The paper improves model robustness by regularizing posterior differences.
problem Improving model robustness in noisy input scenarios.
method Posterior differential regularization with f-divergence. result Regularizing with f-divergence improves model robustness. Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.
problem High nodal variance in BHMC trees, leading to weak separation between nodes at higher levels.
method Employing Posterior Regularization to impose max-margin constraints on nodes at every level.
result Improves cluster separation in BHMC models, enhancing overall model performance.
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the …
Improved VAEs learn consistent posterior distributions from missing data.
problem Learning VAEs from data with missing values, especially in the encoder.
method Formal definition of posterior consistency and regularization approach.
result Regularization leads to improved performance in reconstruction and downstream tasks.
This paper introduces NPR, a technique to improve Bayesian inference for multi-modal, high-dimensional simulations.
problem Challenges in Bayesian inference for multi-modal, high-dimensional simulations.
method Introduces Neural Posterior Regularization (NPR) to enforce exploration of input parameter space.
result Empirically validated that NPR significantly improves performance on various simulation tasks.
Bayesian deep learning faces posterior collapse due to likelihood vs. prior competition.
problem Posterior collapse in Bayesian deep learning models.
method Identified competition between likelihood and prior regularization in a linear latent variable model.
result Posterior collapse is related to neural and dimensional collapse, suggesting a broader learning issue.
New method controls posterior collapse in VAEs without network architecture constraints.
problem Posterior collapse in VAEs reduces diversity of generated samples.
method Introduces Latent Reconstruction (LR) loss to control posterior collapse.
result Controls posterior collapse on various datasets without architectural constraints.
Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through Bayes' rule, imposing posterior regularization is arguably more direct and in s…
Bayesian l0-regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor combinations. Spike-and-slab (a.k.a. Bernoulli-Gaussian) priors are the gold standard f…
Bayesian optimization (BO) is a powerful paradigm for derivative-free global optimization of a black-box objective function (BOF) that is expensive to evaluate. However, the overhead of BO can still be prohibitive for problems with highly expensive function evaluations. In this paper, we investigate how to reduce the r…
Mitigates gender bias amplification in model predictions.
problem Gender bias amplification in model predictions.
method Posterior regularization to mitigate bias.
result Almost removes gender bias amplification in model predictions.
Flexible VAEs using FIFs improve model likelihood on image datasets.
problem Limitations of diagonal Gaussian posteriors in VAEs.
method Regularized Free-form Injective Flow (FIF) for flexible posterior.
result Full covariance VAEs outperform diagonal Gaussian posteriors.
Variational dropout (VD) is a generalization of Gaussian dropout, which aims at inferring the posterior of network weights based on a log-uniform prior on them to learn these weights as well as dropout rate simultaneously. The log-uniform prior not only interprets the regularization capacity of Gaussian dropout in netw…
Variational inference with a factorized Gaussian posterior estimate is a widely used approach for learning parameters and hidden variables. Empirically, a regularizing effect can be observed that is poorly understood. In this work, we show how mean field inference improves generalization by limiting mutual information …
DDVI uses diffusion models for variational inference, improving latent variable model performance.
problem Improving variational inference in latent variable models.
method Introduces diffusion-based variational posteriors trained with a regularized ELBO.
result Outperforms alternative variational posteriors on various benchmarks and a biology task.
Bayesian nonparametric models get better posterior estimates via SPDE methods.
problem Estimating posterior distributions in nonparametric Bayesian models.
method Extending diffusion methods to SPDEs on Hilbert spaces for posterior contraction and Laplace approximation.
result Derivation of posterior contraction rates and finite-sample Bernstein von Mises results.
Study compares chi-squared divergence and KL-divergence posteriors for PAC-Bayesian bounds.
problem Investigates optimal posteriors for PAC-Bayesian bounds using chi-squared divergence.
method Analyzes bounds for three distance functions, derives FP equations for computation.
result Chi-squared divergence based posteriors have weaker bounds and worse test errors.
Improves Bayesian neural networks inference efficiency and accuracy.
problem Inflexibility of factorized structure in Dropout posterior.
method Introduces Variational Structured Dropout (VSD) with orthogonal transformation.
result VSD induces adaptive regularization and better generalization.
In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contain…
New method uses fractional posteriors for semiparametric inference with improved uncertainty quantification.
problem Semiparametric inference with nonparametric priors and fractional posteriors.
method Established a general Bernstein--von Mises theorem for fractional posterior distributions, proposed shifted-and-rescaled credible sets.
result Fractional posterior credible sets provide reliable uncertainty quantification but have inflated size; shifted-and-rescaled set is an efficient confidence set.
We present a Communication-efficient Surrogate Likelihood (CSL) framework for solving distributed statistical inference problems. CSL provides a communication-efficient surrogate to the global likelihood that can be used for low-dimensional estimation, high-dimensional regularized estimation and Bayesian inference. For…
HEBAE improves VAEs by adaptively balancing reconstruction and regularization.
problem Posterior collapse in VAEs leading to over-regularization and poor latent encoding.
method Hierarchical Empirical Bayes approach to probabilistic generative models.
result HEBAE generates higher quality samples with better FID scores.
In the context of recent deep clustering studies, discriminative models dominate the literature and report the most competitive performances. These models learn a deep discriminative neural network classifier in which the labels are latent. Typically, they use multinomial logistic regression posteriors and parameter re…
Method estimates noise transition matrix from noisy labels without relying on unreliable class-posterior estimation.
problem Estimating noise transition matrix from noisy data.
method Total variation regularization to encourage distinguishable predicted probabilities.
result Consistent estimator of the noise transition matrix under mild assumptions.
Autoencoders and their variations provide unsupervised models for learning low-dimensional representations for downstream tasks. Without proper regularization, autoencoder models are susceptible to the overfitting problem and the so-called posterior collapse phenomenon. In this paper, we introduce a quantization-based …
In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is reliably estimated from the observations. As the posterior density of the unknown…
Entropy regularization improves interpretability of probabilistic clustering models.
problem Bayesian nonparametric mixture models often produce unbalanced cluster frequencies.
method Interpreting the posterior as penalized likelihood, entropy regularization reduces sparsely-populated clusters.
result The proposed entropy-regularized estimator enhances interpretability without sacrificing computational convenience.
A new method uses compressive autoencoders for image restoration.
problem Efficient regularization of inverse problems in computational imaging.
method Variational Bayes Latent Estimation (VBLE) with compressive autoencoders.
result VBLE achieves similar performance to state-of-the-art PnP methods but faster.
Variational Autoencoder (VAE), a simple and effective deep generative model, has led to a number of impressive empirical successes and spawned many advanced variants and theoretical investigations. However, recent studies demonstrate that, when equipped with expressive generative distributions (aka. decoders), VAE suff…
The variational autoencoder (VAE) is a powerful generative model that can estimate the probability of a data point by using latent variables. In the VAE, the posterior of the latent variable given the data point is regularized by the prior of the latent variable using Kullback Leibler (KL) divergence. Although the stan…
PAC-Bayesian set up involves a stochastic classifier characterized by a posterior distribution on a classifier set, offers a high probability bound on its averaged true risk and is robust to the training sample used. For a given posterior, this bound captures the trade off between averaged empirical risk and KL-diverge…
Existing methods for CWS usually rely on a large number of labeled sentences to train word segmentation models, which are expensive and time-consuming to annotate. Luckily, the unlabeled data is usually easy to collect and many high-quality Chinese lexicons are off-the-shelf, both of which can provide useful informatio…
GPNs use unlabeled data to estimate uncertainty in Bayesian problems.
problem Limited training data in high-dimensional problems.
method Generative Posterior Networks (GPNs) that approximate the posterior distribution using unlabeled data.
result GPNs improve epistemic uncertainty estimation and scalability.
Variational inference struggles with weight symmetries in neural networks, leading to biased posteriors.
problem Weight space symmetries in neural networks cause multimodal posteriors, challenging variational inference.
method Developed a symmetrization mechanism to create permutation invariant variational posteriors.
result Symmetrized variational posteriors have a better fit to the true posterior and improved predictive performance.
This paper explores Bayesian Neural Network posteriors, uncovering symmetries and their impact.
problem Understanding the complex posterior distribution of deep Bayesian Neural Networks.
method Investigates optimal approaches for approximating posteriors, analyzes modes, and explores visualizations.
result Uncovered weight-space symmetries and their impact on the posterior, particularly scaling symmetries.
Variational Bayesian neural networks combine the flexibility of deep learning with Bayesian uncertainty estimation. However, inference procedures for flexible variational posteriors are computationally expensive. A recently proposed method, noisy natural gradient, is a surprisingly simple method to fit expressive poste…
The paper improves uncertainty quantification for node classification using distance-based regularization.
problem Uncertainty in deep learning models, especially for node classification tasks.
method Graph posterior networks (GPNs) with UCE loss function, followed by a distance-based regularization.
result The proposed distance-based regularization outperforms state-of-the-art methods in OOD detection and misclassification detection.
Bayesian neural networks ignore data in infinite units limit.
problem Pathological behavior of posterior in over-parameterized networks.
method Mean-field variational inference in infinite hidden units limit.
result Posterior mean converges to zero, ignoring data.
New MCMC method for complex models with large variables.
problem Inference on posterior model probabilities in large model spaces.
method Reversible genetically modified mode jumping Markov chain Monte Carlo (GMJMCMC).
result Introduced a proper MCMC with correct limiting distribution.
New method uses CNN for seismic inversion uncertainty quantification.
problem Uncertainty quantification in seismic inversion for noisy data.
method Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) with CNN denoiser.
result High-resolution, trustworthy posterior samples for subsurface structures.
This research improves binary classification by balancing overfitting and generalization with a novel Bayesian approach.
problem Improving binary classification models to avoid overfitting and generalize well.
method Introduces a PAC-Bayes type learning rule with a balancing parameter λ to balance training error and KL divergence to a prior.
result A choice of λ ensures uniformly vanishing excess loss, even in the agnostic case, by under-regularizing or over-regularizing appropriately.
New criterion improves predictive evaluation in weighted inference scenarios.
problem Improving predictive evaluation in scenarios with different likelihoods for estimation and evaluation.
method Developed the posterior covariance information criterion (PCIC) to handle weighted likelihood inference.
result PCIC is asymptotically unbiased for quasi-Bayesian generalization error in weighted inference.
Online distributional prediction with latent cluster geometry
problem Predicting the full data-generating distribution in non-stationary streams
method Representing candidate laws as latent cluster geometry and using Gibbs quasi-posterior
result Achieving sublinear cumulative Wasserstein regret under bounded support and stable latent geometry
Enhances predictive performance in Bayesian deep learning via generalized Laplace approximation.
problem Inconsistency in Bayesian deep learning.
method Interprets posterior tempering as a correction for model misspecification and recalibration of priors. Introduces generalized Laplace approximation.
result Generalized Laplace approximation enhances predictive performance.
The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.
problem Sparse high-dimensional linear regression with random design and unknown error variance.
method Analysis of posterior concentration rates, employing techniques to address model misspecification.
result Adaptiveness and concentration rates of the posterior for sparse high-dimensional linear regression.
New approach to quantify posterior concentration rates using Wasserstein dynamics.
problem Quantifying the speed of posterior distribution concentration in Bayesian statistics.
method Combining local Lipschitz-continuity with dynamic formulation of Wasserstein distance.
result Optimal posterior contraction rates in finite and infinite-dimensional models.
High-dimensional VAEs inevitably collapse to prior, requiring large datasets for good performance.
problem Posterior collapse in VAEs leads to poor representation learning quality.
method Analyzed a minimal VAE in a high-dimensional limit, evaluating conditions for posterior collapse with respect to beta and dataset size.
result VAEs face 'inevitable posterior collapse' beyond a certain beta threshold, regardless of dataset size.
Enhances deep kernel learning with stochastic latent variables for better model regularization.
problem Weak model regularization in deep kernel learning, especially on small datasets.
method Introduces DLVKL model with stochastic latent variables, NSDE for expressive posterior, and hybrid prior.
result DLVKL-NSDE outperforms existing deep GPs on large datasets.