Study stability of measures on Kähler manifolds with Hamiltonian actions.
problem Stability of measures on Kähler manifolds under group actions.
method Identify and apply momentum mapping criteria for stability, semi-stability, and polystability.
result Various stability criteria for measures on Kähler manifolds.
This paper analyzes the probability flow in the stock market using the Black-Scholes model.
problem The non-conservation of probability in the stock market.
method Expressed the Black-Scholes equation in Hamiltonian form and analyzed the flow of probability.
result Conditions under which probability might be conserved in the market, challenging the non-Hermitian nature of the Black-Scholes Hamiltonian.
New stability framework relaxes boundedness assumptions for generalization bounds.
problem Overly restrictive assumptions for modern learning settings with heavy-tailed or unbounded losses.
method Develops a stability-based framework requiring only finite L p L_p L p moment conditions. result Sharp generalization bounds derived for various learning paradigms.
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.
The paper analyzes stability and asymptotic behavior of hedging strategies in binomial and trinomial models.
problem Stability and asymptotic analysis of hedging strategies in incomplete financial models.
method Discrete-time Föllmer-Schweizer decomposition, perturbation analysis, and asymptotic approximation.
result Explicit formulas for leading order correction terms in asymptotic analysis.
New bounds show faster convergence for learning algorithms.
problem Improving risk bounds for learning algorithms.
method Using algorithmic stability and common assumptions like Polyak-Lojasiewicz condition, smoothness, and Lipschitz continuity.
result Achieves convergence rate of O ( log 2 ( n ) / n 2 ) O(\log^2(n)/n^2) O ( log 2 ( n ) / n 2 ) with high probability. New model stabilizes asynchronous LTI systems, independent of synchronous stability.
problem Stability of asynchronous LTI systems under randomization and asynchrony.
method Introduced a new model for random asynchronous LTI systems and developed a method for system identification.
result Stability of random asynchronous LTI systems is independent of synchronous stability.
The paper tackles stable maxima optimization for expensive functions.
problem Finding stable maxima of expensive functions with input variations.
method Uses multiple gradient Gaussian Process models to estimate stability and guide optimization.
result Demonstrates effective finding of stable maxima on synthetic and real-world problems.
Improved generalization bounds for uniformly stable algorithms.
problem Deriving meaningful generalization bounds for uniformly stable algorithms in common settings.
method New analysis techniques to improve generalization bounds for uniformly stable algorithms.
result Improved generalization bounds for uniformly stable algorithms, with a bound of O ( ( γ + 1 / n ) log ( 1 / δ ) ) O(\sqrt{(γ+ 1/n) \log(1/δ)}) O ( ( γ + 1/ n ) log ( 1/ δ ) ) with probability at least 1 − δ 1-δ 1 − δ . 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.
Study linearizes 2-Wasserstein space using optimal transport maps.
problem Stability and linearization of the 2-Wasserstein space.
method Explicit embedding of probability measures into a Hilbert space using optimal transport maps.
result The embedding is (bi-)Hölder continuous, with stability results for optimal transport maps.
This study analyzes AdaGrad's stability and convergence in non-convex optimization.
problem Lack of theoretical analysis for AdaGrad in non-convex optimization.
method Novel stopping time-based techniques from probability theory.
result Established stability and derived convergence rates for AdaGrad.
Study stability of contingent claim solutions under probabilistic perturbations.
problem Stability of solutions to discrete-time contingent-claim problems under uncertainty.
method Use Rockafellian perturbations to analyze stability of solutions.
result Establishes convergence of dual problems and shadow prices.
New methods ensure feature importance rankings are correct with high probability.
problem Stability issues in feature importance scores due to random sampling.
method Hypothesis testing-based techniques to assess and verify the stability of top-ranked features.
result Ensures the most important features are correct with high-probability guarantees.
New study on replicability and stability in machine learning algorithms.
problem Ensuring consistent results in machine learning models without fixing randomness.
method Introduced global stability and list replicability concepts, proving their equivalence and boosting list replicability.
result Global stability can only be achieved weakly, while list replicability can be boosted to achieve high probability of consistent results.
Random forests are stable and provide reliable prediction intervals.
problem Stability and reliability of random forest prediction intervals.
method Established stability under mild conditions and proved coverage bounds.
result Non-asymptotic lower and upper bounds for prediction interval coverage.
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.
Improved GAN training stability through clipping and reweighting.
problem Inconsistent GAN training leading to inferior performance.
method Proposes a variational GAN framework with probability ratio clipping and sample reweighting.
result Significantly improved performance across various GAN tasks.
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.
Develops a framework for distilling flow models from few steps.
problem Improving few-step sampling in diffusion models for better performance.
method Local approximation errors and dynamical amplification controlled through analytical tractability.
result Deep residual compositions efficiently approximate long-horizon transport with controlled global error.
The paper stabilizes PD term structures under forecast uncertainty using a Kalman filter with an anchored observation model.
problem Stable estimation of lifetime PDs under forecast uncertainty.
method Reformulated in state-space framework, introduced an anchored observation model.
result Asymptotic stochastic stability of error dynamics, leading to smoother projections.
This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probabil…
A new method finds stable labels for target data using random walks.
problem Automating the labeling of unlabeled data from a related domain.
method Random walk on a graph with stability probabilities to find stable labels.
result The method yields stable labels for target data, improving domain adaptation.
The paper improves SGD's generalization error bounds for nonconvex optimization.
problem Improving generalization error bounds for SGD in nonconvex optimization.
method Characterizing the on-average stability of SGD iterates and using it to derive probabilistic generalization error bounds.
result Improved generalization error bounds for SGD in both nonconvex and gradient dominant loss functions.
The Martin boundary of certain groups is stable under specific conditions.
problem Stability of Martin boundaries in relatively hyperbolic groups.
method Extending Floyd-Ancona inequalities, defining spectral degenerescence, and proving stability criteria.
result The Martin boundary of admissible symmetric finitely supported probability measures on geometrically finite Kleinian groups of dimension at most 5 is always strongly stable.
Logit dynamics formula reveals self-regulation in softmax policy gradient methods.
problem Understanding the stability and convergence of softmax policy gradient methods.
method Deriving the exact formula for the L2 norm of the logit update vector.
result Logit update magnitudes are modulated by action probability and policy concentration.
Unified stability bounds for noisy SGD across convex and non-convex losses.
problem Deriving generalization bounds for noisy stochastic gradient descent.
method Unified approach using Lyapunov functions and applied probability.
result Time-uniform stability bounds for SGD on various loss functions.
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.
New method predicts neural network performance using free probability theory.
problem Stability and performance prediction of feed-forward neural networks.
method Free Probability Theory and homotopy method for Jacobian spectral density computation.
result FPT metrics correlate highly with final test accuracies of neural networks.
The paper ensures stability of kernel methods under slight changes in probability measure, regularization, and kernel.
problem Stability of kernel-based methods under perturbations of probability measure, regularization, and kernel.
method Conditions for stability are derived based on convex Lipschitz loss functions and smooth kernels.
result Conditions for stability are given under simultaneous changes in probability measure, regularization, and kernel.
TensorFlow Probability MCMC toolkit improves MCMC efficiency for modern hardware.
problem Inefficient MCMC algorithms on modern hardware.
method Design and implementation of a new MCMC toolkit for TensorFlow.
result Improved MCMC efficiency on modern hardware.
Boosting framework for vector-valued prediction with geometric stability.
problem Lack of a general theoretical understanding of aggregation for structured prediction.
method Identifies ( α , β ) (α,β) ( α , β ) -stability property and proposes a boosting framework based on exponential reweighting and geometric-median aggregation. result Obtains exponential decay of empirical divergence error under weak learner condition and ( α , β ) (α,β) ( α , β ) -stability. The semantic map calibrates uncertainty from language model probabilities.
problem Uncertainty in language model probabilities for professional decisions.
method Prespecified semantic map linking probabilities of verbal responses to probabilities of declared states.
result Language-derived probabilities outperform printed numerical probabilities and recover valid uncertainty coverage.
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.
New bound reduces generalization error for stable algorithms, nearly optimal.
problem Improving generalization bounds for uniformly stable algorithms.
method Developed a new high-probability generalization bound with nearly optimal rate.
result Achieved an estimation error bound of O ( γ log ( n ) log ( n / δ ) + log ( 1 / δ ) / n ) O(γ\log(n)\log(n/δ) + \sqrt{\log(1/δ)/n}) O ( γ log ( n ) log ( n / δ ) + log ( 1/ δ ) / n ) for γ γ γ -uniformly stable algorithms. The paper improves SVM and localized SVM stability under triple perturbations.
problem Stability of SVMs and localized SVMs under triple perturbations.
method Generalizes and improves existing results, considering simultaneous variations in probability measure, regularization parameter, and kernel.
result Improved stability of SVMs and localized SVMs under triple perturbations.
We analyze critical points of the Sliced Wasserstein Distance for optimization stability.
problem Understanding the behavior of optimization algorithms for models trained with the Sliced Wasserstein Distance.
method Explicit perturbations and critical point analysis of the SW objective.
result Stable critical points of SW cannot concentrate on segments, providing optimization stability.
Stochastic gradient method stabilizes learning of approximated kernel functions.
problem Learning an approximated kernel function for binary classification.
method Stochastic gradient method applied to online convex optimization with random Fourier features.
result Stochastic gradient method is stable and generalizes well for approximated kernel functions under given assumptions.
This work achieves finite-time stabilization of uncertain LQ systems using random feedbacks.
problem Stabilizing linear systems with unknown dynamics in finite time.
method Random linear feedbacks to achieve finite-time stabilization.
result High probability guarantees for finite time stabilization of LQ systems.
The paper explores how language models can provide reliable state measurements without being interpreted as beliefs.
problem How to use language models to reliably infer states without misinterpreting them as beliefs.
method Developed a semantic map and semiparametric inverse to link language probabilities to state probabilities, avoiding hidden models.
result Conditions for existence, identification, stable recovery, and uniform stability of posterior states from observable language probabilities.
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.
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.
In this paper, we consider voxel selection for functional Magnetic Resonance Imaging (fMRI) brain data with the aim of finding a more complete set of probably correlated discriminative voxels, thus improving interpretation of the discovered potential biomarkers. The main difficulty in doing this is an extremely high di…
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.
Investigates stability properties of Haezendonck-Goovaerts premium principles in Orlicz spaces.
problem Stability properties of Haezendonck-Goovaerts premium principles in various Orlicz spaces.
method Analysis of stability properties including Fatou and Lebesgue properties, and continuity with respect to Φ Φ Φ -weak convergence. result Haezendonck-Goovaerts principles satisfy the Fatou property and Lebesgue property under certain conditions.
The paper solves a stability issue in pricing derivatives using optimal Skorokhod embedding.
problem Optimizing the Skorokhod embedding problem for derivative pricing.
method Derives dualities and geometric characterizations, analyzes convergence rates.
result The optimization problem converges to an optimal Skorokhod embedding problem as more prices are given.
The paper explores the generalization of quantum neural networks using stability theory.
problem Understanding the generalization properties of quantum neural networks.
method The authors use algorithmic stability to establish generalization bounds for quantum neural networks.
result The paper provides practical insights into the design and training of quantum neural networks.
The paper relaxes the stability condition to boost confidence in generalization for randomized learning algorithms.
problem The tension between uniform stability and L 2 L_2 L 2 -stability in generalization bounds. method Establishes in-expectation first moment generalization error bounds for L 2 L_2 L 2 -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.