MFVI can overestimate predictive variance compared to the exact posterior
problem MFVI underestimates posterior variance
method Analyzing conjugate Bayesian Linear Regression
result MFVI can overestimate predictive variance compared to the exact posterior
We quantify predictive uncertainty using the posterior predictive variance.
problem Quantifying uncertainty in predictive models.
method Using the law of total variance, we generate expansions for the posterior predictive variance.
result Identify the main contributors to prediction intervals and quantify term-wise uncertainty.
Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we derive the approximation error of VB in terms of mean, mode, variance, predictive den…
A simple method treats heteroscedastic variance variatively, improving model calibration and sample quality.
problem Brittle optimization impacts model likelihoods for mean and variance estimation.
method Proposes a variational approach to heteroscedastic variance, improving predictive mean and variance calibration.
result The proposed method significantly improves parameter calibration and sample quality for regression and VAEs.
PFN-TS uses Thompson sampling with PFNs to improve contextual bandit performance.
problem Improving contextual bandit performance using Thompson sampling with prior-data fitted networks.
method PFN-TS converts PFN posterior predictives into mean-reward samples using a subsampled predictive central limit theorem.
result PFN-TS achieves the best average rank across nonlinear synthetic and OpenML classification-to-bandit benchmarks.
Improved HGF networks avoid negative precision errors in volatility updates.
problem Negative posterior precision errors in volatility-coupled nodes of HGF networks.
method Introduced a modified quadratic approximation to variational energy.
result Robust update equations across parameter space that track posterior faithfully.
Transformers can approximate posterior predictive distributions through in-context learning.
problem Bayesian prediction tasks, especially beyond point predictions.
method Gradient descent algorithm targeting posterior predictive mean and variance, followed by nonlinear mappings.
result Transformers can implement algorithms to approximate posterior predictive distributions.
New method reduces variance in Bayesian inverse problems.
problem High variance in Monte Carlo estimates for inverse problems.
method Conditional neural control variates based on Stein's identity.
result Substantial variance reduction across different inverse problems.
A method predicts posterior PCs for faster uncertainty quantification in imaging.
problem Uncertainty visualization in image restoration models is limited by per-pixel variances.
method Neural Posterior Principal Components (NPPC) method for predicting PCs in a single forward pass.
result Orders of magnitude faster uncertainty quantification compared to posterior samplers.
We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to make unbiased weight updates to a variance network. Further, we formulate a heurist…
The posterior variance of Gaussian processes is a valuable measure of the learning error which is exploited in various applications such as safe reinforcement learning and control design. However, suitable analysis of the posterior variance which captures its behavior for finite and infinite number of training data is …
One of the most compelling features of Gaussian process (GP) regression is its ability to provide well-calibrated posterior distributions. Recent advances in inducing point methods have sped up GP marginal likelihood and posterior mean computations, leaving posterior covariance estimation and sampling as the remaining …
One way to avoid overfitting in machine learning is to use model parameters distributed according to a Bayesian posterior given the data, rather than the maximum likelihood estimator. Stochastic gradient Langevin dynamics (SGLD) is one algorithm to approximate such Bayesian posteriors for large models and datasets. SGL…
Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.
problem Boundary-induced acquisition bias in Gaussian processes.
method Traced root cause to geometric mechanism of kernel truncation at domain boundaries.
result Boundary effects create distortion that worsens with dimensionality, affecting acquisition behavior.
A new method calibrates Gaussian processes for more accurate uncertainty estimates.
problem Uncertainty estimates from Gaussian processes are often miscalibrated in practice.
method A novel calibration approach using different hyperparameters to generate more accurate predictive quantiles.
result The method yields tighter predictive quantiles and is more flexible than existing approaches.
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset returns. The new approach employs the Bayesian posterior predictive distribution which…
Differential privacy of Gaussian process posterior sampling
problem Privacy of posterior sample paths from Gaussian process
method Intrinsic randomness yields DP guarantees
result Intrinsic randomness yields DP guarantees
Sparse matrices simplify computation of GP variances and likelihoods.
problem Efficient computation of posterior variance and log-likelihood for additive Matérn GPs.
method Represented posterior mean, variance, log-likelihood, and gradient using sparse matrices.
result Efficient computation of posterior mean, variance, log-likelihood, and gradient in O(nlogn) time. WBCP improves conformal prediction for distribution shifts using weighted Dirichlet posteriors.
problem Handling distribution shifts in conformal prediction.
method Generalizes Bayesian Quadrature Conformal Prediction (BQ-CP) to arbitrary importance-weighted settings.
result WBCP maintains coverage guarantees while providing richer uncertainty information.
This paper addresses error bounds and posterior variance for Gaussian process regression.
problem Deriving performance guarantees for Gaussian process regression without prior knowledge.
method Lipschitz continuity and analysis of posterior variance function.
result Uniform error bounds for Gaussian process regression are derived.
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.
BYOV combines SSL and Bayesian methods for uncertainty estimation.
problem Model uncertainty in applications.
method Combines Bootstrap Your Own Latent (BYOL) and Bayes by Backprop (BBB).
result BYOV improves model calibration and reliability with various augmentations.
Two methods improve Gaussian process predictive distributions' calibration.
problem Improving the reliability of Gaussian process predictive intervals.
method Introduces two methods: cps-gp and bcr-gp, both adapting conformal predictive systems to GP interpolation.
result Both methods provide finite-sample marginal calibration and smooth predictive distributions.
Large amounts of labeled data are typically required to train deep learning models. For many real-world problems, however, acquiring additional data can be expensive or even impossible. We present semi-supervised deep kernel learning (SSDKL), a semi-supervised regression model based on minimizing predictive variance in…
The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially underestimated uncertainties. Notably, in the regression case the predictive varian…
Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.
problem Minimizing regret in Gaussian process bandits with unknown reward functions.
method New upper bound on maximum posterior variance, refined MVR and PE algorithms.
result Optimal regret bounds for noiseless, varying noise, and RKHS norms.
Decoupled PFNs improve sequential decision-making by separating epistemic and aleatoric uncertainties.
problem Sequential decision-making requires distinguishing between epistemic uncertainty about latent signals and irreducible aleatoric observation noise.
method Developed a decoupled PFN architecture that uses query-level labels to train separate heads for latent signal and aleatoric noise.
result Empirically, decoupled PFNs mitigate the failure mode of total-variance exploration in noisy and heteroscedastic settings.
Efficiently designs experiments without integrating posterior distributions.
problem Computational inefficiency in Bayesian experimental design for PDE-based models.
method Likelihood-free approach using ANN to approximate conditional expectation.
result Significant reduction in observation model evaluations.
Enhances neural network regression performance by modeling weight and variance uncertainty.
problem Improving predictive performance of neural networks for regression tasks.
method Extended Blundell's framework to include variance uncertainty, using a full posterior distribution over variance parameters.
result Explicitly modeling variance uncertainty improves generalization of Bayesian neural networks.
Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through test-time averaging. In this paper, we introduce variance layers, a different k…
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…
We propose a simple and general variant of the standard reparameterized gradient estimator for the variational evidence lower bound. Specifically, we remove a part of the total derivative with respect to the variational parameters that corresponds to the score function. Removing this term produces an unbiased gradient …
Stochastic gradient descent approximates Gaussian process posteriors efficiently.
problem Efficiently sampling from Gaussian process posteriors with limited computational resources.
method Developed stochastic gradient optimization objectives for sampling from Gaussian process posteriors.
result Stochastic gradient descent produces accurate predictive distributions, even in non-convergent cases.
Bayesian neural networks (BNNs) allow us to reason about uncertainty in a principled way. Stochastic Gradient Langevin Dynamics (SGLD) enables efficient BNN learning by drawing samples from the BNN posterior using mini-batches. However, SGLD and its extensions require storage of many copies of the model parameters, a p…
RVRAE combines deep learning and dynamic factor models for better stock returns prediction.
problem Improving stock returns prediction in volatile markets.
method Combines dynamic factor modeling with variational recurrent autoencoder (VRAE). Uses prior-posterior learning for optimal factor model.
result RVRAE outperforms traditional methods in predicting stock returns and estimating variances.
Variational methods that rely on a recognition network to approximate the posterior of directed graphical models offer better inference and learning than previous methods. Recent advances that exploit the capacity and flexibility in this approach have expanded what kinds of models can be trained. However, as a proposal…
We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise th…
This work tackles posterior collapse in conditional and hierarchical VAEs.
problem Posterior collapse in VAEs leads to poor latent variable representations.
method Theoretical analysis of linear conditional and hierarchical VAEs, empirical validation.
result Theoretical and empirical evidence of posterior collapse causes in conditional and hierarchical VAEs.
Unified framework for causal inference with reliable uncertainty quantification.
problem Causal inference under unobserved confounding with unreliable uncertainty quantification.
method Deconditional Gaussian Process (DGP) framework for uncertainty-aware causal learning.
result Strong predictive performance and informative uncertainty quantification.
Bayesian method predicts asset returns for better portfolio optimization.
problem Uncertainty in financial markets makes traditional portfolio optimization methods unreliable.
method Bayesian predictive synthesis (BPS) combined with dynamic linear models.
result Predicted distribution information improves portfolio performance.
New method for Bayesian inference on large datasets.
problem Scalable sampling for Bayesian generalized linear mixed models on large datasets.
method Mirror Langevin dynamics with data subsampling, post-processing for variance estimation.
result Asymptotic, order-wise correct estimation of posterior variance.
New method for Bayesian neural networks with unbounded weights.
problem Posterior inference for Bayesian neural networks with unbounded weights.
method Conditionally Gaussian representation for efficient posterior inference.
result Interpretable and computationally efficient procedure for posterior inference.
Integrates neural encoders into GLMMs for multimodal data analysis.
problem Scalable Bayesian inference for GLMMs assumes low-dimensional tabular predictors and does not handle high-dimensional modalities.
method Jointly learns modality-specific neural encoders with GLMM objective, performs variance-corrected stochastic-gradient MCMC.
result Preserves interpretable fixed and random effects while scaling to large longitudinal datasets.
Unified framework combines views and optimization for better portfolio management.
problem Optimizing portfolio weights with dynamic adjustment based on volatility.
method Dynamic sliding window adjusting horizon, factor estimates, BL posterior returns, and weights over time.
result Outperforms dynamic mean-variance optimization without BL views, providing stronger downside risk control.
It is well known that Markov chain Monte Carlo (MCMC) methods scale poorly with dataset size. A popular class of methods for solving this issue is stochastic gradient MCMC. These methods use a noisy estimate of the gradient of the log posterior, which reduces the per iteration computational cost of the algorithm. Despi…
Bayesian imputation optimizes bias-variance trade-off in time-series data.
problem Look-ahead bias in imputation of missing time-series data.
method Bayesian consensus posterior that fuses multiple posteriors to optimize bias and variance trade-off.
result Benefit of imputation for portfolio allocation with missing returns demonstrated.
This paper connects RND, deep ensembles, and Bayesian inference, providing a unified theoretical perspective.
problem Uncertainty quantification in deep learning models.
method Analysis of Random Network Distillation (RND) within the neural tangent kernel framework.
result The uncertainty signal from RND is equivalent to the predictive variance of a deep ensemble and can be made to mirror the centered posterior predictive distribution of Bayesian inference.