This work explores the trade-offs between stability and accuracy in statistical estimation.
problem Understanding the statistical cost of algorithmic stability.
method Statistical decision-theoretic perspective, focusing on worst-case and average-case stability.
result Optimal stable estimators for mean estimation and regression settings are developed, revealing trade-offs between stability and accuracy.
A fast method estimates stability of ensemble feature selectors.
problem Improving stability of ensemble feature selectors for better prediction.
method Simulator of a feature selector to estimate stability.
result Reduces computation time for estimating stability.
New proof for stability estimates in complex equations without pluripotential theory.
problem Stability estimates for complex Monge-Ampère and Hessian equations.
method New proof using general degenerations of background metrics.
result Uniform stability estimates for both equations under various degenerations.
The study examines rigidity and stability of gradient estimates on surfaces and manifolds.
problem Rigidity and stability of gradient estimates for positive harmonic functions and solutions to heat equations.
method Sharp gradient estimates for positive harmonic functions and solutions to heat equations on surfaces and manifolds with nonnegative curvature.
result Obtained rigidity and stability results for gradient estimates.
The paper proves LOO CV is reliable under estimator stability.
problem Ensuring the reliability of leave-one-out cross validation.
method Using concentration inequalities based on logarithmic Sobolev inequality.
result LOO CV is a valid procedure under estimator stability.
Study shows stability in X-ray transform on specific hyperbolic manifolds.
problem Stability of X-ray transform on asymptotically hyperbolic manifolds.
method Constructed a parametrix for the normal operator in 0-pseudodifferential calculus.
result Showed a stability estimate for the X-ray transform.
There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an overlooked dichotomy in the type of stability-based generalization bounds we have in …
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.
Optimally estimates stability in Lorentzian isoperimetric inequalities.
problem Stability estimates in Lorentzian isoperimetric inequalities.
method Quantitative stability estimates using Fraenkel asymmetry and Lipschitz bounds.
result Optimal stability estimates with universal constants for Lorentzian isoperimetric inequalities.
New method stabilizes machine learning predictions across random seeds.
problem Machine learning predictions vary across random seeds, causing instability.
method Introduces adaptive cross-bagging to eliminate seed dependence.
result Adaptive cross-bagging achieves targeted stability in debiased machine learning.
Study on stability of quaternion-Kähler manifolds using eigenvalue estimates.
problem Stability problem for positive quaternion-Kähler manifolds.
method Description of infinitesimal Einstein deformations and destabilising directions in terms of Laplace eigenfunctions and symmetric 2-tensors. Improved eigenvalue estimates for the Hodge-Laplacian on 2-forms.
result Sharp lower bound for the first non-zero eigenvalue on the parallel subbundle Sym^2 E of the 2-form bundle.
Study stability of surfaces in spacetimes, proving new estimates and theorems.
problem Stability of surfaces in spacetime and their applications.
method Variational techniques, Christodoulou-Yau estimate, Cohn-Vossen inequality, global theorem, capillary stability, area inequality, diameter estimate.
result Established new estimates and theorems for stable surfaces in spacetime.
The study refines stability results for Yang-Mills fields and harmonic maps.
problem Stability of Yang-Mills fields and harmonic maps.
method Refinement of stability results using Jacobi operator over S^m.
result Refined stability results and Morse index estimates.
For harmonic maps of degree 2, a similar quantitative stability estimate does not hold uniformly.
problem Investigate the quantitative stability of harmonic maps of degree 2.
method Prove a local quantitative stability result for harmonic maps of degree 2, showing dependence on the given harmonic map.
result A uniformly quantitative stability estimate does not hold for degree 2 harmonic maps.
The study proves stability of quermassintegral inequalities in hyperbolic space.
problem Stability of quermassintegral inequalities for horospherically convex hypersurfaces in hyperbolic space.
method Using initial value independent curvature estimates for locally constrained flows of inverse type.
result Explicit exponent of the deficit in the quermassintegral inequality is given and does not depend on dimension.
We prove a sharp stability estimate for the problem of reconstructing a symmetric 2-tensor from its integrals along all maximal geodesics on a simple manifold.
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.
An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis is on several new stability conditions, such as K-stability, Donaldson's infinite…
This paper enhances stability selection by evaluating overall results robustness and identifying optimal regularization values.
problem Improving the robustness and reliability of high-dimensional variable selection.
method Developed a stability estimator to evaluate stability of stability selection results, calibrating key parameters.
result Identified optimal regularization value and improved stability of variable selection.
Proposes stabilized weights for causal inference using isotonic calibration.
problem Stability and bias issues in inverse propensity weighting.
method Post-hoc isotonic calibration of inverse propensity weights.
result Improves performance of doubly robust estimators of average treatment effect.
The paper improves stability estimates for soap bubble theorem in curved domains.
problem Stability estimates for the Soap Bubble Theorem in curved domains.
method Leveraging Gagliardo-Nirenberg-type interpolation inequalities.
result Optimal stability estimates for Lr deviations of mean curvature from being constant. Cubic fourfolds have K-stability and admit Kähler-Einstein metrics.
problem Understanding K-stability and Kähler-Einstein metrics for cubic fourfolds.
method Local volume estimates and Ambro-Kawamata's non-vanishing theorem.
result All smooth cubic fourfolds admit Kähler-Einstein metrics.
The paper examines stability of Minkowski inequalities in warped product spaces.
problem Stability of Minkowski-type inequalities for hypersurfaces in warped product spaces.
method Established a stability estimate for the norm of the traceless second fundamental form.
result Proved stability of Minkowski inequalities in specific warped product examples.
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.
Novel stability bounds for OT maps improve density estimation.
problem Estimating optimal transport maps between probability distributions.
method Developed novel stability bounds for OT maps, reducing the problem to density estimation.
result Stability bounds allow for sharper guarantees without smoothness assumptions.
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.
The paper studies g-stability of surfaces with boundary and derives area estimates.
problem Investigating g-stability of surfaces with boundary. method Analyzing geometric properties and deriving area estimates.
result Derives area estimates and determines the topology of the surface.
Efficient inference for adaptive data with directional stability condition.
problem Efficient inference on scalar targets after adaptive data collection.
method Introduces directional stability, a weaker condition than i.i.d. data, and shows asymptotic normality and efficiency of estimators.
result Estimators remain asymptotically normal and semiparametrically efficient under directional stability.
Paper proves stability for recovering connections from holonomy traces.
problem Recovering a connection from holonomy traces on Riemannian manifolds.
method Combination of microlocal analysis and non-Abelian approximate Livsic Theorem.
result Hölder type stability estimates for holonomy inverse problem.
The paper studies rigidity and stability of minimal submanifolds in hyperbolic space.
problem Conditions for a minimal submanifold to be totally geodesic.
method Analyzes the length of the second fundamental form and eigenvalues of the super stability operator.
result Sharp upper bounds for the first eigenvalue of the super stability operator for surfaces in hyperbolic 4-space.
Extends global stability of Minkowski spacetime to minimal decay assumptions.
problem Global stability of Minkowski spacetime under minimal decay assumptions.
method Uses rp-weighted estimates instead of vectorfield method. result Proves global stability of Minkowski spacetime under minimal decay assumptions.
New proof of Minkowski spacetime stability in exterior regions.
problem Stability of Minkowski spacetime in exterior regions.
method Unified treatment of decay of initial data, use of rp-weighted estimates. result Reduced number of derivatives and simplified last slice treatment.
Bidirectional bounds stabilize training of energy-based models.
problem Training energy-based models is difficult and prone to instability.
method Propose bidirectional bounds linking to gradient penalty and Jacobi-determinant estimator.
result Significant stabilization and high-quality density estimation achieved.
Estimates eigenvalues on weighted manifolds with curvature.
problem Estimating eigenvalues of Dirichlet and Neumann problems.
method Using Bakry-Émery Ricci curvature.
result Established a stability condition for h-minimal hypersurfaces.
New proof of Kerr stability outside null cones.
problem Stability of Kerr spacetime in external regions.
method Unified treatment of initial data and rp-weighted estimates. result Reduced number of derivatives and simplified last slice treatment.
The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.
problem Stability and convergence rates of entropic and Sinkhorn potentials.
method Semiconcavity properties of entropic potentials and Schrödinger bridges.
result Exponential convergence rates for gradient and Hessian of Sinkhorn iterates.
Paper introduces stability in model averaging and proposes a L2-penalty method.
problem Theoretical properties of model averaging from stability perspective.
method Introduces stability, defines asymptotic empirical risk minimizer, and proposes L2-penalty model averaging method.
result Proposed L2-penalty method ensures stability and consistency under reasonable conditions.
Motivation : Molecular signatures for diagnosis or prognosis estimated from large-scale gene expression data often lack robustness and stability, rendering their biological interpretation challenging. Increasing the signature's interpretability and stability across perturbations of a given dataset and, if possible, acr…
Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely occurs when there are aspects of the target distribution that are not well captur…
New estimator stabilizes higher-order influence functions for stable statistical inference.
problem Numerical instability in estimating inverse population Gram matrix.
method Proposes a new stabilized higher-order estimator without sample splitting.
result Stabilized estimator exhibits more stable performance and similar statistical guarantees.
New method for private density estimation of high-dimensional Gaussian mixtures.
problem Private density estimation for mixtures of unrestricted high-dimensional Gaussians.
method Exploits list global stability to prove upper bound on sample complexity.
result First upper bound on sample complexity for agnostic private density estimation.
New algorithms robustly estimate mean with near-optimal error rates.
problem Outlier robust mean estimation in high-dimensional data.
method Stability condition and iterative filtering algorithms.
result Optimal error rates with subgaussian rates for robust mean estimation.
We study volume growth, entropy and stability for translating solitons of mean curvature flow. First, we prove that every complete properly immersed translator has at least linear volume growth. Then, by using Huisken's monotonicity formula, we compute the entropy of the grim reaper and the bowl solitons. We also give …
Study designs for estimating treatment effects in adaptive experiments.
problem Estimating treatment effects under adaptive treatment assignment.
method Propose and analyze IPW and AIPW estimators, establish CLTs under design stability.
result Central limit theorems for IPW and AIPW estimators under design stability.
Estimates Kaehler metrics' diameter in big cohomology classes.
problem Estimating the diameter of Kaehler metrics in big cohomology classes.
method Proves uniform diameter estimates using integrability conditions and stability properties of complex Monge-Ampere equations.
result Uniform diameter estimates for Kaehler metrics in big cohomology classes.
The paper studies stability of commutativity properties of the Dirichlet-to-Neumann map.
problem Characterize manifolds for which the Dirichlet-to-Neumann map commutes with the Laplacian.
method Obtain stability estimates for the commutator of the Dirichlet-to-Neumann map and the Laplacian.
result Stability estimates show that small commutator implies close to a ball.
A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study stability properties of the penalized maximum likelihood estimator, two types of asym…
The paper studies capillary surfaces, proving stability and curvature estimates.
problem Stability and curvature estimates for capillary surfaces.
method Analyzes the index and geometry/topology of capillary surfaces in 3-manifolds.
result Stable capillary surfaces in a half-space are half-planes.