Minimum Probability Flow Learning

By Jascha Narain Sohl-Dickstein, Peter Battaglino, Michael Robert DeWeese. 2009

72 citations recorded by the source corpus.

Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable normalization factor or sampling from the equilibrium distribution of the model. This is achieved by establishing dynamics that would transform the observed data distribution into the model distribution, and then setting as the objective the minimization of the KL divergence between the data distribution and the distribution produced by running the dynamics for an infinitesimal time. Score matching, minimum velocity learning, and certain forms of contrastive divergence are shown to be special cases of this learning technique. We demonstrate parameter estimation in Ising models, deep belief networks and an independent component analysis model of natural scenes. In the Ising model case, current state of the art techniques are outperformed by at least an order of magnitude in learning time, with lower error in recovered coupling parameters.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Probabilistic & Bayesian Methods

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Citations in the corpus

Fast large-scale optimization by unifying stochastic gradient and quasi-Newton methods (2013, methodology): “• An Ising model / Hopﬁeld network trained using code from (Hillar et al., 2012) implementing MPF (Sohl-Dickstein et al., 2011b;a).”
Neural Autoregressive Distribution Estimation (2016, methodology): “Recently, the directed generative model approach has been very successfully applied to model images (Denton et al., 2015; Sohl-Dickstein et al., 2011).”
Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, background): “, pseudo loglikelihood [6], contrastive divergence [30, 67], score matching estimator [31], minimum probability flow [66], noise contrastive estimation [28]) to bypass the calculation of the partition function.”
Generative Modeling by Estimating Gradients of the Data Distribution (2019, background): “While other objectives exist for generative modeling, such as noise contrastive estimation [19] and minimum probability flow [50], these methods typically only work well for low-dimensional data.”
Deep Unsupervised Learning using Nonequilibrium Thermodynamics (2015, background): “A variety of analytic approximations exist which ameliorate, but do not remove, this tradeoff – for instance mean field theory and its expansions [39, 40], variational Bayes [19], contrastive divergence [44, 13], minimum probability flow [36, 35], minimum KL contraction [28], proper scoring rules [9”
A note on the evaluation of generative models (2015, background): “…(Hyv¨arinen, 2005), lower bounds on the log-likelihood (Bishop, 2006), noise-contrastive estimation (Gutmann & Hyv¨arinen, 2010), probability ﬂow (Sohl-Dickstein et al., 2011), maximum mean discrepancy (MMD) (Gretton et al., 2007; Li et al., 2015), or approximations to the Jensen-Shannon…”
Hamiltonian Annealed Importance Sampling for partition function estimation (2012, unknown): “See Sohl-Dickstein et al. (2011) for details.”
How to Train Your Energy-Based Models (2021, background): “Aside from MCMC-based training, Score Matching and Noise Contrastive Estimation, there are also other methods for learning EBMs.”
The Natural Gradient by Analogy to Signal Whitening, and Recipes and Tricks for its Use (2012, background): “There are a number of techniques which can provide approximate learning gradients (eg minimum probability ﬂow [Sohl-Dickstein et al., 2011b, Sohl-Dickstein et al., 2011a], contrastive divergence [Welling and Hinton, 2002, Hinton, 2002], score matching [Hyv¨arinen, 2005], mean ﬁeld theory, and…”
Score-Based Generative Modeling with Critically-Damped Langevin Diffusion (2021, background): “Generative modeling by learning stochastic processes has a long history (Movellan, 2008; Lyu, 2009; Sohl-Dickstein et al., 2011; Bengio et al., 2014; Alain et al., 2016; Goyal et al., 2017; Bordes et al., 2017; Song & Ermon, 2019; Ho et al., 2020).”
Exponential Family Estimation via Adversarial Dynamics Embedding (2019, background): “Markov Similar to CD and score matching, the MPF exploits the 1 -step MCMC.”
Building a better probabilistic model of images by factorization (2011, methodology): “It was trained via Persistent MPF, with J = 400.”
Unifying Non-Maximum Likelihood Learning Objectives with Minimum KL Contraction (2011, unknown): “With the more general framework, we hope to reveal further relations among other types of non-ML learning objectives [16, 25, 28, 27].”
On Maximum Likelihood Training of Score-Based Generative Models (2021, background): “Learning principles Minimum velocity learning [Movellan, 2007] and minimum probability flow [Sohl-Dickstein et al., 2011] are learning principles which are based on minimizing”