Markov Chain Monte Carlo and Variational Inference: Bridging the Gap

By Tim Salimans, Diederik P. Kingma, Max Welling. 2014

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Denoising Diffusion Probabilistic Models (2020, methodology): “Other methods for learning transition operators of Markov chains include infusion training [2], variational walkback [13], generative stochastic networks [1], and others [47, 51, 33, 39].”
Pixel Recurrent Neural Networks (2016, neutral): “, 2014), [6] (Salimans et al., 2015), [7] (Gregor et al.”
Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks (2016, methodology): “Next, we test the effect of weight normalization applied to deep convolutional variational auto-encoders (CVAEs) [13, 24, 25], trained on the MNIST data set of images of handwritten digits and the CIFAR-10 data set of small natural images.”
Stochastic Normalizing Flows (2020, background): “It has been demonstrated that combining learnable proposals/transformations with stochastic sampling techniques can improve expressiveness of the proposals (Salimans et al., 2015; Levy et al., 2017; Song et al., 2017; Hoffman et al., 2019; Hoffman, 2017).”
Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, background): “R | Agakov and Barber [1], Salimans et al. [61], Ranganath et al. [57], Maaløe et al. [46] develop an auxiliary variable variational bound (1)), however, the density of the EIM q ( z x ) is intractable. where r ( | z, x ) is a variational distribution meant to model q ( | z, x ) , and the identity…”
BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling (2019, neutral): “90 C ONV VAE+HVI [47] ≤ 81 .”
Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, background): “Salimans et al. (2015) proposed an alternate scheme based on variational inference.”
A-NICE-MC: Adversarial Training for MCMC (2017, methodology): “Unlike variational approaches, MCMC methods are iterative in nature and do not naturally lend themselves to the use of expressive function approximators [6, 7].”
Learning to Generate Samples from Noise through Infusion Training (2017, methodology): “More recent proposals involve sophisticated approaches to sample from better approximate posteriors, as the work of Salimans et al. (2015) in which Hamiltonian Monte Carlo is combined with variational inference, which looks very promising, though computationally expensive, and Rezende & Mohamed…”
Improved Variational Inference with Inverse Autoregressive Flow (2016, methodology): “In practice, however, Hamiltonian Variational Inference is very demanding computationally.”
Density estimation using Real NVP (2016, background): “Still, the approximation in the inference process limits its ability to learn high dimensional deep representations, motivating recent work in improving approximate inference [42, 48, 55, 63, 10, 59, 34].”
Variational Inference with Normalizing Flows (2015, methodology): “We will use the Hamiltonian ﬂow to make a connection to the recently introduced Hamiltonian variational approach from Salimans et al. (2015) in section 5.”
Denoising Diffusion Implicit Models (2020, methodology): “Our work is based on a large family of existing methods on learning generative models as transition operators of Markov chains (Sohl-Dickstein et al., 2015; Bengio et al., 2014; Salimans et al., 2014; Song et al., 2017; Goyal et al., 2017; Levy et al., 2017).”
On the Quantitative Analysis of Decoder-Based Generative Models (2016, background): “The idea of using an encoder network to predict initial distribution also appeared in [26].”
DRAW: A Recurrent Neural Network For Image Generation (2015, methodology): “…belongs to the family of variational auto-encoders , a recently emerged hybrid of deep learning and variational inference that has led to signiﬁcant advances in generative modelling (Gre-gor et al., 2014; Kingma & Welling, 2014; Rezende et al., 2014; Mnih & Gregor, 2014; Salimans et al., 2014).”
Adversarially Learned Inference (2016, methodology): “One approach improves the quality of the approximate posterior using hybrid Monte Carlo (Salimans et al. , 2014).”
Importance Weighted Autoencoders (2015, positive): “Examples of this approach include normalizing ﬂows (Rezende & Mohamed, 2015) and the Hamiltonian variational approximation of Salimans et al. (2015).”
Variational Lossy Autoencoder (2016, neutral): “| || | Many previous works in Variational Inference have designed ﬂexible approximate posteriors to better approximate true posterior (Salimans et al., 2014; Rezende & Mo-hamed, 2015; Tran et al., 2015; Kingma et al., 2016).”
Professor Forcing: A New Algorithm for Training Recurrent Networks (2016, neutral): “…NLL DBN 2hl (Germain et al. , 2015) ≈ 84.55 NADE (Larochelle and Murray, 2011) 88.33 EoNADE-5 2hl (Raiko et al. , 2014) 84.68 DLGM 8 leapfrog steps (Salimans et al. , 2014) ≈ 85.51 DARN 1hl (Gregor et al. , 2015) ≈ 84.13 DRAW (Gregor et al. , 2015) ≤ 80.97 Pixel RNN (van den Oord et al. , 2016)…”