background): “The base density is a standard Gaussian.”
Building Normalizing Flows with Stochastic Interpolants (2022, positive): “This idea was brought closer to contemporary use cases through the work of Tabak & Vanden-Eijnden (2010) and Tabak & Turner (2013), which devised to expressly map between densities using simple transport functions inferred through maximum likelihood estimation (MLE).”
Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning (2019, background): “Maximizing their likelihood in the Gaussian distribution corresponds to minimizing the loss function (18, 19):”
Block Neural Autoregressive Flow (2019, methodology): “A (ﬁnite) normalizing ﬂow is a bijective function f : X → Y between two continuous random variables X ∈ X ⊆ R d and Y ∈ Y ⊆ R d (Tabak et al., 2010).”