On the convergence of markovian stochastic algorithms with rapidly decreasing ergodicity rates

By Laurent Younes. 1999

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In Optimization & Training

Citations in the corpus

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.”
Learning Energy-Based Spatial-Temporal Generative ConvNets for Dynamic Patterns (2019, methodology): “The convergence of the algorithm has been studied by [26], [58].”
A Theory of Generative ConvNet (2016, background): “We learn a generative ConvNet for each category from a single training image.”
GSNs : Generative Stochastic Networks (2015, methodology): “…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 or DBM…”
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): “One potential drawback of these methods is that depending on the parametrization of the energy function, their computational requirements may scale up to O(nd) worse than CD, SML, FPCD, or denoising score matching (Kingma and LeCun, 2010; Vincent, 2011), discussed below.”
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].”
Learning Energy-Based Models by Diffusion Recovery Likelihood (2020, methodology): “In MLE, we seek to maximize the log-likelihood function, where the gradient approximately follows (Younes, 1999; Xie et al., 2016b)”
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].”
Cooperative Training of Descriptor and Generator Networks (2016, methodology): “According to (Younes, 1999), Algorithm D converges to the maximum likelihood estimate under suitable regularity conditions on the mixing of the transition kernel of the MCMC and the schedule of the learning rate γ t , even if the number of Langevin steps l D is ﬁnite or small (e.g., l D = 1 ), and…”
Alternating Back-Propagation for Generator Network (2016, methodology): “The stochastic gradient algorithm of (Younes, 1999) can be used for learning, where in each iteration, for each Zi, only a single copy of Zi is sampled from p(Zi|Yi,W ) by running a finite number of steps of Langevin dynamics starting from the current value of Zi, i.”
Deep Learning for Health Informatics (2017, methodology): “For this reason, to train a DBM, a stochastic maximum likelihood [12] based algorithm is usually used to maximize the lower bound of the likelihood.”
Cooperative Learning of Energy-Based Model and Latent Variable Model via MCMC Teaching (2018, methodology): “The convergence of such an algorithm is studied by (Younes 1999).”
Maximum Entropy Generators for Energy-Based Models (2019, methodology): “For the RBM, the most commonly used algorithms have been Contrastive Divergence (Hinton, 2000) and Stochastic Maximum Likelihood (Younes, 1998; Tiele-man, 2008), relying on the particular structure of the RBM to perform Gibbs sampling.”
Unsupervised Feature Learning and Deep Learning: A Review and New Perspectives (2012, background): “Contrastive divergence (Hinton, 1999; Hinton et al. , 2006), stochastic maximum likelihood (Younes, 1999; Tieleman, 2008) and fast-weights persistent contrastive divergence or FPCD (Tieleman and Hinton, 2009) are all examples of algorithms that attempt sidestep the need to burn-in the negative phase”
Deep learning for visual understanding: A review (2016, methodology): “…all layers of a speci ﬁ c unsupervised model, and instead of maximizing the likelihood directly, the DBM uses a stochastic maximum likelihood (SML) [161] based algorithm to maximize the lower bound on the likelihood, i.e. performing only one or a few updates using a Markov chain Monte Carlo (MCMC)…”
Learning Dynamic Generator Model by Alternating Back-Propagation Through Time (2018, methodology): “Such a stochastic gradient ascent algorithm has been analyzed by (Younes 1999).”