A new method using energy distance for ensemble and scenario reduction.
problem Solving complex dynamic and stochastic programs, especially in energy systems.
method Proposes a new method based on energy distance for ensemble and scenario reduction.
result Reduced scenario sets exhibit better statistical properties for energy distance than Wasserstein distance.
New neural model learns from sequences without time backpropagation.
problem Learning useful temporal generative models from sequential data.
method Developed Temporal Neural Coding Network and Discrepancy Reduction algorithm based on predictive coding.
result Algorithm shows promise on bouncing balls generative modeling problem.
A new method for density estimation using mixture discrepancy and moments.
problem Generalizing histogram statistics to higher dimensions.
method Density estimation via mixture discrepancy and moments (DSP-mix and MSP).
result DSP-mix and MSP are computationally tractable and maintain accuracy with increased speed.
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.
A new method for kernel tests without data splitting increases power.
problem Lack of power in kernel-based tests due to data splitting.
method Selective inference framework to learn hyperparameters and test on full sample.
result Empirically larger test power without data splitting, regardless of split proportion.
New method reduces data dimensionality using tempered distributions.
problem Unsupervised dimension reduction problem.
method Reformulate UDR as approximating an empirical probability density function by a tempered distribution, inducing a sufficient dimension reduction problem.
result An algorithm for UDR induces an algorithm for SDR and vice versa.
LMC improves sampling from complex distributions using quasi-random sequences.
problem Sampling from complex high-dimensional distributions with high accuracy.
method Using completely uniformly distributed (CUD) sequences in Langevin Monte Carlo (LMC) to generate Gaussian perturbations.
result LMC with low-discrepancy CUD sequences achieves smaller estimation error than standard LMC.
W2S FT often outperforms weak teachers due to low intrinsic dimensionality.
problem Understanding why weak-to-strong finetuning outperforms weak models.
method Analyzing W2S in ridgeless regression setting, focusing on variance reduction.
result Weak teacher's variance is inherited by strong student in shared feature subspace, reduced in discrepancy subspace.
New lower bounds for linear classification problems in high dimensions.
problem Linear classification problems in high-dimensional spaces.
method Reduction from hardness conjectures for Affine Degeneracy testing and k-Sum problems.
result Matching lower bounds of Ω(n^d) and respectively Ω(1/ε^d) for Maximum Halfspace Discrepancy problem.
Generative adversarial networks benefit from optimal input dimension and adaptive generator architecture.
problem Minimizing generalization error in GANs through optimal input dimension.
method Introducing generalized GANs (G-GANs) with group penalty and architecture penalty for adaptive dimensionality reduction and network architecture identification.
result G-GANs achieve superior performance with 40%+ improvements in maximum mean discrepancy or Frechet inception distance compared to off-the-shelf methods.
Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generat…
Optimizes kernel discrepancies by selecting subsets efficiently.
problem Improving kernel discrepancies for QMC methods.
method Introduces a novel subset selection algorithm for kernel discrepancies.
result Efficiently generates low-discrepancy samples from various distributions.
This paper introduces localized discrepancy theories for unsupervised domain adaptation.
problem Improving generalization bounds for unsupervised domain adaptation.
method Localized discrepancies defined on the hypothesis space after localization, leading to smaller and asymmetric values.
result Improved generalization bounds and sample complexity reduction.
New discrepancy function compares discrete probability measures considering space geometry.
problem Comparing discrete probability measures in a geometrically meaningful way.
method Proposes the Fourier Discrepancy Function, proving convexity, differentiability, and providing gradient formula.
result Proves the Fourier Discrepancy is convex, twice differentiable, and provides an explicit gradient formula.
Novel MBRL method for large-scale RL with reduced posterior complexity.
problem Theoretical guarantees for MBRL in large spaces with complex models.
method Kernelized Stein Discrepancy for compression of posterior estimate.
result Sublinear Bayesian regret and up to 50% reduction in training time.
The article introduces practical estimators for kernel discrepancies.
problem Estimating kernel discrepancies accurately and efficiently.
method Presented various estimators for MMD, HSIC, and KSD, including V-statistics, U-statistics, and incomplete U-statistics. Stressed the importance of kernel bandwidth and introduced adaptive estimators.
result Adaptive estimators combining multiple estimators with various kernels address the problem of kernel selection.
Researchers develop methods to reduce simulation costs for cardiovascular modeling.
problem High computational cost of high-fidelity simulations in cardiovascular modeling.
method Use low-fidelity approximations, neural networks, and normalizing flows to construct surrogates.
result Validated methods reduce computational cost while maintaining accuracy.
This study compares MC and QMC methods for derivative pricing, showing QMC's superior convergence rates.
problem Improving derivative pricing accuracy and efficiency in high-dimensional settings.
method Compared Monte Carlo and quasi-Monte Carlo techniques, focusing on convergence rates and low-discrepancy sequences.
result Quasi-Monte Carlo methods achieve superior convergence rates and reduce root mean square error in derivative pricing.
Proposes PHD to measure domain discrepancy for complex models.
problem Insufficient domain discrepancy measures for complex models.
method Introduces PHD, a novel discrepancy measure for complex models.
result PHD is computationally efficient and applicable to multi-class classification.
Paper defines class discrepancy for machine learning problems and provides coresets.
problem Addressing discrepancies in machine learning models.
method Defines class discrepancy, provides techniques for bounding discrepancy, and develops coresets and streaming sketches.
result Establishes coresets of size O(sqrt{d}/epsilon) for various machine learning problems.
Feature noise causes loss discrepancies across groups even with equal data.
problem Loss discrepancies observed in learning procedures across different groups.
method Characterized the effect of feature noise on loss discrepancy in linear regression.
result Feature noise leads to loss discrepancy even when groups have equal data.
New KCC-SDs improve distribution comparison in high dimensions.
problem Challenges in high-dimensional Stein discrepancies.
method Kernelized complete conditional Stein discrepancies (KCC-SDs).
result KCC-SDs outperform baselines in distinguishing distributions.
MPMC generates low-discrepancy points using graph neural networks.
problem Generating efficient low-discrepancy point sets.
method Leveraging Graph Neural Networks to model geometric properties.
result Achieves state-of-the-art performance in generating low-discrepancy points.
Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.
problem The curse-of-dimensionality in kernelized Stein discrepancy (KSD).
method Sliced Stein discrepancy and its scalable variants using optimal one-dimensional projections.
result Significantly outperforms KSD and baselines in goodness-of-fit tests and improves model learning.
Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.
problem Inadmissibility of the corrected Akaike information criterion for estimating Kullback-Leibler discrepancy.
method Loss estimation framework to demonstrate inadmissibility and provide improved estimators.
result Improved estimators of Kullback-Leibler discrepancy are provided and perform well in reduced-rank situations.
A new method detects and compacts saturated entries in antisparse coding.
problem Efficiently solving antisparse coding problems with ℓ∞-norm penalties. method Safe squeezing methodology to detect and compact saturated entries, reducing problem dimensionality.
result The method accelerates the computation of antisparse representation by detecting and compacting saturated entries.
Framework synthesizes geological images minimizing patch distribution discrepancy.
problem Synthesizing realistic geological images from a single exemplar.
method Uses kernel discrepancies and generative neural networks for efficient synthesis.
result Synthesized images match visual patterns and spatial statistics of the exemplar.
Paper warns of metric deformation in manifold learning, leading to incorrect answers.
problem Metric deformation in manifold learning.
method Analysis of manifold learning techniques.
result Metric deformation can lead to incorrect answers in manifold learning.
Semi-parametric framework for nonlinear system identification
problem Nonlinear system identification
method Orthogonal Gaussian process regression
result Interpretable models from incomplete physics
A new discrepancy method improves efficiency and accuracy in unsupervised domain adaptation.
problem Measuring the difference between source and target domains without labeled target data.
method Source-guided discrepancy (S-disc) that uses source domain labels for efficient computation and tighter generalization bounds.
result S-disc provides a tighter generalization error bound than existing discrepancies.
Survey of kernels, RKHS, and their applications in machine learning.
problem Understanding kernels and their applications in machine learning.
method Review of historical context, mathematical definitions, and practical applications of kernels.
result Comprehensive overview of kernels, RKHS, and their applications.
TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.
problem Transfer learning challenges due to domain divergence.
method TMDA uses low-dimensional manifolds to represent subdomains and aligns local data distribution discrepancies across domains using M3D.
result TMDA is a promising method for various transfer learning tasks.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
This work proves the optimal estimation rates for popular kernel discrepancies.
problem Estimating the disagreement of distributions using kernel discrepancies.
method Proving minimax lower bounds for MMD, HSIC, and KSD.
result The minimax lower bound for estimation of MMD, HSIC, and KSD is \( n^{-1/2} \) on general topological spaces.
The paper explores conditions for interval exchange transformations to yield low-discrepancy sequences.
problem Conditions for interval exchange transformations to produce low-discrepancy sequences.
method Analyzes interval exchange transformations and applies ergodic theory.
result Constructs infinitely many interval exchange transformations with low-discrepancy orbits for n≥4. The paper highlights the importance of model discrepancy in cardiac simulations.
problem Uncertainty in model structure and equations affects predictions.
method The authors use Gaussian processes and autoregressive-moving-average models to account for model discrepancy.
result Different methods to account for model discrepancy have advantages and shortcomings.
A new metric DJP-MMD improves domain adaptation by balancing transferability and discriminability.
problem Improving domain adaptation performance by balancing transferability and discriminability.
method Discriminative Joint Probability Maximum Mean Discrepancy (DJP-MMD) replaces the traditional joint MMD.
result DJP-MMD outperforms traditional MMDs in image classification tasks.
We approximate the Sobolev discrepancy for finite dimensional kernels from samples.
problem Estimating the Sobolev discrepancy for complex models from finite data.
method Approximating the Sobolev discrepancy using finite samples and analyzing the approximation error.
result The Sobolev discrepancy can be approximated from finite samples and its error depends on the approximation and statistical errors.
Stochastic Stein Discrepancies improve inference efficiency.
problem Intractable computation of Stein discrepancies.
method Subsampled approximations of Stein operators.
result Stochastic Stein Discrepancies inherit convergence properties of standard SDs.
Bayes-consistent disagreement discrepancy loss improves model robustness.
problem Distribution shift in real-world neural network deployment.
method Introducing a novel disagreement loss that is Bayes consistent.
result Proves existing surrogates for disagreement discrepancy are not Bayes consistent.
New method discovers discrepancies between simplified models and experimental data.
problem Model discrepancies in nonlinear systems lead to significant deviations from true behavior.
method Sparse Identification of Nonlinear Dynamics (SINDy) algorithm to discover sparse model terms.
result Improvement in performance with a discrepancy model in simulations.
New method estimates model discrepancy without sampling for unnormalized models.
problem Evaluating and training unnormalized density models efficiently.
method Estimate Stein discrepancy using neural network parameterized vector function.
result Method outperforms existing goodness-of-fit tests and training methods.
The paper analyzes the value discrepancies of imitation learning methods.
problem Analyzing the value discrepancies of imitation learning methods.
method Discrepancy propagation analysis for infinite-horizon settings.
result GAIL has less compounding errors than behavioral cloning.
Framework identifies discrepancies in physics models, improving sensor accuracy.
problem Model inaccuracies leading to poor control algorithms.
method Learning systematic state-space residuals and deterministic dynamical errors.
result Improved quantification of system dynamics and control algorithms.
New feature Stein discrepancies improve sampler selection and goodness-of-fit testing.
problem Computational inefficiency in existing Stein discrepancies.
method Feature Stein Discrepancies (ΦSDs) and Random Feature Stein Discrepancies (RΦSDs).
result RΦSDs are orders of magnitude faster while maintaining or improving performance.
Study on discrepancy principle for learning algorithms in nonparametric regression.
problem Determining optimal iteration number in nonparametric regression with unknown optimal iteration.
method Investigates discrepancy principle and modified principles for kernelized spectral filters, using deviation inequalities and change-of-norm arguments.
result Classical discrepancy principle is adaptive for slow rates, while modified principles are adaptive for faster rates.
Stein discrepancy improves UDA performance in low-data scenarios.
problem Improving model performance on unlabeled target domains with limited data.
method Proposes a novel UDA framework using Stein discrepancy, an asymmetric measure that depends on the target distribution through its score function.
result Consistently outperforms prior UDA approaches under limited target data across multiple benchmarks.
Inequalities linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.
problem Linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.
method Deriving inequalities linking these measures on Riemannian manifolds.
result Strengthening and extending existing inequalities to Riemannian manifolds.