Gradient Estimators for Implicit Models

Abstract

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.

v5 fixed a typo in Figure 3 of v4 (the version at ICLR 2018 main conference)

References in corpus (12)

• BEGAN: Boundary Equilibrium Generative Adversarial Networks
• Learning in Implicit Generative Models
• Amortised MAP Inference for Image Super-resolution
• Hierarchical Implicit Models and Likelihood-Free Variational Inference
• Measuring Sample Quality with Kernels
• Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learning
• Variational Inference using Implicit Distributions
• Interpretation and Generalization of Score Matching
• Generative Adversarial Nets from a Density Ratio Estimation Perspective
• Approximate Inference with Amortised MCMC
• Adversarial Message Passing For Graphical Models
• Two Methods For Wild Variational Inference

Cited by in corpus (27)

• Differentiable Learning of Quantum Circuit Born Machine
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Monte Carlo Gradient Estimation in Machine Learning
• Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation
• Maximum Mean Discrepancy Gradient Flow
• A Spectral Approach to Gradient Estimation for Implicit Distributions
• Semi-Implicit Variational Inference
• Meta-Learning for Stochastic Gradient MCMC
• Repulsive Deep Ensembles are Bayesian
• Minimum Stein Discrepancy Estimators
• Latent Variable Modelling with Hyperbolic Normalizing Flows
• LiBRe: A Practical Bayesian Approach to Adversarial Detection
• Mutual Information Gradient Estimation for Representation Learning
• Kernel Implicit Variational Inference
• Implicit Policy for Reinforcement Learning
• Bidirectional Generative Modeling Using Adversarial Gradient Estimation
• Blindness of score-based methods to isolated components and mixing proportions
• Implicit Generative Modeling for Efficient Exploration
• Posterior Meta-Replay for Continual Learning
• Backpropagation for Implicit Spectral Densities
• Efficient Learning of Generative Models via Finite-Difference Score Matching
• Doubly Semi-Implicit Variational Inference
• Policy Optimization with Second-Order Advantage Information
• Active Slices for Sliced Stein Discrepancy
• KernelNet: A Data-Dependent Kernel Parameterization for Deep Generative Modeling
• Bridging Explicit and Implicit Deep Generative Models via Neural Stein Estimators
• Amortised Learning by Wake-Sleep