Constructs integrable systems for Lie-Poisson structures at nilpotent elements.
problem Integrability of transverse Lie-Poisson structures at nilpotent elements.
method Using the argument shift method to construct families of functions in involution.
result Provides a uniform construction of completely integrable systems for an infinite family of nilpotent elements.
In this paper, by modifying the argument shift method,we prove Liouville integrability of geodesic flows of normal metrics (invariant Einstein metrics) on the Ledger-Obata n-symmetric spaces $K^n/\diag(K)$, where K is a semisimple (respectively, simple) compact Lie group.
This paper does not contain any new results, it is just an attempt to present, in a systematic way, one construction which establishes an interesting relationship between some ideas and notions well-known in the theory of integrable systems on Lie algebras and a rather different area of mathematics studying projectivel…
Study guarantees convergence of mean shift mode estimation.
problem Ensuring reliable mode estimation in KDE using mean shift.
method Utilizes Łojasiewicz inequality to prove convergence rate.
result Extends convergence guarantees to biweight kernel.
The paper analyzes the generalization error of min-norm interpolators in transfer learning with limited test samples.
problem Characterizing the generalization error of min-norm interpolators in transfer learning with limited test samples.
method Characterizes the bias and variance of pooled min-ℓ2-norm interpolation under covariate shift and model shift. result Shows that adding data can hurt when SNR is low and is beneficial at higher SNR levels under certain conditions.
Corrects distribution shift in target shift scenarios using importance weighting.
problem Analyzes importance weighting for correcting distribution shift under target shift.
method Analyzed importance-weighted kernel ridge regression under target shift.
result Shows that importance weighting corrects the train-test mismatch without altering input-space complexity.
Derives explicit investment strategy with random endowment.
problem Optimal investment with random endowment in a market.
method Duality arguments to derive explicit expression for optimal strategy.
result Explicit expression for optimal trading strategy exists.
New method exploits independence in instrumental variable models for better causal inference.
problem Identify causal functions in the presence of unobserved confounders.
method HSIC-X method that exploits independence between response, hidden confounders, and instruments.
result The method provides better finite sample results and is invariant to distributional shifts.
The paper extends conformal risk control to be valid with high probability over a growing calibration dataset.
problem Valid risk control over a growing calibration dataset.
method Quantile-based arguments for anytime-valid control.
result Guarantees remain valid with high probability over a cumulatively growing calibration dataset.
Unified analysis of KL divergence using shifted composition for sampling.
problem Sampling from target distributions with KL divergence guarantees.
method Shifted composition rule applied to KL divergence, combining local error analysis and Girsanov's theorem.
result Unified KL guarantees for strongly log-concave, weakly log-concave, and log-Sobolev distributions.
The first eigenfunction of a specific domain in hyperbolic space is log-concave.
problem Proving the log-concavity of the first eigenfunction on horoconvex domains in hyperbolic space.
method Proof by contradiction, using properties of Killing derivatives and nodal domains.
result The first eigenfunction is log-concave throughout the domain.
Paper improves differential privacy analysis for machine learning.
problem Quantifying privacy leakage in noisy gradient descent.
method Shifted interpolation in f-differential privacy. result First exact privacy analysis for strongly convex optimization.
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational characterizations that naturally suggest a two-step scheme for their optimizatio…
We study holomorphic integrable systems on the hyperkähler manifold G×Sreg, where G is a complex semisimple Lie group and Sreg is the Slodowy slice determined by a regular sl2(C)-triple. Our main result is that this manifold carries a canonical \textit{abstract int…
New theorem shows curvature concentration depends linearly on volume ratio.
problem Gap theorem for nonnegative Ricci curvature manifolds with small curvature concentration.
method Exhibited Ricci flow solution with faster than 1/t curvature decay.
result Curvature concentration depends linearly on asymptotic volume ratio.
The history of research in finance and economics has been widely impacted by the field of Agent-based Computational Economics (ACE). While at the same time being popular among natural science researchers for its proximity to the successful methods of physics and chemistry for example, the field of ACE has also received…
We propose nonparametric methods for individual calibration in regression models.
problem Uncertainty quantification and individual calibration for regression models.
method Nonparametric methods agnostic of the underlying model, combining nonparametric and covering number arguments.
result Established matching upper and lower bounds for calibration error.
STAD adapts models to evolving time-based data shifts.
problem Gradual distribution shifts over time challenge existing test-time adaptation methods.
method Bayesian filtering method that learns time-varying dynamics in hidden features.
result STAD excels in handling small batch sizes and label shift on real-world data.
New research shows LLMs can't be explained by statistical generalization alone.
problem Understanding why large language models (LLMs) perform well despite statistical generalization limitations.
method Examined the non-identifiability of AR probabilistic models and their implications for LLMs.
result Non-identifiability of LLMs leads to different behaviors and requires a separate theoretical explanation.
In this paper, we study how the mean shift algorithm can be used to denoise a dataset. We introduce a new framework to analyze the mean shift algorithm as a denoising approach by viewing the algorithm as an operator on a distribution function. We investigate how the mean shift algorithm changes the distribution and sho…
Study evaluates methods for improving model robustness to various real-world distribution shifts.
problem Improving model robustness to real-world distribution shifts like geographic changes.
method Introduced new datasets and evaluated existing methods on four types of shifts (style, blurriness, location, camera operation).
result Data augmentations and larger models can improve robustness on real-world distribution shifts, contrary to prior claims.
RLSbench benchmarks domain adaptation under label proportion shifts, revealing widespread failures and proposing a two-step meta-algorithm.
problem Domain adaptation under label proportion shifts is poorly understood and inconsistent across methods.
method RLSbench introduces a large-scale benchmark with 500 distribution shift pairs. It proposes a two-step meta-algorithm to improve domain adaptation methods under label proportion shifts.
result The two-step meta-algorithm improves domain adaptation methods by 2-10% accuracy points under large label proportion shifts.
Proposes SGShift to identify shifted features causing model performance degradation under concept shift.
problem Concept shift leading to miscalibration in ML models across domains.
method SGShift method for identifying sparse set of shifted features using feature selection and statistical tools.
result SGShift identifies shifted features more accurately than baseline methods, requires few samples in the shifted domain, and is robust to complex cases.
Study detects concept shift in online data using martingales.
problem Detecting concept shift in online datasets.
method Exchangeable martingales and conformal prediction techniques.
result Decomposes concept shift into detectable components.
Proposes a method to improve regression model performance with limited target data using fused-regularizer.
problem Model shifts and covariate shifts in high-dimensional regression.
method Two-step method with fused-regularizer to leverage source data for target task.
result Robust to covariate shifts, minimax-optimal under certain conditions, and validated by numerical tests.
Combines adversarial and interventional robustness for machine learning models.
problem Designing robust models for distribution shifts in machine learning.
method RISe formulation using distributionally robust optimization.
result Demonstrates efficacy of RISe approach with synthetic and real-world datasets.
A new method for adapting to label shifts using class probability matching.
problem Adapting to label shifts where class probabilities differ between source and target domains.
method Class Probability Matching using Kernel Methods (CPMKM) framework.
result CPMKM outperforms existing methods on real datasets.
New approach models how explanations shift with distribution changes.
problem Model performance drops with changing input data distributions.
method Models explanation shifts and compares them to state-of-the-art techniques.
result Modeling explanation shifts better detects out-of-distribution behavior.
Method identifies shifts leading to large model performance differences.
problem Detecting shifts in distribution that affect model performance.
method Parametric changes in causal mechanisms define robustness sets; worst-case optimization problem approximated as non-convex quadratic.
result Second-order approximation of worst-case loss for small shifts, leading to efficient algorithms.
RIA method improves OoD generalization for covariate shift.
problem Improving out-of-distribution generalization under covariate shift.
method Adversarial label invariant graph data augmentations for OoD generalization.
result RIA method achieves high accuracy compared to OoD baselines.
FJS method improves multinomial classification accuracy.
problem Improving multinomial classification accuracy under dataset shift.
method Derive FJS representation and propose alternative methods.
result Factorizable joint shift is not fully identifiable without additional assumptions.
UTS improves DNN uncertainty calibration without labels, robust to domain shift.
problem Improving uncertainty calibration of DNNs under domain shift.
method UTS uses unlabeled test samples and a novel weighted NLL loss function.
result UTS outperforms other methods in domain shift scenarios.
Federated learning method improves covariate shift adaptation for missing target values.
problem Missing target values in federated learning.
method Federated covariate shift adaptation algorithm for missing target output values.
result Asymptotically unbiased and efficient algorithm for federated learning.
New CPS model tackles conditional probability shift in machine learning.
problem Discrepancy between source and target distributions in machine learning.
method Conditional Probability Shift Model (CPSM) using multinomial regression and EM algorithm.
result Superior balanced classification accuracy on target data compared to existing methods.
We prove the shifting theorems of the critical groups of critical points and critical orbits for the energy functionals of Finsler metrics on Hilbert manifolds of H1-curves, and two splitting lemmas for the functionals on Banach manifolds of C1-curves. Two results on critical groups of iterated closed geodesics a…
Method improves simulation accuracy by mitigating distribution shift in hybrid systems.
problem Mitigating distribution shift in machine-learning augmented hybrid simulation.
method Tangent-space regularized estimator to control distribution shift.
result Marked improvements in simulation accuracy, especially for systems with high distribution shift.
Paper proposes a new regularization method to prevent model degradation under distribution shifts.
problem Model performance degrades under distribution shifts.
method Supervised contrastive learning with heterogeneous similarity.
result The proposed method outperforms existing regularization methods on benchmark datasets.
Proxy methods adapt to distribution shifts without explicitly modeling latent confounders.
problem Adapting to distribution shifts under latent variable confounding.
method Proximal causal learning, two-stage kernel estimation.
result Proxy methods outperform other methods in adapting to complex distribution shifts.
Paper develops a new method to improve model calibration under distribution shifts.
problem Challenges in uncertainty quantification with different training and test distributions.
method Develops multi-domain temperature scaling to handle distribution shifts.
result Outperforms existing methods on in-distribution and out-of-distribution test sets.
New method learns models to adapt to domain shifts at test time.
problem Learning models robust to distribution shifts in practical applications.
method Adaptive Risk Minimization (ARM) framework.
result Performance gains of 1-4% on image classification problems.
New risk decompositions clarify domain adaptation issues.
problem Domain adaptation challenges with different training and test distributions.
method Representation Bayesian Risk Decompositions, hybrid argument.
result Clarifies factors (2) and (3) as reasons for generalization failure.
Paper tackles high-dimensional quantile regression with distribution shift using transfer learning.
problem Efficiency of knowledge transfer is severely impacted by distribution shift in high-dimensional regression.
method Proposes a novel transferable set and framework for three types of distribution shift: parameter, covariate, and residual.
result Establishes estimation error bounds and source detection consistency for the proposed method.
A feature-weighted mean shift algorithm improves clustering in high-dimensional data.
problem Clustering high-dimensional data with traditional mean shift algorithms.
method Feature-weighted mean shift algorithm.
result The algorithm outperforms conventional mean shift and preserves computational simplicity.
Paper tackles distribution shifts in prediction models with unobserved confounding.
problem Distribution shifts in prediction models with unobserved confounding.
method Linear structural causal model, invariant covariate representations, data-driven representation learning method.
result Optimizes for a lower-dimensional linear subspace and a prediction model confined to that subspace, achieving nearly ideal gap between target and source risk.
A method corrects feedback shift in predicting conversion rates with delayed feedback.
problem Delayed feedback leads to mislabeling of positive instances in training data.
method Uses importance weight approach to correct feedback shift.
result Proposed method outperforms existing methods in offline and online experiments.
Proposes a method to adapt to new classes in a domain shift.
problem Learning new classes in a domain shift without labeled supervision.
method Inspired by prototypical networks, the method classifies target samples into shared and novel classes.
result Superior performance compared to DA and CI methods in the CIDA paradigm.
This paper rethinks confidence calibration under covariate shifts.
problem Calibration methods struggle with covariate shifts and unstable importance weighting.
method Derives Expectation consistency condition and proposes Expectation consistency loss (ECL).
result ECL loss is compatible with various types of calibration and has the same sample complexity as ECE.
A new method detects distribution shifts faster than existing CTMs.
problem Detecting distribution shifts in data streams with contamination issues.
method Uses a fixed reference dataset to compare each new sample, avoiding contamination.
result Detects distribution shifts faster and more reliably than standard CTMs.