The natural gradient of ELBO vanishes in unconstrained optimization, simplifying learning.
problem The gap between evidence and ELBO has a vanishing natural gradient.
method Analyzes the Fisher-Rao gradient of ELBO and its implications for learning.
result Maximizing ELBO is equivalent to minimizing KL divergence, simplifying learning.
Analytical method approximates ELBO gradient in clutter problem.
problem Clutter problem in Bayesian networks with Gaussian likelihood.
method Reparameterization trick, local approximation of likelihood factors.
result Good accuracy and linear computational complexity compared to classical methods.
VarGrad reduces variance in ELBO gradient estimation for variational inference.
problem Improving the variance of gradient estimators in variational inference.
method VarGrad uses a new log-variance loss to estimate the ELBO gradient, achieving lower variance than the score function method.
result VarGrad offers a lower variance gradient estimator compared to other methods.
Quantized Variational Inference improves ELBO optimization with fast convergence.
problem Maximizing Evidence Lower Bound (ELBO) for variational inference.
method Optimal Voronoi Tesselation for variance-free gradients, Richardson extrapolation for asymptotic improvement.
result Quantized Variational Inference leads to fast convergence with comparable computational cost.
PVI improves SIVI by directly optimizing ELBO without parametric assumptions.
problem Intractable variational densities in SIVI methods.
method Particle Variational Inference (PVI) using empirical measures to approximate optimal mixing distributions.
result PVI directly optimizes the ELBO and performs favorably compared to other SIVI methods.
Proposes a new Langevin flow approach for VAEs.
problem Difficulty in constructing low variance ELBO for VAEs with large datasets.
method Integrates Langevin dynamic with quasi-symplectic integrator to improve posterior estimation.
result Shows theoretical and practical effectiveness compared to gradient flow-based methods.
SMI uses mixture models to improve SVGD's performance in Bayesian inference.
problem Variance collapse in SVGD for Bayesian inference, especially with small models.
method Generalizes SVGD to Stein mixture models, optimizing an ELBO lower bound.
result SMI avoids variance collapse and accurately estimates uncertainty for small BNNs.
Variational Auto-Encoders (VAEs) have become very popular techniques to perform inference and learning in latent variable models as they allow us to leverage the rich representational power of neural networks to obtain flexible approximations of the posterior of latent variables as well as tight evidence lower bounds (…
Improves understanding of stochastic NGVI convergence rates.
problem Lack of knowledge about non-asymptotic convergence rates in stochastic NGVI.
method Proved non-asymptotic convergence rates for conjugate likelihoods and showed implicit optimization for non-conjugate likelihoods.
result First O(T1) non-asymptotic convergence rate for stochastic NGVI in conjugate likelihoods. We explore a new research direction in Bayesian variational inference with discrete latent variable priors where we exploit Kronecker matrix algebra for efficient and exact computations of the evidence lower bound (ELBO). The proposed "DIRECT" approach has several advantages over its predecessors; (i) it can exactly co…
Variational Laplace improves Bayesian neural networks performance.
problem Improving Bayesian neural networks performance.
method Develops variational Laplace for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms other inference methods.
Efficiently estimates online variational learning using importance sampling.
problem Online variational estimation in state-space models.
method Variational approach with Monte Carlo importance sampling.
result Proposed efficient algorithm for streaming data.
Variational Laplace improves Bayesian neural network performance without sampling.
problem Improving Bayesian neural network performance and calibration.
method Develops a new variational Laplace method for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms standard VI methods in test performance and calibration.
ELBO of VAEs converges to a sum of three entropies.
problem Understanding the convergence of ELBO in VAEs.
method Analytical derivation of ELBO convergence for standard Gaussian VAEs.
result ELBO converges to a sum of three entropies at stationary points.
Improves learning of spectral mixture kernels with approximate Bayesian inference.
problem Difficult optimization of large number of SM kernel parameters.
method Approximate Bayesian inference using variational distribution of spectral points and random Fourier features.
result Accelerates convergence and leads to better optimal parameters.
Bayesian model selection can be misled by ELBO under certain conditions.
problem Misleading model selection when using ELBO for Bayesian inference.
method Analysis of ELBO-based hyperparameter learning in a simple regression model.
result Bayesian model selection can prefer overfit models when ELBO is used, contrary to evidence.
Diffusion models optimize objectives similar to ELBO with Gaussian noise augmentation.
problem Optimizing diffusion models for high perceptual quality.
method Showed diffusion objectives are weighted ELBOs over noise levels, with Gaussian noise augmentation.
result Diffusion objectives equate to ELBO with Gaussian noise augmentation under monotonic weighting.
Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defi…
Semi-implicit variational inference (SIVI) is introduced to expand the commonly used analytic variational distribution family, by mixing the variational parameter with a flexible distribution. This mixing distribution can assume any density function, explicit or not, as long as independent random samples can be generat…
New ELBO formulation improves multimodal learning.
problem Existing ELBO models struggle with multimodal data.
method Proposes a generalized ELBO for multimodal data.
result Demonstrates improved performance over state-of-the-art models.
BaM improves BBVI by optimizing a score-based divergence, leading to faster convergence.
problem Slow convergence of black-box variational inference methods.
method Batch and match (BaM) approach based on a score-based divergence.
result BaM converges exponentially quickly to the target mean and covariance.
Posterior inference in directed graphical models is commonly done using a probabilistic encoder (a.k.a inference model) conditioned on the input. Often this inference model is trained jointly with the probabilistic decoder (a.k.a generator model). If probabilistic encoder encounters complexities during training (e.g. s…
Generative models' ELBOs converge to entropy sums, proving for various models.
problem Proving convergence of ELBOs to entropy sums for various generative models.
method Proofs for individual models under realistic conditions.
result ELBOs of various generative models converge to entropy sums at all stationary points.
DLM for BNNs fails to improve over ELBO optimization.
problem Performance of DLM for Bayesian Neural Networks (BNNs).
method Direct Loss Minimization (DLM) compared to ELBO optimization.
result DLM does not significantly improve over ELBO optimization for BNNs.
Improved co-clustering for robust data analysis.
problem Noise and posterior collapse in co-clustering.
method Fully variational Co-clustering framework with Compositional ELBO.
result Enhanced robustness and accuracy in co-clustering.
The paper proposes a method to learn hyperparameters without validation sets, improving efficiency and accuracy.
problem Training large models on limited data to avoid overfitting and reduce validation set usage.
method Gradient-based learning of hyperparameters via a data-emphasized evidence lower bound (ELBO) objective.
result The data-emphasized ELBO reduces hyperparameter search time from 88+ hours to under 3 hours while maintaining comparable accuracy.
ED-VAE improves VAEs by explicitly including entropy components in ELBO.
problem Limitations of traditional VAEs with ELBO in generating high-quality samples and interpreting latent spaces.
method Introduces ED-VAE, a re-formulation of ELBO that includes entropy and cross-entropy components.
result Significantly enhances model flexibility and improves interpretability and generative performance.
We provide theoretical and empirical evidence that using tighter evidence lower bounds (ELBOs) can be detrimental to the process of learning an inference network by reducing the signal-to-noise ratio of the gradient estimator. Our results call into question common implicit assumptions that tighter ELBOs are better vari…
When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the …
InfoNCE objective is equivalent to ELBO in RPM, linking to self-supervised learning.
problem Improving self-supervised learning methods by connecting them to variational inference.
method Recognizing RPM and showing InfoNCE as a simplified lower bound on MI, equal to ELBO in infinite sample limit.
result The actual InfoNCE objective is equal to the ELBO (up to a constant) in the infinite sample limit.
SigGPDE scales sparse Gaussian processes for sequential data.
problem Predicting and quantifying uncertainty in sequential data.
method Sparse variational inference framework for Gaussian Processes, leveraging GP signature kernel gradients as PDE solutions.
result Significant computational gains and state-of-the-art performance on large sequential datasets.
A new method for VAEs improves latent space disentanglement without violating probability laws.
problem Improving latent space disentanglement in VAEs without violating probability laws.
method Developed a Renyi VAE with a conditional distribution not learned, using Singular Value Decomposition for evaluation.
result Improved latent space disentanglement without violating probability laws.
Scalable Gaussian process models trained with unbiased stochastic ELBO.
problem Training large capacity Gaussian process models on huge datasets.
method Unbiased stochastic variational inference for scalable GPs.
result Accurate inference on large datasets with up to 10 million basis functions.
Geometric analysis improves convergence of variational inference.
problem Challenges in analyzing convergence of variational inference due to non-convexity and non-smoothness.
method Exploits exponential family structure and Bregman divergences to geometrically analyze the optimization landscape.
result Establishes non-asymptotic convergence rates for gradient descent algorithms.
New entropy-based objective for sparse coding improves learning.
problem Sparse coding with probabilistic priors and non-Gaussian observables.
method Derive a solely entropy-based learning objective for sparse coding parameters.
result Fully analytical ELBO objective for sparse coding with non-trivial posterior approximations.
This paper analyzes VAE approximation errors in conditional exponential families.
problem Posterior collapse and approximation errors in VAEs.
method Analysis of ELBO objective and conditional exponential families.
result The ELBO optimizer pulls away from the likelihood optimizer towards a consistent subset of models.
We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a hierarchical manner using a simple reparameterizable distribution whose variational …
We develop an automated variational inference method for Bayesian structured prediction problems with Gaussian process (GP) priors and linear-chain likelihoods. Our approach does not need to know the details of the structured likelihood model and can scale up to a large number of observations. Furthermore, we show that…
New method guarantees global convergence in variational inference.
problem Limited convergence to local optima in variational inference.
method Minimizes inclusive KL divergence using neural networks and neural tangent kernel.
result Gradient descent dynamics converge to a unique solution in function space.
VFG model embeds flow-based models with hierarchical structures using variational inference.
problem Flow-based models struggle with high-dimensional latent spaces and lack of tractable inference for graphical structures.
method Integrates flow-based functions through variational inference with aggregation nodes for hierarchical information integration.
result VFG models achieve improved ELBO and likelihood values on multiple datasets.
We investigate the use of alternative divergences to Kullback-Leibler (KL) in variational inference(VI), based on the Variational Dropout \cite{kingma2015}. Stochastic gradient variational Bayes (SGVB) \cite{aevb} is a general framework for estimating the evidence lower bound (ELBO) in Variational Bayes. In this work, …
A discrete diffusion model learns denoising, scoring, and bridging in different coordinates.
problem Understanding what a discrete diffusion model learns in different coordinate systems.
method Rigorous derivation of continuous-time Markov chain ELBO, Oracle Distance theorem, and exact coordinates for optimizer.
result The negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one.
VAEs improve representation learning by inverting the data-generating process through self-consistency.
problem VAEs struggle to invert the data-generating process, yet often succeed in representation learning.
method Studied VAEs in the limit of near-deterministic decoders, proving self-consistency and showing ELBO convergence to a regularized log-likelihood.
result VAEs can perform independent mechanism analysis (IMA), recovering true latent factors under specific conditions.
Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g.~fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive w…
New method selects FMM components via variational Bayes.
problem Selecting the correct number of components in finite mixture models.
method Variational Bayes with mean-field approximation.
result Consistency of model selection based on ELBO maximization.
One-step diffusion samplers reduce sampling time and computational costs.
problem Efficient sampling from complex distributions.
method One-step diffusion, self-distillation, deterministic flow.
result Achieves competitive sample quality with fewer evaluations.
Paper establishes a density formula for diffusion models, linking target density to score function.
problem Lack of theoretical foundation for optimizing DDPMs using ELBO.
method Developed a density formula for continuous-time diffusion processes, revealing the connection between target density and score function.
result The minimizer of the ELBO objective for DDPMs nearly coincides with the true objective, providing a theoretical foundation.
ELBO converges to a sum of entropies for many generative models.
problem Understanding the convergence of variational lower bounds in unsupervised learning.
method Analyzing the ELBO for a broad class of generative models, showing it equals a sum of entropies.
result The ELBO is equal to a sum of entropies at stationary points for many generative models.