New variational flows improve Monte Carlo and normalization tasks.
problem Intractable global optimum in expressive variational families.
method Constructing asymptotically exact variational flows from involutive MCMC kernels.
result Provable total variation convergence of new variational families.
New path-gradient estimator for continuous normalizing flows.
problem Limitation of simple Gaussian variational distributions in complex applications.
method Proposed a path-gradient estimator for continuous normalizing flows.
result Empirical evidence of superior performance of the new estimator.
Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single…
Paper introduces VDE, a variance-reduced determinant estimator.
problem Estimating determinants with low variance and efficiency.
method Combines variational inference and spherical normalizing flows.
result VDE achieves zero variance in ideal cases, requiring only one sample.
FlowVAT improves variational inference for multi-modal distributions.
problem Mode-seeking behavior and collapse in variational inference for complex posteriors.
method Conditional tempering approach for normalizing flow variational inference.
result FlowVAT outperforms traditional and adaptive annealing methods in multi-modal distributions, finding more modes and achieving better ELBO values.
Combines variational autoencoders with normalizing flows for faster training.
problem Training normalizing flow models like Glow is slow and requires deep architectures.
method Integrates Glow with a variational autoencoder to speed up training.
result The combined model achieves similar image quality and likelihood to Glow but trains faster.
Improves NF for complex data distributions with multiple modes.
problem Difficulty in handling data distributions with multiple isolated modes.
method Proposes a new framework using variational latent representation to improve NF.
result Significantly more powerful for generating data distributions with multiple modes.
New method models longitudinal data using variational inference and normalizing flows.
problem Handling high-dimensional longitudinal data with time dependency.
method Variational inference with normalizing flows for latent variables.
result The method achieves better likelihood estimates and more reliable missing data imputation.
Cascading flows improve variational inference in structured programs.
problem Challenges in variational inference for complex probabilistic programs.
method Integrates normalizing flows and ASVI to create cascading flows, which embed the forward-pass of probabilistic programs.
result Cascading flows outperform normalizing flows and ASVI in structured inference problems.
New method for mesh denoising using TGV of normal vector field.
problem Improving mesh quality by removing noise.
method Proposes a novel TGV formulation for normal vector fields on triangular meshes.
result New method outperforms existing techniques in mesh denoising experiments.
Study eigenvalues of conformal Laplacian under Sire-Xu normalization.
problem Existence and properties of extremal eigenvalues under a specific normalization.
method Variational analysis of eigenvalue functional under Sire-Xu normalization.
result Necessary conditions and existence results for extremal eigenvalues.
The study examines stability of triharmonic hypersurfaces in space forms.
problem Stability of triharmonic hypersurfaces in space forms.
method Derivation of general stability statements, focus on specific cases of constant mean curvature in Euclidean and hyperbolic spaces, and analysis of small proper triharmonic hyperspheres and Clifford tori.
result Triharmonic hypersurfaces of constant mean curvature in Euclidean space are weakly stable with respect to normal variations, while in hyperbolic space they are stable.
Variational auto-encoders (VAE) are scalable and powerful generative models. However, the choice of the variational posterior determines tractability and flexibility of the VAE. Commonly, latent variables are modeled using the normal distribution with a diagonal covariance matrix. This results in computational efficien…
This paper investigates Frequentist consistency properties of the posterior distributions constructed via Generalized Variational Inference (GVI). A number of generic and novel strategies are given for proving consistency, relying on the theory of Γ-convergence. Specifically, this paper shows that under minimal regul…
Method for conditional sampling with pre-trained normalizing flows.
problem Conditional sampling for incomplete observations.
method Variational Schur conditional sampling with normalizing flows.
result Successfully applied to invertible residual networks for inference and classification.
Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are considered. The use of variational Bayes approximations here is a substantial departure fr…
A new method for categorical variational inference using discrete normalizing flows.
problem Challenges in optimizing variational approximations for discrete latent variables.
method Differentiable reparameterization using a mixture of discrete normalizing flows.
result Improves optimization of evidence lower bound and reduces sensitivity to hyperparameters.
Improved phylogenetic inference with normalizing flows.
problem Limitations of current diagonal Lognormal branch length approximation in VBPI.
method Proposes VBPI-NF using normalizing flows to handle non-Euclidean branch length space.
result Significantly improves phylogenetic posterior estimation on real data.
A new model combines normalizing flows with mixture components for better density estimation.
problem Lack of explicit probability density functions in deep generative models.
method Variational mixture of normalizing flows, using variational inference and neural network parameters.
result The model can perform density estimation, semi-supervised learning, and clustering.
New method clusters matrix-variate data with outliers.
problem Clustering matrix-variate data with outliers.
method Iterative approach using subset log-likelihoods.
result Extends OCLUST algorithm to matrix-variate normal data.
Stable training of deep normalizing flows for high-dimensional variational inference.
problem Training deep normalizing flows for high-dimensional posterior distributions is infeasible due to high stochastic gradient variance.
method Proposed a combination of soft-thresholding of scale and bijective soft log transformation to stabilize training.
result Stable training of Real NVPs for posterior distributions with thousands of dimensions is possible.
Normalizing flows improve density estimation from noisy data.
problem Estimating underlying density from noisy samples.
method Use normalizing flows for density estimation with arbitrary noise distributions, using amortized variational inference.
result Normalizing flows can outperform Gaussian mixtures for density deconvolution.
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 restricti…
Enhances multimodal generation with Normalizing Flows and correlation analysis.
problem Generating coherent cross-modal data from multiple sources.
method Uses Deep Canonical Correlation Analysis for shared information, Normalizing Flows for diversity, and Product of Experts for scalability.
result Improves likelihood, diversity, and coherence in conditional generation.
The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.
problem The expressivity of bi-Lipschitz Normalizing Flows in approximating specific target distributions.
method Characterization of expressivity through lower bounds on Total Variation distance and discussion of potential remedies.
result Several target distributions are difficult to approximate using bi-Lipschitz Normalizing Flows, and lower bounds on their approximation are provided.
A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) methods. VB methods tend to be faster while achieving comparabl…
In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate, or three-w…
Bayesian neural networks improve uncertainty calibration without sacrificing accuracy.
problem Bayesian neural networks struggle with uncertainty calibration and high-dimensional geometry.
method Model uncertainty only in weight directions using a von Mises-Fisher posterior on the unit sphere, deriving a compact KL term.
result A lightweight, dimension-aware variational unit improves calibration without sacrificing accuracy.
SoftCVI uses contrastive estimation to infer complex posteriors.
problem Estimating complex posteriors in Bayesian inference.
method Contrastive variational inference with self-generated soft labels.
result SoftCVI outperforms other variational approaches in stability and coverage.
Variational autoencoder is a powerful deep generative model with variational inference. The practice of modeling latent variables in the VAE's original formulation as normal distributions with a diagonal covariance matrix limits the flexibility to match the true posterior distribution. We propose a new transformation, …
In this note we consider setups in which variational objectives for Bayesian neural networks can be computed in closed form. In particular we focus on single-layer networks in which the activation function is piecewise polynomial (e.g. ReLU). In this case we show that for a Normal likelihood and structured Normal varia…
Derives Lagrangian for minimal surfaces, proving tangential variations vanish.
problem Variational calculus for minimal surfaces.
method Lagrangian formulation, pullback covariant derivative, geometric argument.
result Tangential variations vanish for minimal surfaces.
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
The paper defines and studies new types of submanifolds in a unit sphere.
problem Variational problems of curvature tensors for submanifolds.
method Euler-Lagrange equations for Normal-Yang-Mills and Tangent-Yang-Mills submanifolds.
result Infinitely many non-trivial examples of Normal-Yang-Mills and Tangent-Yang-Mills submanifolds are constructed.
Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.
problem Estimating KL divergences for normalizing flows efficiently and accurately.
method Path-gradient estimators for reverse and forward KL divergences.
result Path-gradient estimators lead to faster convergence and better approximation results.
Small hypersphere is unstable in both 4-harmonic and ES-4-harmonic settings.
problem Stability of small hypersphere in 4-harmonic and ES-4-harmonic settings.
method Analysis of normal variations of small hypersphere.
result Normal index of small hypersphere is one in both 4-harmonic and ES-4-harmonic settings.
Advances variational Bayesian neural networks using singular learning theory.
problem Discrepancies between predictive performance and variational objective in BNNs.
method Corrected asymptotic form of singular posterior distributions to inform variational family design.
result Improvements in variational free energy and generalization error with proposed normalizing flow.
vOED-NFs uses normalizing flows to improve Bayesian OED without likelihood evaluations.
problem Optimizing experiments to maximize information gain in model parameters.
method vOED-NFs combines variational approximations with normalizing flows for efficient EIG estimation.
result vOED-NFs achieves lower EIG estimation bias compared to previous methods.
CRAFT improves on existing methods for sampling complex distributions.
problem Sampling from complex probability distributions.
method Combines SMC with variational inference using normalizing flows.
result Improves on Annealed Flow Transport Monte Carlo and MCMC-based Stochastic Normalizing Flows.
NeVI-Cut uses neural networks to efficiently propagate uncertainty without feedback.
problem Efficiently propagating uncertainty in downstream Bayesian analysis without feedback.
method NeVI-Cut combines neural networks and normalizing flows for variational inference.
result NeVI-Cut achieves significant computational gains and higher accuracy than traditional methods.
FTIP uses normalizing flows to improve posterior inference in function space.
problem Challenges in posterior inference with implicit-process priors.
method FTIP uses normalizing flows to define a richer variational distribution over combination weights.
result FTIP captures asymmetric and multimodal posterior structure better than Gaussian coefficient approximations.
Paper advances black-box VI using flows and Monte-Carlo methods.
problem Improving automatic posterior inference in black-box VI.
method Combines normalizing flows, Monte-Carlo methods, and optimization considerations.
result Significant improvement in state-of-the-art variational inference.
Study high-dimensional Bayesian linear regression using variational inference.
problem High-dimensional Bayesian linear regression with product priors.
method Non-linear large deviations theory and variational inference.
result Unique optimizer in variational problem governs posterior distribution under separation condition.
The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed f…
NoFAS combines variational inference and adaptive surrogate models for efficient inference of computationally expensive models.
problem Efficient inference of parameters from data with computationally expensive models.
method Variational inference with normalizing flow and adaptive surrogate model training.
result NoFAS reduces computational cost without sacrificing inferential accuracy.
New method improves variational inference for better posterior approximation.
problem Challenges in minimizing inclusive KL divergence for amortized variational inference.
method Likelihood-tempered sequential Monte Carlo samplers to estimate inclusive KL gradient.
result SMC-Wake method fits variational distributions more accurately than existing methods.
A new path gradient estimator speeds up normalizing flows without sacrificing accuracy.
problem High computational cost and limited scalability of path gradient estimators for normalizing flows.
method Proposed a fast path gradient estimator that improves computational efficiency and scalability.
result The new estimator achieves superior performance and reduced variance across various applications.
We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and epistemic uncertainty in a coherent manner. The intractable posterior probability dis…