Paper tackles uncertainties in reduced-order modeling of complex systems.
problem Model-form uncertainties in reduced-order modeling of complex systems.
method Combines Riemannian projection and retraction operators on a subset of the Stiefel manifold with an information-theoretic formulation.
result Identifies and quantifies the impact of model-form uncertainties on inferred operators.
New framework quantifies uncertainty in reduced-order models for PDEs.
problem Quantifying reliability of reduced-order model predictions for PDEs.
method Combining stochastic representation of reduced bases with conformal-type methods.
result Provides prediction sets with coordinate miscoverage guarantees.
Framework corrects model form errors in structural dynamics predictions.
problem Model form errors in parametric models of structural dynamics.
method Gaussian Process Latent Force Model (GPLFM) for non-parametric discrepancy representation, linear Bayesian filtering for state and discrepancy estimation, modal reduction for computational tractability.
result Significant reduction of displacement and rotation prediction errors under unseen excitations.
Physics-informed IFT models physical systems with uncertainty, independent of numerical schemes.
problem Modeling physical systems with unknown elements like missing parameters and noisy data.
method Physics-informed Information Field Theory (PIFT) that combines measurements with physical laws, independent of numerical schemes.
result PIFT can capture multiple modes and solve ill-posed problems, robust to model-form uncertainty.
This work improves RANS predictions and quantifies uncertainties using Bayesian deep neural networks.
problem Uncertainty in data-driven turbulence models for RANS simulations.
method Invariant Bayesian deep neural network trained with Stein variational gradient descent, uncertainties propagated via Monte Carlo simulation.
result Quantitative measurement of model confidence and uncertainty quantification for flows with limited data.
Proposes a framework to identify and correct model-form errors in nonlinear systems.
problem Model-form errors in nonlinear dynamical systems due to unknown or approximated governing equations.
method Uses a hybrid approach combining machine learning and Bayesian filtering to estimate and correct model-form errors.
result Improves the predictive capability of known but approximate governing equations for nonlinear dynamical systems.
Framework predicts responses in misspecified systems using GPLFM and BNNs.
problem Predicting responses in dynamical systems with model misspecification.
method Integrates GPLFM and BNNs for uncertainty-aware inference and prediction.
result Systematic propagation of uncertainty from diagnosis to prediction.
SGMs are robust to practical errors via uncertainty quantification.
problem Robustness of SGMs to practical implementation errors.
method Wasserstein uncertainty propagation (WUP) theorem and Bernstein estimates.
result SGMs are provably robust to multiple sources of error.
Neural network fusion reduces data acquisition costs for multi-fidelity sources.
problem Reducing cost in acquiring information from multiple data sources with varying fidelity.
method Employing a novel neural network architecture for nonlinear manifold learning of multi-fidelity data.
result Our approach provides high predictive power and quantifies various sources uncertainties.
New Wasserstein divergence improves generative model robustness and structure preservation.
problem Improving generative model robustness and structure preservation.
method Introduces a novel Wasserstein-1 path-space divergence and a WUP theorem.
result Derives robustness and generalization bounds for flow-based models.
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate co…
Unified HS and related methods with explicit modeling assumptions.
problem Lack of clear assumptions in HS methods for Value-at-Risk.
method Explicitly defined parametric model for asset returns and extraction of innovation process.
result HS and related methods require more assumptions than commonly acknowledged.
Paper combines latent state space with CRF for improved autoregressive text generation.
problem Autoregressive models expose hidden state trajectory to biases.
method Combines latent state space model with CRF observation model.
result Improved performance on unconditional sentence generation compared to RNN and GAN baselines.
This paper investigates the hedging effectiveness of a dynamic moving window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dy…
Estimates complex models without assuming Gaussian symmetry, achieving near-optimal performance.
problem Estimating high-dimensional non-Gaussian models with non-linear relationships.
method Uses Stein's identities and thresholding for robust estimation.
result Achieves near-optimal statistical rate of convergence in various settings.
The study analyzes how large language models form and express investor risk profiles.
problem Understanding how large language models (LLMs) form and express investor risk profiles.
method Examined three LLMs (GPT, Gemini, and Llama) and assessed their responses to a standardized risk questionnaire under varying prompts.
result LLMs generally form long-term investment profiles, but they exhibit different risk tolerance levels.
Model shows how advisors can manipulate naive investors.
problem How financial advisors manipulate naive investors.
method Agent-Based Model with Nash equilibria and best response functions.
result Greediness/naivety of investors emerge naturally from the model.
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights in the linear combination is modelled by another linear Gaussian dynamical model…
This work tackles the challenge of aligning generative models without explicit reward signals.
problem Aligning generative models without explicit reward signals.
method A Bilevel Optimization framework where the reward function is treated as the optimization variable of an outer-level problem.
result Theoretical analysis and insights generalize to tabular classification and model-based reinforcement learning.
New algorithm for fitting Gaussian mixtures using Wasserstein-Fisher-Rao geometry.
problem Hard problem of fitting Gaussian mixture models to data computationally.
method Gradient descent over Wasserstein-Fisher-Rao geometry for probability measures.
result Established convergence guarantees for the proposed algorithm.
Paper presents faster, robust adversarial training methods.
problem Increasing neural network robustness against adversarial attacks.
method Integrates FGSM with Pixelwise Noise Injection Layer (PNIL) and uniform noise.
result Achieves comparable results to PGD-based adversarial training but faster.
The paper defines supermanifolds via multilinear bundles and shows their structure.
problem Defining and understanding supermanifolds in a clear, accessible way.
method Categorical approach, using multilinear bundles and projective limits.
result Supermanifolds can be seen as infinite-dimensional fiber bundles.
LMGPs enable efficient, accurate data fusion across multiple data sources.
problem Data fusion across multi-fidelity data sources in engineering design.
method Latent-map Gaussian processes (LMGPs) for efficient and accurate data fusion.
result LMGPs provide increased accuracy, reduced costs, and flexibility to fuse any number of data sources.
The Brownian bridge serves as a physics-informed prior for solving the Poisson equation.
problem Reconstructing physical fields from limited and noisy data with known governing equations.
method Formalizing inverse problems via Bayesian inference in function spaces using a Brownian bridge Gaussian process.
result The Brownian bridge Gaussian process can be viewed as a physics-constrained prior for the Poisson equation, allowing for a fully Bayesian framework.
Combines neural networks and probabilistic graphical models for efficient higher-order inference.
problem Lack of efficient higher-order relational information in graph neural networks and probabilistic graphical models.
method Derives efficient approximate sum-product loopy belief propagation for higher-order PGMs, embeds into neural network, proposes methods for constructing higher-order factors.
result Substantially outperforms state-of-the-art k-order graph neural networks in molecular datasets.
Deep learning predicts human survival from cardiac MRI motion data.
problem Predicting human survival from cardiac MRI motion data.
method Fully convolutional network for dense motion modeling, autoencoder for latent code learning, Cox partial likelihood loss for right-censored data.
result Predictive accuracy (C-index) significantly higher (p < .0001) for deep learning model (C=0.73) than human benchmark (C=0.59).
Enhances neural models with simple functions to improve language modeling.
problem Neural models struggle with certain spatial, temporal, or quantitative relationships.
method Integrates simple functions into neural architecture to form a hierarchical NSLM.
result NSLMs significantly reduce perplexity in small-corpus language modeling.
Model stitching compares neural representations, revealing insights not captured by CKA.
problem Understanding internal neural representations.
method Model stitching connects neural network layers to study representations.
result Good networks trained differently can be stitched without performance drop.
Bayesian Neural Networks combine neural networks and stochastic models for probabilistic predictions.
problem Creating probabilistic guarantees for neural network predictions.
method Combines neural networks and stochastic models, focusing on posterior distribution generation.
result BNNs provide probabilistic guarantees and distribution of learned parameters.
The paper proposes a new method to calibrate multiple computer models simultaneously.
problem Calibrating multiple computer models one at a time is inefficient.
method Developed a probabilistic framework using customized neural networks.
result Simultaneous calibration improves predictive accuracy but can be non-identifiable in high dimensions.
New model explains neural collapse and limits on minority classes in imbalanced datasets.
problem Understanding and predicting performance limits of deep learning models on imbalanced datasets.
method Layer-Peeled Model, a nonconvex optimization program isolating top layers and applying constraints.
result Reveals a new phenomenon called Minority Collapse that limits deep learning models on minority classes.
Novel trading strategy for generalized lattice markets ensures positive profits.
problem Trading in markets with serially correlated returns and asset correlation.
method Multi-double linear policies in a generalized lattice market model.
result Proposed policies ensure positive expected profits in a lattice market.
Enhances TCK for missing data and incomplete labels in time series.
problem Missing data and incomplete labels in time series analysis.
method Ensemble learning with Bayesian mixture models, representation of missing patterns, semi-supervised learning.
result Improved accuracy in similarity learning for time series with missing and incomplete labels.
Unified method for input, data, and model uncertainty in neural networks.
problem Uncertainty in neural network inputs and outputs.
method Propagating uncertainty through inputs using a unified formulation.
result More stable decision boundaries with input noise, and propagation of input uncertainty to model outputs.
This paper benchmarks uncertainty disentanglement across various tasks.
problem Disentangling multiple sources of uncertainty for specialized tasks.
method Reimplemented and evaluated a wide range of uncertainty estimators.
result No existing approach provides disentangled uncertainty estimators in practice.
Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of these models is their interpretability: the transfer functions provide visual means…
Unified Bayesian framework for quantifying GNN uncertainty.
problem Quantifying uncertainty in GNN predictions due to modeling errors and measurement uncertainty.
method Unified Bayesian framework with aleatoric uncertainty from probabilistic links and feature noise, and epistemic uncertainty from model parameter distribution. Uses Assumed Density Filtering for aleatoric uncertainty and Monte Carlo dropout for model parameter uncertainty.
result Bayesian model performs similarly to frequentist model and provides additional uncertainty information.
Paper recovers uncertainty from dynamic valuation rules.
problem Recovering latent uncertainty from observable valuation rules.
method Developed procedures to identify and characterize uncertainty structures from valuation rules.
result Valuation rules contain sufficient information to identify and recover uncertainty structures.
Proposes a new criterion for reliable uncertainty estimation in deep neural networks.
problem Inability of existing approaches to provide reliable uncertainty estimates for deep neural networks.
method Develops a density uncertainty layer architecture that satisfies the proposed criterion.
result Density uncertainty layers provide more reliable uncertainty estimates and robust out-of-distribution detection.
PNs model distributional uncertainty in predictive AI predictions.
problem Uncertainty in AI predictions, distinguishing between model and data uncertainty.
method Prior Networks (PNs) parameterize a prior distribution over predictive distributions.
result PNs outperform previous methods in identifying out-of-distribution samples and detecting misclassification.
Proposes a method to quantify uncertainty in graph neural networks for node classification.
problem Uncertainty in graph neural networks for node classification.
method Bayesian uncertainty propagation (BUP) method embedding GNNs in a Bayesian framework.
result Demonstrates superior performance of the proposed method on benchmark datasets.
A framework for estimating both epistemic and aleatoric uncertainties in reinforcement learning.
problem Estimating risk and uncertainty in deep reinforcement learning.
method Proposed a framework for disentangling and estimating epistemic and aleatoric uncertainties on learned Q-values, derived unbiased estimators, and introduced an uncertainty-aware DQN algorithm.
result The uncertainty-aware DQN algorithm exhibits safe learning behavior and outperforms other DQN variants on the MinAtar testbed.
Survey on uncertainty in ML and DL, covering sources, quantification, and decision-making.
problem Understanding and quantifying uncertainty in ML and DL for risk-sensitive applications.
method Structured review of literature, categorizing uncertainty, assessing uncertainty quantification techniques.
result Broadened scope of uncertainty discussion and updated DL uncertainty quantification methods.
Unified Uncertainty Calibration improves AI predictions by combining different types of uncertainty.
problem AI classifiers struggle with uncertainty, leading to miscalibrated predictions and poor performance.
method Unified Uncertainty Calibration (U2C) combines aleatoric and epistemic uncertainties to improve prediction quality.
result U2C outperforms traditional reject-or-classify methods across various ImageNet benchmarks.
Proposes a new principle for active learning based on epistemic uncertainty.
problem Active learning and uncertainty quantification in machine learning.
method Distinction between epistemic and aleatoric uncertainty; proposes epistemic uncertainty sampling.
result Epistemic uncertainty sampling shows promising performance in experimental studies.
New method combines ODE filters and numerical quadrature to propagate model uncertainty.
problem Propagation of model uncertainty in ODE solutions with uncertain parameters.
method Combining ODE filters with numerical quadrature.
result Effective propagation of both numerical and parametric uncertainty.
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.
New method estimates model uncertainty in regression.
problem Challenges in distinguishing aleatoric and epistemic uncertainty.
method Conditional predictions with model's initial output.
result Rigorous frequentist approach to epistemic uncertainty.