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 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.
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.
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.
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.
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.
Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier-Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning algorithms have opened up a new area of black-box turbulence models allowing for the tuning of RANS simulati…
Autoregressive state transitions, where predictions are conditioned on past predictions, are the predominant choice for both deterministic and stochastic sequential models. However, autoregressive feedback exposes the evolution of the hidden state trajectory to potential biases from well-known train-test discrepancies.…
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.
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…
We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine learning and statistics. Our estimators leverage the score function based first and…
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.
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.
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…
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.
Investors usually resort to financial advisors to improve their investment process until the point of complete delegation on investment decisions. Surely, financial advice is potentially a correcting factor in investment decisions but, in the past, the media and regulators blamed biased advisors for manipulating the ex…
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…
In this paper, we provide an accessible introduction to the theory of locally convex supermanifolds in the categorical approach. In this setting, a supermanifold is a functor M:Gr→Man from the category of Grassmann algebras to the category of locally convex manifolds that has certai…
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.
Motion analysis is used in computer vision to understand the behaviour of moving objects in sequences of images. Optimising the interpretation of dynamic biological systems requires accurate and precise motion tracking as well as efficient representations of high-dimensional motion trajectories so that these can be use…
This paper describes and discusses Bayesian Neural Network (BNN). The paper showcases a few different applications of them for classification and regression problems. BNNs are comprised of a Probabilistic Model and a Neural Network. The intent of such a design is to combine the strengths of Neural Networks and Stochast…
Neural network language models (NNLMs) have achieved ever-improving accuracy due to more sophisticated architectures and increasing amounts of training data. However, the inductive bias of these models (formed by the distributional hypothesis of language), while ideally suited to modeling most running text, results in …
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.
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.
The time series cluster kernel (TCK) provides a powerful tool for analysing multivariate time series subject to missing data. TCK is designed using an ensemble learning approach in which Bayesian mixture models form the base models. Because of the Bayesian approach, TCK can naturally deal with missing values without re…
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.
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.
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.
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…
A new method for efficient neural network fine-tuning using queryable low-rank update atoms.
problem Rigidity of static low-rank adaptation methods when input and depth-wise computation vary.
method A shared queryable memory of low-rank update atoms, allowing dynamic and context-sensitive adaptation.
result Improves final test performance and training stability compared to standard low-rank adaptation.
This paper studies gradient flows for sampling using various metrics and their affine invariance.
problem Sampling from probability distributions with unknown normalizations.
method Gradient flows in the space of probability measures, focusing on Kullback-Leibler divergence and affine invariance of metrics.
result Gradient flows of Kullback-Leibler divergence do not depend on the normalization constant, and affine invariance is achieved for certain metrics.
This work bounds classification error in machine learning for low Bayes error conditions.
problem Understanding the error mismatch between Bayes error and model-based classification error.
method Applying classification error bounds to study the relationship with Kullback-Leibler divergence and proposing a linear approximation for low Bayes error conditions.
result A linear approximation of the classification error bound for low Bayes error conditions is proposed.
Paper assesses error estimates of Random Forests classification.
problem Quantitative assessment of Random Forests error estimates.
method Theoretical and empirical investigation of various error estimation methods.
result Random Forests' error estimates are closer to true error rate than average prediction error.
This paper tackles worst-class error rate in classification tasks.
problem Minimizing worst-class error rate in classification tasks, especially in medical image classification.
method Designing a boosting approach to bound the worst-class error rate using Deep Neural Networks (DNNs).
result The proposed boosting approach lowers worst-class test error rates while avoiding overfitting.
Study identifies and analyzes three types of errors in learning Fourier operators.
problem Statistical, discretization, and truncation errors in learning Fourier operators.
method Analysis of a Discrete Fourier Transform (DFT) based least squares estimator.
result Established upper and lower bounds on statistical, discretization, and truncation errors.
This paper examines error bounds for deep learning classifiers with noisy labels.
problem Understanding the performance of classifiers trained on noisy data.
method Derives error bounds for excess risk, decomposing it into statistical and approximation errors. Uses independent block construction for statistical dependencies and vector-valued setting for approximation error.
result Established theoretical results for error bounds in deep learning with noisy labels, mitigating the impact of high-dimensional input spaces.
The paper analyzes CycleGAN's error components for unpaired data generation.
problem Analyzing approximation and estimation errors in CycleGAN for unpaired data.
method Decomposes risk into approximation and estimation errors, analyzing each separately and considering their trade-offs.
result Theoretical insights into CycleGAN's performance through error analysis.
Curiosity-Critic improves world model training by focusing on cumulative prediction error.
problem Training world models with intrinsic rewards that consider cumulative prediction error.
method Curiosity-Critic uses a surrogate reward based on the difference between current and asymptotic prediction errors, estimated online by a co-trained critic.
result Curiosity-Critic outperforms other methods in training speed and final world model accuracy.
End-to-end ASR error detection using audio-transcript entailment.
problem Detecting transcription errors in ASR systems to prevent error propagation.
method Proposes a novel end-to-end approach using audio-transcript entailment, with acoustic and linguistic encoders.
result Achieves CER of 26.2% on all transcription errors and 23% on medical errors specifically, improving by 12% and 15.4% respectively over a strong baseline.
The study analyzes and mitigates errors in PC-based causal discovery methods.
problem Errors in PC-based causal discovery methods can lead to incorrect graphs.
method The study introduces coherency scores to detect assumption violations and small sample errors in PC-based methods.
result The coherency scores can detect errors that other methods cannot, bridging between global and local error detection.
The paper bounds the mean absolute error in DNN vector-to-vector regression.
problem Bounding the mean absolute error in deep neural network based vector-to-vector regression.
method Error decomposition techniques in statistical learning theory and non-convex optimization theory were used to derive upper bounds for approximation, estimation, and optimization errors.
result Theoretical upper bounds for mean absolute error in DNN vector-to-vector regression were derived and validated experimentally.
This paper analyzes error in SKI for Gaussian Processes, providing conditions for linear time inference.
problem Lack of rigorous theoretical error analysis for SKI.
method Proved error bounds for SKI Gram matrix, examined error effects, provided practical guidelines.
result Identified two dimensionality regimes for SKI's scalability-accuracy trade-offs.
New truthful calibration errors improve model ranking in multiclass prediction.
problem Non-truthful calibration errors can mislead model comparisons.
method Introduced perfectly truthful calibration errors for multiclass predictions.
result Truthful calibration errors preserve decision-theoretic dominance and stabilize model rankings.
Study loop corrections in random feature models affecting training and test errors.
problem Analyzing loop corrections in random feature models to understand training and test errors.
method Statistical physics and effective field theory approach to study loop corrections.
result Derived loop corrections to training error, test error, and generalization gap.