In this short note we provide an unbiased multilevel Monte Carlo estimator of the log marginal likelihood and discuss its application to variational Bayes.
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48 results for “log-marginal likelihood”
Improved Gaussian process regression with tighter log marginal likelihood bounds.
problem Improving predictive performance in Gaussian process regression models.
method Lower bound on log marginal likelihood using conjugate gradients.
result Improved predictive performance compared to other conjugate gradient based approaches.
Improves Gaussian process regression without bias.
problem Bias in Gaussian process regression estimates.
method Adaptive computation selection to minimize bias.
result Guaranteed small bias in log marginal likelihood estimates.
SUMO provides unbiased log marginal likelihood estimation for latent variable models.
problem Biased estimates of log marginal likelihood in latent variable models.
method Randomized truncation of infinite series for unbiased estimation.
result Models trained with SUMO give better test-set likelihoods than standard methods.
A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of…
Robust GP model detects and corrects sparse outliers.
problem Non-Gaussian noise in real-world data.
method Relevance pursuit for data-point-specific noise levels.
result Strong concavity and approximation guarantees for subset selection.
Improved GP decoder training with SAS approximations.
problem Training expensive Gaussian process decoders is challenging and computationally expensive.
method Developed a new stochastic estimate of log-marginal likelihood based on cross-validation.
result SAS-GP improves robustness and reduces computational cost compared to variational autoencoders.
Posterior collapse in Variational Autoencoders (VAEs) arises when the variational posterior distribution closely matches the prior for a subset of latent variables. This paper presents a simple and intuitive explanation for posterior collapse through the analysis of linear VAEs and their direct correspondence with Prob…
Training deep generative models with maximum likelihood remains a challenge. The typical workaround is to use variational inference (VI) and maximize a lower bound to the log marginal likelihood of the data. Variational auto-encoders (VAEs) adopt this approach. They further amortize the cost of inference by using a rec…
We show that unconverged stochastic gradient descent can be interpreted as a procedure that samples from a nonparametric variational approximate posterior distribution. This distribution is implicitly defined as the transformation of an initial distribution by a sequence of optimization updates. By tracking the change …
Evaluation of the marginal likelihood plays an important role in model selection problems. The widely applicable Bayesian information criterion (WBIC) and singular Bayesian information criterion (sBIC) give approximations to the log marginal likelihood, which can be applied to both regular and singular models. When the…
We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in time. Our GRIEF kernel consists of eigenfunctions found using a Nystrom approximation from a dense Cartesian product grid of inducing points. B…
We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies on the efficiency of sequential Monte Carlo (SMC) for performing inference in st…
A new method for efficient Gaussian process regression reduces complexity and improves scalability.
problem Efficient Gaussian process regression for large datasets.
method Learnable coreset-based variational inference for Gaussian processes.
result CVGP reduces the dimensionality of the variational parameter search space to linear complexity.
This paper introduces the variational Rényi bound (VR) that extends traditional variational inference to Rényi's alpha-divergences. This new family of variational methods unifies a number of existing approaches, and enables a smooth interpolation from the evidence lower-bound to the log (marginal) likelihood that is co…
Neural Empirical Bayes estimates source distributions from noisy simulations.
problem Estimating source distributions from noisy, simulated data.
method Uses neural density estimators to estimate a prior or source distribution over uncorrupted samples, then performs posterior inference.
result Recovering ground truth source distributions up to symmetries.
We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variatio…
Thermodynamic integration (TI) for computing marginal likelihoods is based on an inverse annealing path from the prior to the posterior distribution. In many cases, the resulting estimator suffers from high variability, which particularly stems from the prior regime. When comparing complex models with differences in a …
This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across the data instances. This enables efficient training using stochastic gradients an…
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 autoencoders learn distributions of high-dimensional data. They model data with a deep latent-variable model and then fit the model by maximizing a lower bound of the log marginal likelihood. VAEs can capture complex distributions, but they can also suffer from an issue known as "latent variable collapse," …
Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large datasets require to resort to approximations. In this work, the computation of …
Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior. As the minimization can only be carried out approximately, this approximation i…
Stochastic variational inference (SVI) plays a key role in Bayesian deep learning. Recently various divergences have been proposed to design the surrogate loss for variational inference. We present a simple upper bound of the evidence as the surrogate loss. This evidence upper bound (EUBO) equals to the log marginal li…
The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the GP-LVM and propose an efficient variational inference procedure that gives a lower …
SIXO improves inference by learning smoothing distributions from all observations.
problem Inference limitations due to ignoring future observations in filtering distributions.
method Density ratio estimation to warp filtering distributions into smoothing distributions, then use SMC with learned targets.
result Proves tighter log marginal lower bounds and more accurate inferences and estimates.
Sparse Gaussian Processes simplify GP inference for large datasets.
problem Efficiently handling large datasets in Gaussian Process models.
method Sparse Gaussian Processes combined with variational inference.
result Sparse GPs enable approximate inference with reduced memory and computational requirements.
Exemplar VAEs link generative models with nearest neighbor retrieval and data augmentation.
problem Improving generative model performance and data augmentation effectiveness.
method Exemplar VAEs with Parzen window prior, retrieval augmented training, exemplar leave-one-out, and subsampling.
result Generative data augmentation reduces classification error on MNIST and Fashion MNIST.
Bayesian model selection via mean-field variational approximation improves efficiency and accuracy.
problem Bayesian model selection under model mis-specification and latent variables.
method Mean-field variational approximation with non-asymptotic properties and geometric convergence.
result ELBO tends to select models closer to the true model than BIC as sample size increases.
Latent Dirichlet allocation (LDA) is useful in document analysis, image processing, and many information systems; however, its generalization performance has been left unknown because it is a singular learning machine to which regular statistical theory can not be applied. Stochastic matrix factorization (SMF) is a res…
Modern statistical applications involving large data sets have focused attention on statistical methodologies which are both efficient computationally and able to deal with the screening of large numbers of different candidate models. Here we consider computationally efficient variational Bayes approaches to inference …
New method differentiates square-root Kalman filters robustly.
problem Gradient calculation issues in square-root Kalman filters.
method Closed-form chain rule derived from Gramian identity, resolves non-orthogonal and rank-deficient issues.
result Robust automatic differentiation for Kalman filters, resolving numerical stability and gradient issues.
An implicit goal in works on deep generative models is that such models should be able to generate novel examples that were not previously seen in the training data. In this paper, we investigate to what extent this property holds for widely employed variational autoencoder (VAE) architectures. VAEs maximize a lower bo…
Enhances ENet's prediction accuracy while maintaining uncertainty estimation.
problem Gradient shrinkage problem in ENet's loss function.
method Proposes a multi-task learning framework with a modified MSE loss function.
result Improves ENet's prediction accuracy without losing uncertainty estimation.
Towards Model-Agnostic Posterior Approximation for Fast and Accurate Variational Autoencodersstat.ML
A new method approximates posterior for VAEs without iterative training.
problem Inference models in VAEs are poor early on, leading to suboptimal models.
method Train generative and inference models independently, using a model-agnostic posterior approximation (MAPA).
result MAPA approximates the true posterior deterministically and can improve density estimation.
Novel method uses Gaussian process to estimate particle sizes from scattering data.
problem Estimating particle size distributions from noisy optical scattering measurements.
method Constrained Gaussian process regression with normalization constraints.
result Accurately reconstructs particle size distributions from noisy data.
New proof shows diffusion models implicitly estimate intrinsic dimensionality.
problem Estimating intrinsic dimensionality of data from diffusion models.
method Formal proof of FLIPD under realistic assumptions.
result FLIPD's correctness proven under realistic conditions.
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our proposed VBKS algorithm considers the kernel as a random varia…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and thus invariant to the translations in the input space. The optimization of the hyp…
DPGIIL clusters structural anomalies using transmissibility functions with deep learning and Dirichlet process.
problem Clustering structural anomalies in high-dimensional streaming data with optimal cluster number determination.
method Combines Dirichlet process and deep generative models for incremental learning and anomaly detection.
result DPGIIL outperforms traditional methods in anomaly detection and clustering.
New convergence rates found for PnP methods using MMSE denoisers.
problem Asymptotic convergence of PnP methods with MMSE denoisers.
method Explicitly represented MMSE denoiser as an upper Moreau envelope, derived sublinear convergence rates.
result First sublinear convergence guarantee for PnP proximal gradient descent with MMSE denoiser.
Bayesian free energy remains bounded for deep ReLU networks in overparametrized cases.
problem Understanding the generalization performance of deep ReLU neural networks.
method Analyzes Bayesian free energy in overparametrized deep ReLU neural networks.
result Bayesian free energy is bounded even in overparametrized deep ReLU networks.
Corrects pseudo log-likelihood method issues in various applications.
problem Log-likelihood function unbounded issues in pseudo log-likelihood methods.
method Provided a counterexample and corrected algorithms in previous literature.
result Ensured well-definedness of maximum pseudo log-likelihood estimation.
Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In this paper, we propose a novel way of approximating the likelihood function throug…
A new method for training diffusion models using likelihood matching.
problem Training efficient and accurate diffusion models.
method Likelihood Matching approach, quasi-likelihood approximation, score and Hessian estimation.
result Consistent matching of first two transitional moments between diffusion steps.
Maximum likelihood training improves the performance of score-based diffusion models.
problem Training score-based diffusion models with maximum likelihood.
method Trained by minimizing a weighted combination of score matching losses, with a specific weighting scheme that bounds negative log-likelihood.
result Maximum likelihood training improves the log-likelihood of score-based diffusion models across multiple datasets.
Neural networks estimate spatial process likelihoods efficiently.
problem Challenges in estimating spatial processes with slow or intractable likelihoods.
method Convolutional neural networks trained on a classification task to learn likelihood function.
result Neural likelihood surfaces provide fast and accurate parameter estimation.
Proposes efficient Gaussian approximations for non-Gaussian likelihoods.
problem Computational challenges in learning and inference with non-Gaussian likelihoods.
method Variational inference and moment matching in transformed bases.
result Good approximation quality for binary and multiclass classification.