Gradient Estimators for Implicit Models

By Yingzhen Li, Richard E. Turner. 2017

127 citations recorded by the source corpus.

Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press approximate inference techniques relying on implicit distributions. The majority of existing approaches to learning implicit models rely on approximating the intractable distribution or optimisation objective for gradient-based optimisation, which is liable to produce inaccurate updates and thus poor models. This paper alleviates the need for such approximations by proposing the Stein gradient estimator, which directly estimates the score function of the implicitly defined distribution. The efficacy of the proposed estimator is empirically demonstrated by examples that include meta-learning for approximate inference, and entropy regularised GANs that provide improved sample diversity.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Posterior Meta-Replay for Continual Learning (2021, methodology): “Li and Turner [43] and Shi et al. [65] observed that the training of implicit distributions (e.g., via VI) often only requires access to ∇ w log q θ ( w ) , a quantity that appears in Stein’s identity.”
Sliced Score Matching: A Scalable Approach to Density and Score Estimation (2019, methodology): “In both situations we outperformed kernel-based score estimators (Li & Turner, 2018; Shi et al., 2018) by achieving better test likelihoods and better sample quality in image generation.”
Monte Carlo Gradient Estimation in Machine Learning (2019, methodology): “By expanding Stein’s identity as a Monte Carlo estimator using several samples, Li and Turner (2017) use kernel substitution to develop a kernelised method for gradient estimation in implicit probabilistic models.”
A Spectral Approach to Gradient Estimation for Implicit Distributions (2018, methodology): “Unlike the Stein gradient estimator (Li & Turner, 2018), our approach allows for a direct and principled out-of-sample extension.”
Kernel Implicit Variational Inference (2017, background): “It was further shown in Li & Turner (2017) that the core identity in SVGD (Stein’s identity) could also be employed to approximate the gradients of implicit distributions.”
Backpropagation for Implicit Spectral Densities (2018, background): “Very recent work [Li and Turner, 2017] uses Stein’s identity to cast gradient computation for implicit densities as a sparse recovery problem.”
Doubly Semi-Implicit Variational Inference (2018, background): “They can be divided roughly into two main groups: those that require the probability density function of the approximate posterior to be analytically tractable (which we will call explicit models) [30, 12, 9, 5, 36, 38, 6, 27, 20] and those that do not (implicit models) [11, 22, 37, 17, 21, 31, 40].”
Efficient Learning of Generative Models via Finite-Difference Score Matching (2020, methodology): “Different variants of SM have been proposed, including approximate back-propagation [25], curvature propagation [39], denoising score matching (DSM) [65], a bi-level formulation for latent variable models [3] and nonparametric estimators [35, 55, 59, 62, 74], but they may suffer from high computatio”
Semi-Implicit Variational Inference (2018, background): “…the variational family that Q belongs to, there has been signiﬁcant recent interest in deﬁning Q with an implicit model, which makes the PDF of Q become intractable (Husz´ar, 2017; Mohamed & Lakshminarayanan, 2016; Tran et al., 2017; Li & Turner, 2017; Mescheder et al., 2017; Shi et al., 2017).”
Interacting Particle Solutions of Fokker–Planck Equations Through Gradient–Log–Density Estimation (2020, methodology): “We favoured this approach over other estimators [22,23] due to its flexibility to adapt to different function classes chosen to approximate the GLD.”
On Fenchel Mini-Max Learning (2019, background): “More recently, dynamic dual embedding (DDE) explored a primal-dual view of MLE [15, 16], while Stein implicit learning (SIL) [46, 41] and kernel score estimation [60] match the landscape of the potential with that of kernel-smoothed empirical observations.”