New stability measures for similar features improve feature selection accuracy.
problem Existing stability measures fail to distinguish similar features in highly correlated datasets.
method Introduce new adjusted stability measures that consider feature similarities.
result One new stability measure considers highly similar features as interchangeable.
Kim-Milman flow map stable under regular target measures
problem Stability of Kim-Milman flow map under target measure variations
method Stability in relative entropy and 2-Wasserstein distance result Lipschitz stability up to logarithmic factor
Proves stability of cone-volume measure with nearly constant density.
problem Stability of cone-volume measure with near constant density.
method Proves stability of cone-volume measure with near constant density.
result Homothetic copy of the body is close to the unit ball in the L2-distance. Let (M,ω) be a Kähler manifold and let K be a compact group that acts on M in a Hamiltonian fashion. We study the action of KC on probability measures on M. First of all we identify an abstract setting for the momentum mapping and give numerical criteria for stability, semi-stability and polystabili…
Proposes a new stability measure for model fitting on similar feature data sets.
problem Model fitting on data sets with similar features is challenging.
method Tuning hyperparameters in a multi-criteria fashion with predictive accuracy and feature selection stability.
result Our approach achieves similar or better predictive performance than single-criteria and stability selection approaches.
Derives stability for curvature measure near constant density, proving dual Minkowski problem solutions.
problem Stability of curvature measure near constant density
method Derives stability result for curvature measure, proves existence and uniqueness of solutions to dual Minkowski problem.
result Existence and uniqueness of solutions to dual Minkowski problem for positive indices, stability result for curvature measure.
Paper uses Ricci curvature to measure and forecast China's stock market stability.
problem Measuring and predicting systemic stability of China's stock market.
method Geometric measure derived from discrete Ricci curvature applied to financial networks.
result Ricci curvature effectively captures market stability and predicts future trends.
The study examines stability of metric measure spaces with integral Ricci curvature bounds.
problem Stability and compactness of metric measure spaces with integral Ricci curvature bounds.
method Proves convergence to metric measure spaces satisfying CD(K,n) condition under certain curvature bounds. result Proves convergence of sequences of Riemannian manifolds to metric measure spaces satisfying CD(K,n) condition. A new stable similarity measure for time series using persistent homology.
problem Constructing a robust measure of time series similarity.
method Persistent homology for stability, bi-conditional periodicity score for similarity.
result Stability of the bi-conditional periodicity score under perturbations and dimension reduction.
Paper shows stability of metric reconstruction for orbifolds from spectral data.
problem Determining the metric structure of collapsing orbifolds from spectral data.
method Improved quantitative unique continuation for wave operator on Riemannian manifolds.
result Quantitative stability of inverse problem for Riemannian orbifolds.
The paper proves stability of eigenvalue inequalities on surfaces.
problem Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces.
method Employing eigenvalues of measures and Sobolev space W−1,2, the paper proves stability estimates for the first and second nonzero Laplace eigenvalues on surfaces. result Metrics almost maximizing the normalized eigenvalue are W−1,2-close to a maximal metric. Study of irreversible metric-measure spaces, proving convergence and stability results.
problem Understanding Gromov-Hausdorff convergence and stability in noncompact irreversible metric-measure spaces.
method Introducing a nondecreasing function to bound reversibility of larger balls, proving convergence/stability results in Gromov-Hausdorff topology.
result Satisfactory convergence/stability results in Gromov-Hausdorff topology for various irreversible spaces, including Finsler manifolds.
Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global market…
We show that the cone-volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition. This implies, among others, a conjectured best possible inequality for the U-functional of a convex body. For both results we provide stronger versions in the sense of stability i…
The recent financial crisis have generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. In particular, a potential vulnerability of the financial networks is the "financial contagion" process in which insolvencies of individual entities propagate through the…
Decision trees and logistic regression are one of the most popular and well-known machine learning algorithms, frequently used to solve a variety of real-world problems. Stability of learning algorithms is a powerful tool to analyze their performance and sensitivity and subsequently allow researchers to draw reliable c…
Geometric stability measures neural network robustness, distinguishing from similarity metrics.
problem Lack of robustness in neural network representations.
method Introduces geometric stability, quantified by Shesha metric measuring self-consistency.
result Stability and similarity are uncorrelated, revealing distinct properties of neural network robustness.
We provide a dual characterisation of the weak∗-closure of a finite sum of cones in L∞ adapted to a discrete time filtration Ft: the tth cone in the sum contains bounded random variables that are Ft-measurable. Hence we obtain a generalisation of Delbaen's m-stability condition…
New findings on maximizing noise stability in partitions of Gaussian space.
problem Maximizing noise stability in partitions of Gaussian space.
method Analyzing the correlation between sets and their noise stability, proving conditional conjectures and hardness results.
result Hyperstable partitions maximize noise stability and have specific properties.
Develops a minimax optimal estimator for system stability under distribution shift.
problem Ensuring system reliability under changes in the underlying environment.
method Minimax optimal estimation of stability defined in terms of acceptable performance degradation.
result Characterizes the minimax convergence rate and demonstrates practical utility.
Wasserstein GAN(WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we prove the local stability of optimizing the simple gradien…
Establishes relationships between prudence and stability properties of risk functionals.
problem Stability properties of risk functionals
method General relationships and preservation of prudence under cash-additive hulls and inf-convolutions
result General methods for constructing prudent risk measures
The paper examines stability of ReLU networks in tangent space and activation regions.
problem Stability and sensitivity of ReLU networks to small changes.
method Tangent sensitivity measure for ReLU networks, focusing on stability induced by individual examples.
result Tangent sensitivity correlates with the distribution of activation regions and generalization gap.
We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the gaussian, mean or anisotropic curvature measures of the offset of a compact set K with positive μ-reach can be estimated by the same curvature measures of the offset of a compact set…
Paper explores stability, regularization, and gradient flows for stochastic inverse problems.
problem Recovering random probability distributions from measurements.
method Direct inversion, variational formulation with regularization, and optimization via gradient flows.
result The choice of metric impacts stability and properties of the optimizer.
Survey explores geometric aspects of policy optimization in control systems.
problem Understanding the geometric relationships between control design and optimization.
method Geometric perspective on policy optimization, focusing on parameterization and topology.
result Implications of policy geometry on stability and performance of local search algorithms.
We present sufficient conditions for topological stability of continuous functions f:R→R having finitely many local extrema with respect to averagings by discrete measures with finite supports.
A new method for feature selection robust to noise and design variability.
problem Feature selection in high-dimensional regression under sampling variability and measurement error.
method Injects controlled additive noise into the design matrix, fits a base selector, and aggregates selection frequencies.
result Improved robustness compared to Stability Selection and standard base selectors.
Study introduces a new copula-based measure for financial asset cointegration.
problem Traditional correlation coefficient's limitations in measuring financial asset relationships.
method Utilizes copulas to measure dependence among financial asset returns.
result Enhanced stability and informativeness in measuring financial asset relationships.
New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.
problem Characterizing cyclicity in weighted Besov spaces.
method Defining cyclicity indices based on potential theory and capacity, studying stability under perturbations, and linking zero set structure to cyclicity.
result Novel invariants and conditions for cyclicity in various function spaces.
The paper studies stability of mean-field variational inference for log-concave distributions.
problem Stability of mean-field variational inference for log-concave distributions.
method Novel approach via linearized optimal transport, lifting non-convex problem to convex optimization over transport maps.
result Dimension-free Lipschitz continuity of the MFVI optimizer with respect to the target distribution, measured in 2-Wasserstein distance.
Geometric stability predicts steerability and detects drift in language models.
problem Predicting steerability and detecting drift in language models.
method Supervised and unsupervised geometric stability measures.
result Supervised geometric stability predicts steerability with high accuracy and detects drift earlier.
This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion τ(t) of the state trajectory. For a system r˙(t)=Ar(t) where A is invertible, we show that (1) if there exists a measurable set E1 with positive Lebesgue measure, such that r(0)∈E1 implies t…
Study tackles inverse problems on low-dimensional manifolds, proving stability and proposing a reconstruction algorithm.
problem Inverse problems in infinite-dimensional spaces with nonlinear and ill-posed nature.
method Assumption of low-dimensional manifold, proving stability, proposing Landweber-type algorithm.
result Global convergence of the proposed algorithm, Lipschitz stability for specific inverse problems.
New estimates show spectral gap stability in RCD spaces, close to Beta distribution.
problem Stability of spectral gap bounds in metric-measure spaces.
method Combines L1-functional inequality and Stein's method. result Sharp quantitative estimate for spectral gap stability.
Paper examines stability of Bayesian posterior measures using integral probability metrics.
problem Stability of Bayesian inference in large-scale inverse problems.
method New families of integral probability metrics for likelihood and prior perturbations.
result Constructs new stability results for Bayesian posterior measures.
Paper addresses travel time tomography stability and statistical inversion.
problem Determining conformal factors of metrics from geodesic lengths.
method Established forward and inverse stability estimates; applied to Bayesian statistical inversion.
result Consistency of statistical inversion technique for travel time tomography.
The aim of this paper is to provide new stability results for sequences of metric measure spaces (Xi,di,mi) convergent in the measured Gromov-Hausdorff sense. By adopting the so-called extrinsic approach of embedding all metric spaces into a common one (X,d), we extend the results of Gigli-Mondino-Savaré by prov…
We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the geodesic X-ray transform encountered in other inverse boundary problems like the…
We develop efficient algorithms to estimate the stability of Ordinary Least Squares regression results.
problem Measuring the stability of regression conclusions in low dimensions.
method Efficient algorithms for estimating the minimum number of samples that need to be removed to change a regression conclusion.
result We can estimate stability up to a factor of 3 better than the greedy heuristic and certify stability even for dropping a majority of samples.
Study on stability of optimal transport problems for probability measures.
problem Stability of supermartingale optimal transport problems.
method Approximation in adapted Wasserstein distance and continuity of functional.
result Continuity and monotonicity principles for weak supermartingale optimal transport.
Sharp upper bounds on inscribed radius for metric spaces with convex boundary.
problem Bounding inscribed radius in metric measure spaces with convex boundary.
method Proves sharp upper bounds on inscribed radius for subsets with convex boundary.
result Sharp upper bounds on inscribed radius for subsets with convex boundary.
Study stability of curvature-dimension condition for negative dimensions.
problem Stability of curvature-dimension condition with negative dimension parameters.
method Introduced CD(K, N)-condition for N < 0, defined distance d_{\mathsf{iKRW}}, proved convergence stability.
result Limit structure of converging metric measure spaces remains CD(K, N) for N < 0.
Mathematical approach defines stability conditions for ML models.
problem Ensuring stability of machine learning models.
method Adopted topological and metric spaces theory to define stability.
result Stability of ML models depends on topological properties of classification sets.
Stability of hypersurface immersions in Riemannian manifolds proved for Lp perturbations.
problem Stability of isometric immersions of hypersurfaces in Riemannian manifolds under Lp perturbations of their fundamental forms. method Young measure approach, relaxation of energy, regularity result for immersions.
result Sequence of immersions converges to an isometric immersion with the reference shape operator.
New method improves reliability of LDA topic modeling by assessing stability across replicated runs.
problem LDA's reproducibility issues due to initial values and Gibbs sampling.
method Cluster replicated LDA runs using modified Jaccard coefficient and pruning algorithm.
result New measure S-CLOP quantifies LDA topic stability, improving reproducibility.
Study shows stability of travel time data reconstruction from closed subsets.
problem Reconstruction of length spaces from travel time data on a closed subset.
method Lipschitz stability proof for certain types of length spaces.
result Reconstruction of length spaces is Lipschitz stable from travel time data on a closed subset.
In this paper we measured the stability of stochastic gradient method (SGM) for learning an approximated Fourier primal support vector machine. The stability of an algorithm is considered by measuring the generalization error in terms of the absolute difference between the test and the training error. Our problem is to…