Bayesian neural network models improve uncertainty quantification in multivariate regression.
problem Uncertainty quantification in multivariate regression models with heteroscedastic noise.
method Proposes Bayesian Last Layer neural network models and EM algorithms for parameter learning.
result Capable of disentangling aleatoric and epistemic uncertainty.
Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes filters are typically assumed to be a fixed covariance matrix. This assumption is r…
TQF models multivariate uncertainty by learning conditional quantiles.
problem Challenges in fully nonparametric estimation of multivariate conditional distributions.
method Tomographic Quantile Forests (TQF) learns conditional quantiles of directional projections.
result TQF reconstructs multivariate conditional distribution efficiently without convexity restrictions.
Paper proposes a new method to evaluate joint risk under uncertainty.
problem Evaluating joint risk of multiple insurance risks under dependence uncertainty.
method Axiomatic approach to scalar and vector-valued distortion joint risk measures.
result Established a new scalar distortion joint risk measure with positive homogeneity.
NGBoost boosts multivariate probabilistic regression.
problem Joint probabilistic regression for multivariate targets.
method Natural Gradient Boosting for nonparametric modeling.
result Competitive performance in oceanographic velocity prediction.
Optimal transport improves multivariate prediction uncertainty quantification.
problem Uncertainty quantification in multivariate learning tasks, especially in regression and classification.
method Introducing a novel Conformal Prediction procedure using optimal transport to handle multivariate score functions and construct flexible prediction regions.
result Ensures finite-sample, distribution-free coverage guarantees for multivariate prediction sets.
AdaPTS adapts univariate FMs for multivariate time series forecasting.
problem Challenges in managing feature dependencies and uncertainty quantification in multivariate time series forecasting.
method Adapters that transform multivariate inputs into a latent space and apply univariate FMs independently to each dimension.
result AdaPTS enhances forecasting accuracy and uncertainty quantification compared to baseline methods.
Develops a method for multivariate time series prediction intervals.
problem Uncertainty quantification in multivariate time series forecasting.
method Conformal prediction method for multivariate time series.
result Empirically demonstrates valid coverage of prediction regions.
The paper bounds solutions to complex optimization problems with uncertain data.
problem Distributionally robust optimization problems with multivariate uncertainty sets.
method Conditions and bounds derived for multivariate and univariate Wasserstein distances, Bregman-Wasserstein divergences, and signed Choquet integrals.
result Computable lower and upper bounds for DRO problems, derived from scalar-valued aggregation functions and Wasserstein distances.
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the training sample. The estimated uncertainties can be propagated into the optimal…
Bayesian method for multivariate autoregressive models with exogenous inputs.
problem Estimating uncertainties in autoregressive models with exogenous inputs.
method Recursive Bayesian estimation via message passing in a factor graph.
result Produces full posterior distributions for autoregressive coefficients and noise precision.
This paper introduces a novel recalibration method for multivariate forecasts.
problem Multivariate calibration for potentially misspecified models.
method Local mappings between marginal probability integral transform values and observed space, using K-nearest neighbors or normalizing flows.
result Demonstrated effectiveness on currency exchange rate and childhood malnutrition data.
Bayesian method improves multivariate periodontal outcome modeling.
problem Modeling periodontal outcomes is challenging and requires consideration of demographic differences.
method Jointly models multivariate outcomes using an online Bayesian transfer learning framework.
result Significant improvement over univariate RECaST method demonstrated.
New method extends conformal prediction to multivariate settings using optimal transport.
problem Limited applicability of conformal prediction to multivariate real-valued scores.
method Use optimal transport to define vector-ranks and multivariate quantile regions for finite-sample coverage.
result Constructs the first multivariate conformal predictive distributions with finite-sample calibration.
New method extracts aleatoric and epistemic uncertainties from regression-based neural networks.
problem Need for principled uncertainty reasoning in machine learning systems.
method Learning evidential distributions for aleatoric and epistemic uncertainties.
result Allows for the simultaneous extraction of both uncertainties without sampling or out-of-distribution data.
Develops a framework for inferring causal relationships in networked data with uncertainty quantification.
problem Extracting reliable inference from complex Hawkes network data with uncertainty.
method Statistical inference framework based on maximum likelihood estimation and concentration inequalities of continuous-time martingales.
result Provides a non-asymptotic confidence set for uncertainty quantification.
OTCP extends conformal prediction to multivariate data using optimal transport.
problem Uncertainty quantification in multivariate machine learning models.
method OTCP leverages optimal transport to rank multivariate conformity scores.
result Preserves distribution-free coverage guarantees in multidimensional settings.
Proposes a method to generate multivariate prediction intervals for random forests.
problem Uncertainty estimates for iterative design of experiments with multiple correlated model outputs.
method Recalibrated bootstrap method for bagged models.
result Significantly decreases the number of iterations required for satisfactory candidate in sequential learning problems.
In this paper, we analyze the behavior of the multivariate symmetric uncertainty (MSU) measure through the use of statistical simulation techniques under various mixes of informative and non-informative randomly generated features. Experiments show how the number of attributes, their cardinalities, and the sample size …
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantag…
Enformer and GEnformer use Transformers with stochastic learning to forecast multivariate and spatiotemporal data with uncertainty.
problem Uncertainty quantification in multivariate time series and spatiotemporal forecasting.
method Synthesizing Transformer's expressive power with stochastic learning to model conditional distributions directly.
result Enformer and GEnformer yield calibrated probabilistic forecasts and outperform state-of-the-art baselines.
Framework for optimizing portfolios under model uncertainty.
problem Optimizing portfolios in volatile markets considering model uncertainty.
method Dynamic programming and robust optimization for Markov decision processes.
result Robust optimization leads to better portfolio strategies in uncertain market conditions.
Proposes mCS for multivariate selection with FDR control.
problem Selecting high-quality candidates from multivariate datasets.
method Introduces regional monotonicity and multivariate nonconformity scores.
result Significantly improves selection power with FDR control.
We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion and multivariate Rosenblatt motion. Conditions for no-arbitrage and market comp…
DRF improves confidence and uncertainty assessment for multivariate conditional distributions.
problem Estimating multivariate conditional distributions with confidence and uncertainty.
method Developed a bootstrap approximation of the asymptotic distribution of DRF to derive inferential tools.
result Asymptotic coverage guarantees for confidence regions and hypothesis testing.
The paper introduces a method to model error correlations in multivariate time series forecasting.
problem Accurate modeling of error correlations for reliable uncertainty quantification.
method Plug-and-play method that learns error covariance over multiple steps using low-rank-plus-diagonal and independent latent temporal processes.
result Improves predictive accuracy and uncertainty quantification without significantly increasing parameter size.
Paper proposes a new method for predicting DER adoption with hierarchical guarantees.
problem Accurately predicting DER adoption in electric grids with uncertainty and spatial disparity.
method Multivariate Hawkes process for modeling DER adoption dynamics and split conformal prediction algorithm for hierarchical validity.
result Empirical evaluation shows superior predictive accuracy and uncertainty calibration compared to existing methods.
New method assesses financial and cyber risks under uncertainty.
problem Uncertainty in risk assessment for financial and cyber systems.
method Combines stochastic approximation and distorted mix method to compute worst case average value at risk.
result Efficient algorithm for tail uncertainty in multivariate distributions.
In this paper we investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black-Scholes type financial market which may be incomplete. We impose a constraint on the admissible strategies that prevents a pure bond investment and we include uncertainty by means of ellipsoidal un…
Proposes MVG-CRPS for robust multivariate forecasting.
problem Outliers in multivariate forecasting lead to significant errors.
method Integrates CRPS for MVG distributions, optimizing with MVG-CRPS.
result Improves robustness, accuracy, and uncertainty quantification.
LSSDM improves imputation of multivariate time series data.
problem Imputation of multivariate time series data without labels.
method LSSDM projects observed data into latent space, reconstructs missing values without labels, and uses a conditional diffusion model for precise imputation.
result LSSDM achieves superior imputation performance and uncertainty analysis.
TSMB handles time delays in multivariate time series data.
problem Varying time delays in multivariate time series data complicate predictions.
method Time Series Model Bootstrap (TSMB) framework for nonparametric time delay estimation.
result TSMB improves model performance in dynamic data environments.
This tutorial simplifies Gaussian process regression for beginners.
problem Understanding Gaussian process regression for machine learning.
method Explains basic concepts, provides a concise GPR description, and reviews implementation packages.
result Clear understanding of Gaussian process regression fundamentals.
We introduce a model for causal structure learning from multivariate functional data, even when graphs have cycles.
problem Discovering causal relationships from multivariate functional data with cycles.
method Functional linear structural equation model with a low-dimensional causal embedded space.
result The proposed model is causally identifiable under standard assumptions.
A new kernel-based nonconformity score improves multivariate prediction regions.
problem Tackling the challenge of compressing multivariate residual vectors into scalars while preserving geometric structure.
method Introducing a Multivariate Kernel Score (MKS) that decomposes into an anisotropic MMD, providing finite-sample coverage guarantees and convergence rates.
result The MKS produces prediction regions that explicitly adapt to geometric structure, reducing volume compared to ellipsoidal baselines.
BayOTIDE tackles imputation of irregularly sampled multivariate time series with uncertainty quantification.
problem Imputation of irregularly sampled multivariate time series with missing values and noises.
method BayOTIDE treats multivariate time series as a combination of low-rank temporal factors with different patterns, using Gaussian Processes (GPs) as functional priors and converting them into state-space priors for scalable online inference.
result BayOTIDE can handle imputation over arbitrary time stamps and offers uncertainty quantification and interpretability.
Decision-calibrated prediction sets improve power system operations by reducing unnecessary costs.
problem Balancing operating costs and reliability in power systems with renewable uncertainty.
method Learn conditional prediction sets as sub-level sets of norm-based score functions, calibrate uncertainty sets based on reliability of downstream decisions.
result Decision-calibrated sets lead to more efficient operations with smaller uncertainty sets and lower costs compared to standard coverage-based calibration.
Optimizes minimum-volume prediction sets for multivariate regression.
problem Lack of efficient methods for multivariate conformal prediction.
method Optimization-driven framework for minimum-volume covering sets.
result Efficient and informative prediction sets with tight coverage.
Novel framework for uncertainty quantification in metric spaces.
problem Uncertainty quantification in regression models with metric responses.
method Developed algorithms for large datasets, agnostic to predictive models, with asymptotic and non-asymptotic guarantees.
result Asymptotic and non-asymptotic guarantees for special cases, demonstrated in clinical applications.
Framework for imputing time series data with uncertainty measures.
problem Handling missing values in time series data, especially in healthcare.
method Uncertainty-aware multivariate time series imputation framework.
result Selective imputation of less uncertain values improves downstream tasks.
Robust fuzzy clustering for EEG driver alertness with outlier detection.
problem Ambiguous state boundaries in multivariate time series data.
method RFCPCA, a robust fuzzy subspace-clustering method for MTS.
result RFCPCA improves clustering accuracy and characterizes uncertainty and outliers in MTS.
GP model calibration improves optimization algorithm performance.
problem GP model uncertainty calibration issues degrade optimization performance.
method Kernel validation procedure to calibrate GP predictions.
result Proper calibration enhances optimization algorithm convergence.
We develop a sparse representation method for neural network uncertainty.
problem Estimating model uncertainty in neural networks.
method Sparse representation of model uncertainty using inverse Multivariate Normal Distribution (MND), with a novel sparsification algorithm and analytical sampler.
result The information form of neural networks can be effectively applied for model uncertainty representation, showing competitive performance.
Paper proposes a new method for probabilistic electricity price forecasting.
problem Accurate estimation of forecast uncertainties for optimal decision making.
method Implicit generative ensemble post-processing using an ensemble of point forecasting models.
result Method outperforms well-established model combination benchmarks.
MES-LSTM hybrid method improves multivariate time series forecasting and mortality modeling.
problem Challenges in applying hybrid forecast methods to multivariate data.
method Generalized multivariate extension of ES-RNN, utilizing vectorized implementation.
result MES-LSTM shows significant improvement over pure statistical and deep learning methods in forecast accuracy and prediction interval construction.
Bayesian approach for multivariate density regression of complex data.
problem Regression of multivariate density-valued responses on predictors.
method Bayesian inference using sliced Wasserstein barycenter and SW distance.
result Accurate fits and reliable predictions for complex data.
Improved multivariate conformal prediction by standardizing residuals.
problem Weak conditional coverage in heteroskedastic multivariate settings.
method Natural extension of univariate normalization to multivariate setting, whitening residuals and standardizing local variance.
result Standardized residuals yield asymptotic conditional coverage under certain distributions.
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation …