New framework models uncertainty with uncertainty variables.
problem Modeling uncertainty in state estimation and inference.
method Developed uncertainty variables, sets, and graphical models.
result Preserves independence properties and builds useful concepts.
Bayesian deep learning accounts for input uncertainty using Errors-in-Variables models.
problem Uncertainty in deep regression models, especially from input data.
method Bayesian treatment with Errors-in-Variables model to decompose predictive uncertainty.
result The approach yields more complete and consistent uncertainty estimates.
Decadal climate predictions, which are initialized with observed conditions, are characterized by two main sources of uncertainties--internal and model variabilities. Using an ensemble of climate model simulations from the CMIP5 decadal experiments, we quantified the total uncertainty associated with these predictions …
Unified framework for selecting variables with uncertainty quantification.
problem Uncertainty in nonlinear variable selection for various models.
method Develops a unified framework using integrated partial derivatives for quantifying variable importance and uncertainty.
result The approach provides a principled method for quantifying variable selection uncertainty and is generalizable to non-differentiable models.
Deep Bayesian neural networks effectively select variables with rigorous uncertainty quantification.
problem High-dimensional variable selection with uncertainty.
method Developed new Bayesian non-parametric theorems for deep BNNs.
result BNNs can learn variable importance effectively in high dimensions and rigorously quantify uncertainty.
The paper sets limits on the accuracy of macroeconomic forecasts based on statistical moments and trade volumes.
problem Uncertainty in predicting macroeconomic variables like prices and returns.
method Defines theoretical lower bounds of uncertainty and upper limits on forecast accuracy based on statistical moments and trade volumes.
result Accuracy of forecasts of probabilities of macroeconomic variables doesn't exceed Gaussian approximations.
New method improves uncertainty quantification in latent variable models.
problem Uncertainty quantification in latent variable models with SGLD-Gibbs.
method Statistical scaling limit theory for SGLD-Gibbs, proposing hyperparameter tuning.
result Explicit guidance on hyperparameter tuning for SGLD-Gibbs ensures meaningful uncertainty quantification.
Paper quantifies epistemic uncertainty in deep learning.
problem Uncertainty in deep learning models, especially epistemic uncertainty.
method Dissects epistemic uncertainty into procedural and data variability, proposes estimation methods.
result Demonstrates how proposed methods overcome computational challenges and provide guidance for modeling and data collection.
Novel framework for contextual anomaly detection models uncertainty.
problem Identifying anomalies in target variables influenced by contextual variables.
method Normalcy score (NS) framework using heteroscedastic Gaussian process regression.
result NS outperforms state-of-the-art methods in detection accuracy and interpretability.
New Thompson sampling uses local uncertainty for better decision making.
problem Sequential decision making with exploration-exploitation dilemma.
method Proposes a new probabilistic modeling framework using local latent variable uncertainty for Thompson sampling, with variational inference and semi-implicit structure.
result Thompson sampling guided by local uncertainty achieves state-of-the-art performance with low computational complexity.
CE improves climate uncertainty quantification using GCM ensembles and observational data.
problem Uncertainty in climate projections due to model inadequacies and variability.
method Conformal ensembles integrating GCM ensembles and observational data.
result CE generates statistically rigorous, easy-to-interpret uncertainty estimates.
New method mitigates bias in BNN+LVs due to non-identifiability.
problem Non-identifiability in BNN+LVs causes biased posterior mode.
method Developed novel inference procedure to mitigate bias.
result Inference method yields high-quality predictions and uncertainty estimates.
Bayesian optimization reduces materials design costs by 10x.
problem Expensive materials design search space with mixed variables.
method Uncertainty-aware machine learning models for mixed numerical and categorical variables.
result Frequentist and Bayesian models perform differently in mixed-variable BO.
Overparametrized neural networks retain significant epistemic uncertainty even with sufficient data.
problem Epistemic uncertainty in overparametrized neural networks persists despite model identifiability.
method Analysis of non-identifiability and characterization of residual uncertainty in one-hidden-layer ReLU networks.
result Substantial parameter uncertainty remains even when the underlying function is fully identified.
Framework for uncertainty estimation in training parameters.
problem Estimating uncertainty in training parameters.
method Marginalizing hyperparameters as random variables, investigating various forms of marginalisation.
result Some marginalisations can reliably estimate uncertainty without extensive tuning.
SVB method provides scalable Bayesian proportional hazards model for high-dimensional gene expression data.
problem Bayesian methods for high-dimensional sparse survival data often sacrifice uncertainty quantification or computational scalability.
method Mean-field variational approximation for scalable Bayesian proportional hazards model.
result SVB method offers posterior distribution for parameters and variable selection via posterior inclusion probabilities.
TSCoNet forecasts correlated geophysical fields with uncertainty estimates.
problem Accurate and reliable forecasts of correlated geophysical fields across many locations.
method Two-stage CNN-LSTM coupled with Gaussian copula.
result Calibrated prediction intervals without sacrificing point accuracy.
DSVNP uses global and local latent variables for improved neural process predictions.
problem Limited expressiveness of vanilla neural processes in capturing target-specific local variation.
method Introduces DSVNP combining global and local latent variables for prediction.
result Competitive prediction performance in multi-output regression and uncertainty estimation.
Proposes a new method for efficient model reconstruction with uncertain parameters.
problem Reconstructing models with latent variables or parameters of unknown distribution.
method Local squared Wasserstein-2 (W_2) method.
result Efficiently reconstructs output distributions from observation data.
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
problem Limited ability of stationary kernels to represent heterogeneous correlation structures.
method Introduces variably scaled kernels to modify correlation structures explicitly.
result Improved reconstruction accuracy and better uncertainty estimates for non-stationary data.
Paper uses PCE to quantify ML model and input uncertainties.
problem Accurately quantify and propagate combined uncertainties in ML predictions.
method Polynomial Chaos Expansion (PCE) for joint input and model uncertainty.
result Efficient and accurate calculation of output variability and sensitivity.
Paper proposes a method to estimate intra-observer variability in echocardiography quality assessment.
problem Intra-observer variability in echocardiography quality assessment impacts deep neural network reliability.
method Modeling intra-observer variability as aleatoric uncertainty in a regression problem.
result The proposed method reduces error from 0.11 to 0.09, improving test accuracy by 5.7%.
Rule-based classifiers quantify uncertainty using Bernoulli random variables.
problem Quantifying the uncertainty of precision estimates for rule-based text classifiers.
method Treat partitions of sub-strings as Bernoulli random variables, compare means using statistical tests, and combine classifiers using Dempster-Shafer theory.
result The approach can be used to combine binary classifiers into a multi-label classifier.
Bayesian sensitivity analysis accounts for model uncertainty.
problem Assessing variable importance in nonlinear models.
method Differentiating Rényi divergence of predictive distribution.
result Accurate and reliable identification of important variables and interactions.
We derive a novel sensitivity analysis of input variables for predictive epistemic and aleatoric uncertainty. We use Bayesian neural networks with latent variables as a model class and illustrate the usefulness of our sensitivity analysis on real-world datasets. Our method increases the interpretability of complex blac…
New method explains sensitivity of test data uncertainty in Bayesian inference.
problem Widespread belief that test data similarity reduces epistemic uncertainty.
method Information-theoretic decomposition of predictive uncertainty.
result Defines sensitivity using information-theoretic quantities.
We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume that we have partial or even no knowledge of the operator but have training data …
This work provides uncertainty intervals for semantic latent variables in disentangled latent spaces.
problem Challenges in providing meaningful uncertainty quantification for semantic information in disentangled latent spaces.
method Uses quantile regression to output heuristic uncertainty intervals, calibrates these intervals to contain true latent values, and propagates them through the generator.
result Reliably communicates semantically meaningful, principled, and instance-adaptive uncertainty in image super-resolution and image completion.
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo estimate for the marginal likelihood that approximately integrates over the late…
SEMF predicts prediction intervals for ML models using latent variables.
problem Uncertainty quantification in ML models, especially for diverse data distributions.
method Supervised Expectation-Maximization Framework (SEMF) extending EM algorithm for latent variable modeling.
result SEMF produces narrower prediction intervals with desired coverage probability.
Deep ensembles effectively capture epistemic uncertainty through training stochasticity, providing a frequentist perspective.
problem Understanding and quantifying epistemic uncertainty in machine learning models.
method Bootstrap-based estimator and decomposition of deep ensembles into data variability and training stochasticity.
result Deep ensembles primarily capture training stochasticity, explaining their effectiveness in quantifying epistemic uncertainty.
LVM-GP solves PDEs with uncertainty using latent variables and Gaussian processes.
problem Uncertainty quantification in PDE solutions with noisy data.
method Combines latent variable model and Gaussian process for uncertainty-aware prediction.
result Efficiently captures functional dependencies and robust uncertainty quantification.
The paper analyzes uncertainty quantification in sparse Gaussian process regression with a Brownian motion prior.
problem Analyzing uncertainty in sparse Gaussian process regression with a Brownian motion prior.
method Theoretical guarantees and limitations for pointwise credible sets are derived for a rescaled Brownian motion prior with a sparse variational Gaussian process method.
result Theoretical characterization of asymptotic frequentist coverage for credible sets, distinguishing conservative and overconfident cases.
Improved covariate shift handling with node-based Bayesian neural networks.
problem Improving generalization under covariate shift in neural networks.
method Introduced node-based Bayesian neural networks that learn latent noise variables to represent input corruptions.
result Node-based BNNs perform well under covariate shift due to input perturbations, improving uncertainty estimation and robustness.
This study shows how trade policy uncertainty affects stock-T bill correlations.
problem The impact of trade policy uncertainty on stock-T bill relationships.
method Extended Dynamic Conditional Correlation (DCC) framework incorporating exogenous variables.
result Trade policy uncertainty significantly alters stock-T bill correlations, especially under specific political conditions.
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.
Deep state space model forecasts time series with uncertainty.
problem Probabilistic forecasting for risk management.
method Parameterized deep networks for non-linear models, recurrent neural nets for dependency, ARD network for exogenous variables.
result Accurate and sharp probabilistic forecasts with realistic uncertainty growth.
Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns in the data. We show how to extract and decompose uncertainty into epistemic and…
Mean Field Variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, it is well known that a major failing of MFVB is its (sometimes severe) underestimates of the uncertainty of model variables and lack of information about model variable covariance.…
Bayesian neural networks improve uncertainty quantification in non-linear dimensionality reduction.
problem Current neural network models lack adequate uncertainty quantification.
method Deploy Markov chain Monte Carlo sampling algorithms for Bayesian inference in ANN models with latent variables.
result New research directions are needed due to fundamental challenges in neural networks with latent variables.
High-risk domains require reliable confidence estimates from predictive models. Deep latent variable models provide these, but suffer from the rigid variational distributions used for tractable inference, which err on the side of overconfidence. We propose Stochastic Quantized Activation Distributions (SQUAD), which im…
Mean field variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, it is well known that a major failing of MFVB is that it underestimates the uncertainty of model variables (sometimes severely) and provides no information about model variable cova…
Precisely forecasting wind speed is essential for wind power producers and grid operators. However, this task is challenging due to the stochasticity of wind speed. To accurately predict short-term wind speed under uncertainties, this paper proposed a multi-variable stacked LSTMs model (MSLSTM). The proposed method uti…
Develops fully Bayesian LVGP for better uncertainty quantification.
problem Uncertainty in qualitative inputs for GP models.
method Maps qualitative inputs to latent variables, uses standard GP over LVs, estimates LVs through ML, develops fully Bayesian approach.
result Significant improvements in prediction accuracy and uncertainty quantification over plug-in approach.
Paper decomposes risk into aleatoric and epistemic uncertainties and generates predictive uncertainty measures.
problem Unclear relationships between various predictive uncertainty measures in literature.
method Bayesian estimation to decompose risk into aleatoric and epistemic uncertainties, generating different predictive uncertainty measures.
result Experimental validation confirms usefulness of derived predictive uncertainty measures for detecting out-of-distribution and misclassified instances.
Framework estimates multiple plausible solutions with uncertainty measures.
problem Machine learning models need to propose multiple plausible solutions with meaningful uncertainty.
method Discrete latent variables model one-to-many mappings, allowing effective conditional probability estimation.
result Framework outperforms state-of-the-art in uncertainty estimation and is practical.
Proposes a new method for variable importance using targeted learning.
problem Uncertainty quantification in variable importance metrics.
method Employing the targeted learning (TL) framework for conditional permutation variable importance.
result Improved accuracy in finite sample contexts compared to traditional methods.
We provide single-model estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty, we propose Simultaneous Quantile Regression (SQR), a loss function to learn all the conditional quantiles of a given target variable. These quantiles can be used to compute well-calibrat…