Variational Inference with Normalizing Flows

Abstract

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

Proceedings of the 32nd International Conference on Machine Learning

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• Integrable Nonparametric Flows
• Model-based micro-data reinforcement learning: what are the crucial model properties and which model to choose?
• Benefiting Deep Latent Variable Models via Learning the Prior and Removing Latent Regularization
• Decoupling Global and Local Representations via Invertible Generative Flows
• Scalable Approximate Inference and Some Applications
• A Fourier State Space Model for Bayesian ODE Filters
• Flow-based Generative Models for Learning Manifold to Manifold Mappings
• Training Invertible Linear Layers through Rank-One Perturbations
• Learning Bijective Feature Maps for Linear ICA
• Inverse Learning of Symmetries
• Generative networks as inverse problems with fractional wavelet scattering networks
• Amortised Learning by Wake-Sleep
• Probabilistic Mapping of Dark Matter by Neural Score Matching
• Variational Bayes latent class approach for EHR-based phenotyping with large real-world data
• Deep Out-of-Distribution Uncertainty Quantification via Weight Entropy Maximization
• Blind Image Restoration with Flow Based Priors
• MaskAAE: Latent space optimization for Adversarial Auto-Encoders
• The Renyi Gaussian Process: Towards Improved Generalization
• Causal Autoregressive Flows
• Deep inference of simulated strong lenses in ground-based surveys
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory
• Diffeomorphic Transformations for Time Series Analysis: An Efficient Approach to Nonlinear Warping
• Dissecting Non-Vacuous Generalization Bounds based on the Mean-Field Approximation
• Text Modeling with Syntax-Aware Variational Autoencoders
• Efficient Multimodal Sampling via Tempered Distribution Flow
• Graph Embedding VAE: A Permutation Invariant Model of Graph Structure
• Variationally Inferred Sampling Through a Refined Bound for Probabilistic Programs
• Noncooperative dynamics in election interference
• Variational Gaussian Topic Model with Invertible Neural Projections
• Black-Box Inference for Non-Linear Latent Force Models
• Variational Inference with Mixture Model Approximation: Robotic Applications
• Copula-like Variational Inference
• Imitation Learning of Factored Multi-agent Reactive Models
• Re-examination of the Role of Latent Variables in Sequence Modeling
• Deep Learning: Hydrodynamics, and Lie-Poisson Hamilton-Jacobi Theory
• Differentiable Antithetic Sampling for Variance Reduction in Stochastic Variational Inference
• Augmented KRnet for density estimation and approximation
• Symmetric Wasserstein Autoencoders
• PRRS Outbreak Prediction via Deep Switching Auto-Regressive Factorization Modeling
• Deep Image Synthesis from Intuitive User Input: A Review and Perspectives
• ByPE-VAE: Bayesian Pseudocoresets Exemplar VAE
• Learning ODEs via Diffeomorphisms for Fast and Robust Integration
• IID-GAN: an IID Sampling Perspective for Regularizing Mode Collapse
• Implicitly Regularized RL with Implicit Q-Values
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC
• Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Sampling
• Black-box Adversarial Example Generation with Normalizing Flows
• Stay Positive: Non-Negative Image Synthesis for Augmented Reality
• A Divergence Bound for Hybrids of MCMC and Variational Inference and an Application to Langevin Dynamics and SGVI
• Diffusion Normalizing Flow
• Minimax Analysis for Inverse Risk in Nonparametric Planer Invertible Regression
• Iterative Alignment Flows
• Convolutional Normalizing Flows for Deep Gaussian Processes
• Structured Policy Representation: Imposing Stability in arbitrarily conditioned dynamic systems
• Stochastic Contrastive Learning
• Trust the Critics: Generatorless and Multipurpose WGANs with Initial Convergence Guarantees
• Out-of-Distribution Detection of Melanoma using Normalizing Flows
• Molecular Attributes Transfer from Non-Parallel Data
• Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimension
• Knothe-Rosenblatt transport for Unsupervised Domain Adaptation
• Parallelized Computation and Backpropagation Under Angle-Parametrized Orthogonal Matrices
• Transformation Models for Flexible Posteriors in Variational Bayes
• Fisher Auto-Encoders
• Learning Neural Models for Continuous-Time Sequences
• Fully differentiable model discovery
• Learning Identity-Preserving Transformations on Data Manifolds
• Separation Results between Fixed-Kernel and Feature-Learning Probability Metrics
• GFlowNet Foundations
• Continuous Latent Process Flows
• Contributions to Large Scale Bayesian Inference and Adversarial Machine Learning
• Learning Probabilistic Sentence Representations from Paraphrases
• Spot the Difference: Detection of Topological Changes via Geometric Alignment
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories
• Counterfactual Maximum Likelihood Estimation for Training Deep Networks
• A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment
• EMFlow: Data Imputation in Latent Space via EM and Deep Flow Models
• On the Generative Utility of Cyclic Conditionals
• Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data
• Enhanced Variational Inference with Dyadic Transformation
• Encoded Prior Sliced Wasserstein AutoEncoder for learning latent manifold representations
• Generative Temporal Difference Learning for Infinite-Horizon Prediction
• Input Invex Neural Network
• Learning Deep-Latent Hierarchies by Stacking Wasserstein Autoencoders
• Bootstrap Your Flow
• Efficient Semi-Implicit Variational Inference
• Hybrid Memoised Wake-Sleep: Approximate Inference at the Discrete-Continuous Interface
• TzK: Flow-Based Conditional Generative Model
• Regularization with Latent Space Virtual Adversarial Training
• On the Encoder-Decoder Incompatibility in Variational Text Modeling and Beyond
• Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps
• Multilevel Stein variational gradient descent with applications to Bayesian inverse problems
• Unsupervised Video Prediction from a Single Frame by Estimating 3D Dynamic Scene Structure
• Exploiting Invertible Decoders for Unsupervised Sentence Representation Learning
• Inferring Black Hole Properties from Astronomical Multivariate Time Series with Bayesian Attentive Neural Processes
• Structured Stochastic Gradient MCMC
• Continuous normalizing flows on manifolds
• FastMVAE2: On improving and accelerating the fast variational autoencoder-based source separation algorithm for determined mixtures
• Generalization of the Change of Variables Formula with Applications to Residual Flows
• Invertible Attention
• Probabilistic Autoencoder using Fisher Information
• Boosting Summarization with Normalizing Flows and Aggressive Training
• Viscos Flows: Variational Schur Conditional Sampling With Normalizing Flows
• Amortized Variational Deep Q Network
• Convolutional Normalization
• Fixed-kinetic Neural Hamiltonian Flows for enhanced interpretability and reduced complexity
• System identification using Bayesian neural networks with nonparametric noise models
• A Surprisingly Effective Fix for Deep Latent Variable Modeling of Text
• Enriching and Controlling Global Semantics for Text Summarization
• Gradient Boosted Normalizing Flows
• Be More Active! Understanding the Differences between Mean and Sampled Representations of Variational Autoencoders
• Accelerating Continuous Normalizing Flow with Trajectory Polynomial Regularization
• Co-Training Realized Volatility Prediction Model with Neural Distributional Transformation
• Calibrated Adaptive Probabilistic ODE Solvers
• Neural representation and generation for RNA secondary structures
• Text-to-speech for the hearing impaired
• Efficient sampling generation from explicit densities via Normalizing Flows
• Generative Particle Variational Inference via Estimation of Functional Gradients
• Rapid Risk Minimization with Bayesian Models Through Deep Learning Approximation
• Uncertainty quantification for ptychography using normalizing flows
• Convex Nonparanormal Regression
• NP-DRAW: A Non-Parametric Structured Latent Variable Model for Image Generation
• Generative Parameter Sampler For Scalable Uncertainty Quantification
• Representation Learning: A Statistical Perspective
• A Linear Systems Theory of Normalizing Flows
• Towards Robust Classification with Deep Generative Forests
• Self-Reflective Variational Autoencoder
• Efficient Approximate Inference with Walsh-Hadamard Variational Inference
• Counterfactual Explanations via Latent Space Projection and Interpolation