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.
New framework limits testing algorithmic stability under computational constraints.
problem Testing algorithmic stability is computationally hard.
method Unified framework for quantifying stability hardness.
result Exhaustive search is the only universally valid mechanism for certifying stability.
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.
Unified techniques improve stability and replicability in changing data.
problem Concept drift in data generating distribution.
method Removing hidden confounding and causal regularization.
result Improves stability, replicability, and robustness in heterogeneous data.
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.
Cluster stability selection improves feature selection in correlated data.
problem Feature selection stability in correlated data.
method Cluster stability selection exploiting known cluster structure.
result Better predictive performance than lasso alone and stability selection.
The study establishes stability in WMOT, crucial for finance with imprecise data.
problem Stability in weak martingale optimal transport for finance with imprecise data.
method Established stability through rigorous mathematical analysis.
result Stability of WMOT is proven, with applications to VIX futures and Brownian motion.
New method creates vacuum data at minimal and borderline decay thresholds.
problem Creating vacuum initial data at specific decay thresholds.
method Conical solution-operator method applied to vacuum asymptotically flat initial data.
result Demonstrates global and exterior stability of Minkowski spacetime.
Bayesian algorithm stabilizes unknown continuous-time systems from unstable data.
problem Learning and stabilizing unknown continuous-time systems with uncertain dynamics.
method Bayesian learning algorithm that learns from unstable data to stabilize the system in finite time.
result The algorithm stabilizes unknown continuous-time stochastic linear systems effectively after a short time period.
Proteins are commonly used by biochemical industry for numerous processes. Refining these proteins' properties via mutations causes stability effects as well. Accurate computational method to predict how mutations affect protein stability are necessary to facilitate efficient protein design. However, accuracy of predic…
Stabilizing black-box algorithms through task-oriented randomization
problem Ensuring stability of black-box models
method Task-oriented randomization
result Established rigorous theoretical foundations and demonstrated effectiveness through simulations and real-world applications
Proves stability of Minkowski space for specific initial data.
problem Stability of Minkowski space under spacelike-characteristic initial data.
method Vectorfield method and bootstrapping argument, with new geometric constructions.
result Global nonlinear stability of Minkowski space proved for the spacelike-characteristic Cauchy problem.
Study on stability of GCNNs under graph perturbations.
problem Limited theoretical understanding of GCNN stability.
method Proposes a probabilistic framework to analyze GCNN stability under various graph perturbations.
result Demonstrates the importance of data distribution in stability analysis.
New algorithms learn stability certificates from data, avoiding complex dynamics.
problem Synthesizing stability certificates from complex dynamical systems.
method Developed algorithms to learn certificate functions from trajectory data, establishing generalization error bounds.
result Efficiently learned certificates can be used for adaptive control.
Bagging stabilizes models without distributional assumptions.
problem Stability of machine learning models without distributional assumptions.
method Derives a finite-sample guarantee on bagging stability for any model.
result Guarantee applies to many bagging variants and is optimal.
Neural nets learn robust geometric data representations.
problem Ensuring neural networks are robust to adversarial attacks.
method Topological Data Analysis via persistence diagrams, Lipschitz stability.
result Certified ε-robustness on ORBIT5K dataset. 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.
Copula-based normalizing flows improve flexibility and stability for heavy-tailed data.
problem Limited expressive power of vanilla normalizing flows.
method Generalize base distribution to copula for more accurate representation of target distribution.
result Copula-based normalizing flows improve flexibility, stability, and effectiveness for heavy-tailed data.
reval package selects best clustering solutions via stability-based validation.
problem Challenges in determining best clustering solutions due to lack of validation methods.
method Stability-based relative clustering validation methods.
result Determines best clustering solutions that generalize to unseen data.
The paper relaxes the stability condition to boost confidence in generalization for randomized learning algorithms.
problem The tension between uniform stability and L2-stability in generalization bounds. method Establishes in-expectation first moment generalization error bounds for L2-stable randomized learning algorithms and uses subbagging to achieve near-tight exponential bounds. result Improves generalization bounds for convex and non-convex optimization problems with SGD.
New method improves feature selection by integrating stability paths.
problem Improving feature selection with tighter false positive control.
method Integrating stability paths to strengthen theoretical bounds on E(FP).
result Significantly more true positives with same E(FP) control.
We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any computations that respond to bounded-sensitivity linear queries while providing acc…
We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization bound for data-dependent hypothesis sets expressed in terms of a notion of hypothe…
The paper simplifies K-stability conditions for spherical varieties.
problem K-stability of polarized spherical varieties.
method Expressed K-stability in combinatorial terms, provided sufficient conditions.
result G-uniform K-stability provides a checkable condition for existence of constant scalar curvature metrics.
Pipeline learns topological features for protein stability prediction.
problem Predicting protein stability using topological features.
method Data-driven method to learn topological features, comparing with expert features.
result Topological features achieve 92%-99% of SME-based models' performance.
Paper proves stability of complex equations under various conditions.
problem Stability of backward stochastic differential equations with jumps.
method General framework for convergent sequences of data and solutions.
result Convergent sequence of solutions for associated data.
The study identifies conditions under which algorithmic stability explains generalization in interpolating learning systems.
problem Understanding when algorithmic stability explains generalization in interpolating learning systems.
method Modeling training as a function-space trajectory and measuring sensitivity to single-sample perturbations.
result There exist interpolating regimes with small risk where contractive sensitivity cannot hold, showing that stability is not a universal explanation.
New method stabilizes model selection with theoretical guarantees.
problem Stability of model selection methods in the face of noisy or incomplete data.
method Combines bagging with an 'inflated' argmax operation to select a stable set of models.
result Stable model selection with high probability of overlap after removing any data point.
Effective Yau-Tian-Donaldson conjecture for spherical varieties.
problem Finding effective K-stability criteria for spherical varieties.
method Formulated an effective variant of the Yau-Tian-Donaldson conjecture and reviewed effective K-stability criteria for spherical varieties.
result Effective K-stability criteria can be computed given combinatorial data.
Study on stability of geodesic maps in non-isotropic manifolds.
problem Stability of totally geodesic wave maps in non-isotropic manifolds.
method Factorization property, PDE system in geodesic normal coordinates, global existence result via hyperboloidal foliation.
result Established global existence for small initial data, leading to geometric stability.
Paper improves stability analysis of SGD for various loss functions and data distributions.
problem Improving stability analysis of SGD for non-convex loss functions and data distributions.
method Analyzes stability of SGD for convex and non-convex loss functions, and improves data-dependent bounds.
result Improved stability bounds for non-convex loss functions and convex regularized loss functions.
Paper uses Time Series Transformer for bank stability prediction.
problem Predicting bank stability using complex financial data.
method Time Series Transformer model with self-attention mechanism.
result Time Series Transformer model outperforms other models in MSE and MAE.
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.
New methods provide stable ranking without assumptions on data distributions.
problem Stability issues in ranking problems with noisy data.
method Developed a stability framework and two ranking operators.
result Guaranteed stability without assumptions on data distributions.
This paper analyzes HTL using stability theory for binary classification.
problem Analyzing HTL's theoretical behavior in binary classification tasks.
method Stability analysis of regularized empirical risk minimizers.
result Derives generalization bounds for training error, excess risk, and cross-validation.
Proposes a stability evaluation criterion for learning models using distributional perturbations.
problem Ensuring reliable deployment of learning models in out-of-sample environments.
method Uses optimal transport discrepancy with moment constraints to quantify minimal perturbation required for model deterioration.
result Validates the practical utility of the stability evaluation criterion across various real-world applications.
To date, the instability of prognostic predictors in a sparse high dimensional model, which hinders their clinical adoption, has received little attention. Stable prediction is often overlooked in favour of performance. Yet, stability prevails as key when adopting models in critical areas as healthcare. Our study propo…
Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jac…
Modern biotechnologies often result in high-dimensional data sets with much more variables than observations (n ≪ p). These data sets pose new challenges to statistical analysis: Variable selection becomes one of the most important tasks in this setting. We assess the recently proposed flexible framework for variab…
We study the recently introduced stability training as a general-purpose method to increase the robustness of deep neural networks against input perturbations. In particular, we explore its use as an alternative to data augmentation and validate its performance against a number of distortion types and transformations i…
Study shows minimizing the norm of the ERM solution stabilizes kernel ridge-less regression.
problem Stability of kernel ridge-less regression.
method Minimizing the norm of the ERM solution to minimize CV stability.
result Interpolating solution with minimum norm minimizes CV stability.
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.
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.
Inspired by convolutional neural networks on 1D and 2D data, graph convolutional neural networks (GCNNs) have been developed for various learning tasks on graph data, and have shown superior performance on real-world datasets. Despite their success, there is a dearth of theoretical explorations of GCNN models such as t…
The paper classifies test configurations and derives a criterion for uniform K-stability of certain algebraic varieties.
problem Uniform K-stability of G-varieties of complexity 1. method Classification of G-equivariant normal test configurations via combinatorial data and derivation of a criterion for uniform K-stability. result Derivation of a criterion for uniform K-stability in terms of combinatorial data.
Lyapunov exponents help understand RNN stability.
problem Optimizing RNNs is sensitive to various parameters.
method Use Lyapunov exponents as dynamical system tools.
result Lyapunov spectrum measures training stability.
Paper stabilizes persistent homology rank functions for statistical inference.
problem Stability issues in persistent homology rank functions.
method Derive stability results for rank functions under FDA metrics.
result Rank functions stabilize, improving statistical inference.
Proves stability of Schwarzschild black holes without symmetry assumptions.
problem Stability of Schwarzschild black holes under general conditions.
method Teleologically normalised double null gauges, analysis of linear stability, and control of non-linearities.
result Proves non-linear asymptotic stability of Schwarzschild family as solutions to Einstein vacuum equations.