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.
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.
We contribute to the arithmetic/topology dictionary by relating asymptotic point counts and arithmetic statistics over finite fields to homological stability and representation stability over $\Cb$ in the example of configuration spaces of n points in smooth varieties. To do this, we import the method of homological …
Author presents the second variational formula for statistical biharmonic maps.
problem Developing a formula for statistical biharmonic maps.
method Introduced the second variational formula for the statistical bi-energy functional.
result The second variational formula can be represented using Hessian curvature in Hessian manifolds.
Paper derives second variational formula for statistical manifold mappings.
problem Variational formulas for mappings between statistical manifolds.
method Develops second variational formula for harmonic mappings, defines stability, index, and nullity.
result Shows weakly stability for harmonic mappings into statistical manifolds of non-positive curvature.
LLMs fail to match statistical ground truth despite stable run-to-run performance.
problem LLMs lack validation against statistical ground truth in automated scientific workflows.
method Introduced a behavioral evaluation framework for LLMs, separating four decision-making dimensions.
result LLMs can exhibit near-perfect stability but diverge from statistical ground truth.
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.
Flexible approach for normal approximations in geometric and topological statistics.
problem Normal approximation for complex statistics not expressible as sums of score functions.
method Flexible add-one cost operator combined with strong stabilization theory.
result Established normal approximation results for geometric and topological statistics.
We continue the study of a general class of spaces of 0-cycles on a manifold defined and begun by Farb-Wolfson-Wood. Using work of Gadish on linear subspace arrangements, we obtain representation stability for the cohomology of the ordered version of these spaces. We establish subexponential bounds on the growth of uns…
Paper explores using bootstrap methods to improve SGD's stability and robustness.
problem Improving the stability and robustness of SGD.
method Investigates empirical bootstrap approaches for SGD from algorithmic stability and statistical robustness perspectives.
result Demonstrates construction of purely distribution-free confidence intervals using bootstrap SGD.
Paper analyzes stability and generalization of SCO algorithms.
problem Understanding how SCO algorithms perform on unseen data.
method Algorithmic stability analysis in statistical learning theory.
result Derives dimension-independent excess risk bounds for SCGD and SCSC.
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 findings show many popular bandit algorithms are unstable, contradicting minimax optimality.
problem Challenges in statistical inference from bandit algorithms due to adaptive, non-i.i.d. nature.
method Analysis of stability properties of optimism-based bandit algorithms.
result Widely used minimax-optimal UCB-style algorithms are unstable.
The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same underlying population. In this paper, we introduce a general measure of classif…
The study analyzes the performance of statistical estimators under stability and computational efficiency.
problem Understanding the performance of statistical estimators in relation to stability and computational efficiency.
method Developed a framework to bound statistical accuracy based on the interplay between algorithm convergence rates and stability.
result Unstable algorithms can achieve the same statistical accuracy as stable ones in fewer steps.
LIME method provides stability indices to ensure reliable explanations for machine learning models.
problem Difficulty in understanding machine learning model decisions.
method LIME method with stability indices.
result Stability indices ensure reliable explanations for machine learning models.
The paper examines the stability of binary choice models using Gini index and scoring indicators.
problem Stability and discriminatory power of binary choice models.
method Derives the real Gini index and incorporates PSI and KS statistics into the model.
result The real Gini index should be less than the calculated Gini index when the population distribution changes.
New framework formalizes estimating valid transport maps, revealing their statistical limits.
problem Estimating valid transport maps in generative modeling.
method Formalized a minimax framework for estimating valid transport maps.
result Estimating any valid transport map is as hard as estimating the optimal transport map under standard stability assumptions.
Proposes a new measure to evaluate stability of statistical parameters under distributional shifts.
problem Difficulty in transferring knowledge across data sets due to distributional changes.
method Introduces a measure of instability quantifying sensitivity of statistical parameters to Kullback-Leibler divergence and directional shifts.
result The proposed measure can elucidate the type of shifts a parameter is sensitive to and improve estimation accuracy under shifted distributions.
Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation, statistical equilibrium and temporal stability of market weights.
Cramming method evaluates learned policies from contextual bandits efficiently.
problem Evaluating final learned policies from contextual bandit algorithms.
method On-policy evaluation using a single pass of data, ensuring consistency and asymptotic normality.
result Cramming method reduces evaluation standard error by approximately 40% compared to off-policy methods.
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.
The paper analyzes Tikhonov regularization in Hilbert scales for statistical inverse problems.
problem Statistical inverse problems in Hilbert scales with general noise.
method Tikhonov regularization scheme with conditional stability estimates and high probability error bounds.
result Explicit rates of convergence for oversmoothing and regular cases over defined regularity classes.
This is a sequel to the paper [Cas]. Here, we extend the methods of Farb-Wolfson using the theory of FI_G-modules to obtain stability of equivariant Galois representations of the etale cohomology of orbit configuration spaces. We establish subexponential bounds on the growth of unstable cohomology, and then use the Gro…
New estimator stabilizes higher-order influence functions for bilinear forms.
problem Stability issues in estimating bilinear forms using higher-order influence functions.
method Proposes a new stabilized higher-order estimator for a class of bilinear forms without sample splitting.
result New estimator exhibits more stable finite-sample performance compared to the empirical higher-order estimator.
Kernel networks' stability edge linked to Fisher Information singularity.
problem Understanding the stability edge in high-capacity kernel Hopfield networks.
method Statistical manifold analysis and Riemannian geometry.
result The Ridge of Optimization corresponds to the Edge of Stability, revealing a dual equilibrium.
Proposes φ-table for statistical SHAP explanations in regression models.
problem Lack of clear directional summaries, uncertainty, and fidelity in SHAP feature importance.
method SHAP importance selection, fitting a standardized linear surrogate, reporting coefficients, uncertainty, fidelity, and stability.
result Extends SHAP into a statistical global explanation with direction, uncertainty, fidelity, and stability.
Study shows exponential sample complexity for stabilizing certain linear systems.
problem Statistical hardness of learning to stabilize linear time-invariant systems.
method Analysis of sample complexity and co-stabilizability using robust control ideas.
result Sample complexity increases exponentially with system dimension.
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.
Study accelerates gradient methods in machine learning, revealing risk and stability connections.
problem Understanding the statistical risk of accelerated gradient methods in machine learning.
method Continuous-time analysis of Nesterov's accelerated gradient method and Polyak's heavy ball method for least squares regression.
result Connections between early stopping, stability, and curvature of loss function are revealed.
Randomness is crucial for stability in learning and statistics, especially for differential privacy.
problem Quantifying the amount of randomness needed for algorithmic stability.
method Weak-to-strong boosting theorem for stability, characterizing randomness complexity of PAC Learning.
result Randomness complexity is tightly controlled by the best replication probability of any deterministic algorithm solving the task.
Statistical inference for misspecified contextual bandits is challenging due to adaptivity issues.
problem Statistical inference for misspecified contextual bandits
method Inverse-probability-weighted Z-estimation framework
result Consistent and asymptotically normal estimator with sandwich variance estimator
The paper provides stability guarantees for non-parametric maximum likelihood estimation using statistical mechanics.
problem Non-parametric maximum likelihood estimation and Gaussian mixture models.
method Statistical mechanics analysis to establish stability guarantees for NPMLE.
result High probability upper bounds on the Kullback-Leibler divergence between NPMLE estimators and the true density.
This paper analyzes stability and generalization of Markov chain stochastic gradient methods.
problem Analyzing stability and generalization of Markov chain stochastic gradient methods.
method Algorithmic stability in statistical learning theory.
result Established optimal generalization bounds for both smooth and non-smooth cases.
We derive Gaussian approximations for random forest predictions using region-based stabilization.
problem Improving the accuracy of random forest predictions for Poisson process data.
method Region-based stabilization and Malliavin-Stein method for multivariate Gaussian approximation.
result Established Gaussian approximation bounds for random forest predictions under Poisson process.
Study shows resampling can drastically alter PCA results.
problem Stability and sensitivity of PCA under data resampling.
method Analyzed resampling sensitivity of high-dimensional PCA.
result PCA's principal components become asymptotically orthogonal when resampling is significant.
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
In this paper we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function depending on pairs of instances among which notable examples are bipartite ranking,…
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…
Building and expanding on principles of statistics, machine learning, and scientific inquiry, we propose the predictability, computability, and stability (PCS) framework for veridical data science. Our framework, comprised of both a workflow and documentation, aims to provide responsible, reliable, reproducible, and tr…
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.
This paper extends stability analysis to non-convergent neural network training.
problem Generalization of neural networks whose training does not converge to fixed points.
method Introduces statistical algorithmic stability (SAS) to study non-convergent algorithms and their generalization.
result Stability of non-convergent training dynamics correlates with generalization performance.
A new algorithm reduces inference error in adaptive contextual bandits.
problem Challenges in statistical inference for adaptive contextual bandits.
method Proposes a regularized EXP4 algorithm that satisfies the Lai-Wei stability condition.
result Valid Wald-type confidence intervals for linear functionals can be achieved without the price of adaptivity.
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.
In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for data clustering and density estimation in statistics, control systems, and machine…
M-FISHER detects and adapts to streaming data shifts with statistical validity and stability.
problem Detecting and adapting to distributional shifts in streaming data.
method Constructs an exponential martingale from non-conformity scores and applies Ville's inequality for detection. Fisher-preconditioned updates for adaptation.
result Establishes M-FISHER as a principled approach for robust, anytime-valid detection and geometrically stable adaptation.
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.
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…