Training restricted Boltzmann machines using approximations to the likelihood gradient

By Tijmen Tieleman. 2008

1,066 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Optimization & Training

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Citations in the corpus

Generative Adversarial Nets (2014, methodology): “This strategy is analogous to the way that SML/PCD [31, 29] training maintains samples from a Markov chain from one learning step to the next in order to avoid burning in a Markov chain as part of the inner loop of learning.”
Pylearn2: a machine learning research library (2013, background): “For exa mple, the persistent contrastive divergence [55, 51] algorithm minimizes an intractable cost with in ractable gradients–the log likelihood of a Boltzmann machine.”
Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling (2020, methodology): “As with other energy-based models, we can use an MCMC procedure such as Langevin dynamics to generate samples from pt [19].”
Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One (2019, methodology): “Following Du & Mordatch (2019) we use persistent contrastive divergence (Tieleman, 2008) to estimate the expectation in the right-hand-side of Equation 2 since it gives an order of magnitude savings in computation compared to seeding new chains at each iteration as in Nijkamp et al. (2019b).”
Flow Contrastive Estimation of Energy-Based Models (2019, background): “CD has been generalized to persistent CD [67], and has more recently been generalized to modiﬁed CD [13], adversarial CD [29, 5, 22] with modern CNN structure.”
Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, methodology): “R � To ﬁt the model, many approximate methods have been developed ( e.g. , pseudo log-likelihood [6], contrastive divergence [29, 65], score matching estimator [30], minimum probability ﬂow [64], noise contrastive estimation [27]) to bypass the calculation of the partition function.”
Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model (2019, background): “CD has been generalized to persistent CD [44].”
On the Anatomy of MCMC-based Maximum Likelihood Learning of Energy-Based Models (2019, background): “The persistent chains can be initialized from noise as in (Zhu, Wu, and Mumford 1998; Lu, Zhu, and Wu 2016; Xie et al. 2016) or from data samples as in Persistent Con-trastive Divergence (PCD) (Tieleman 2008).”
Learning Generative ConvNets via Multi-grid Modeling and Sampling (2017, methodology): “A modiﬁcation of CD is persistent CD [42], where the MCMC is still initialized from the observed example at the initial learning epoch.”
GSNs : Generative Stochastic Networks (2015, methodology): “…the Restricted Boltzmann Machine or RBM) such as contrastive divergence (Hinton, 2000; Hinton et al., 2006) and persistent contrastive divergence (Tieleman, 2008; Younes, 1998) directly aim at estimating the gradient of the log-likelihood using a MCMC. Exact inference in a Deep Boltzmann Machine…”
Generative adversarial networks (2014, neutral): “ ksteps of optimizing Dand one step of optimizing G. This results in Dbeing maintained near its optimal solution, so long as Gchanges slowly enough. This strategy is analogous to the way that SML/PCD [31, 29] training maintains samples from a Markov chain from one learning step to the next in order ”
Representation Learning: A Review and New Perspectives (2012, methodology): “The SML algorithm (also known as persistent contrastive divergence or PCD) [220], [204] is an alternative way to sidestep an extended burn in of the negative phase Gibbs sampler.”
Deep Learning: Methods and Applications (2014, methodology): “There are other techniques for estimating the log-likelihood gradient of RBMs, in particular the stochastic maximum likelihood or persistent contrastive divergence (PCD) [363, 406].”
Online Contrastive Divergence with Generative Replay: Experience Replay without Storing Data (2016, background): “Examples of these are: persistent contrastive divergence (Tieleman, 2008), fast persistent contrastive divergence (Tieleman and Hinton, 2009), parallel tempering (Desjardins et al, 2010), and the replace of the Gibbs sampling with a transition operator to obtain a faster mixing rate and an improved…”
Discrete Variational Autoencoders (2016, methodology): “We stochastically approximate the expectation with respect to the RBM prior p ( z | θ ) in Equation 11 using block Gibbs sampling on persistent Markov chains, analogous to persistent contrastive divergence (Tieleman, 2008).”
Herding Dynamic Weights for Partially Observed Random Field Models (2009, methodology): “We also compared these results against models learned with contrastive divergence [3] (CD) and persistent CD [8]”
Learning with Hierarchical-Deep Models (2013, methodology): “2 A Stochastic Approximation Approach for Estimating the Data-independent Statistics Given the variational parameters μ, the model parameters ψ are then updated to maximize the variational bound using an MCMC-based stochastic approximation [29], [39], [46].”
Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learning (2016, methodology): “Other more traditional approaches for training energy-based models (e.g., Ngiam et al., 2011; Xie et al., 2016) are often based on variants of MCMC-MLE or contrastive divergence (Geyer, 1991; Hinton, 2002; Tieleman, 2008), and have difﬁculty generating realistic-looking images from scratch.”