New flexible confidence sequences for robust statistical inference.
problem Creating robust statistical inference methods that work under mild assumptions.
method Proposed a new class of asymptotic time-uniform confidence sequences.
result Sharp asymptotic time-uniform confidence sequences achieved under mild assumptions.
This paper introduces time-uniform CLT-based confidence intervals for statistical inference.
problem Developing valid statistical inference methods for sequential data.
method Time-uniform central limit theory and strong invariance principles.
result Asymptotic confidence sequences (CSs) that are uniformly valid over time.
Paper shows how online betting algorithms' regret can be used to create tight confidence sequences.
problem Estimating the expectation of random variables from samples and creating time-uniform confidence sequences.
method Converts the regret guarantee of universal portfolio algorithms into time-uniform concentration inequalities and confidence sequences.
result Numerically obtained confidence sequences are never vacuous and satisfy the law of iterated logarithm.
New methods for private statistical inference under local differential privacy.
problem Private statistical inference for population means with bounded observations.
method Nonparametric, nonasymptotic statistical inference using a generalized randomized response mechanism.
result Private confidence intervals and sequences for population means under LDP constraints.
We develop time-uniform confidence spheres for estimating means of random vectors.
problem Sequential mean estimation in high-dimensional spaces.
method Derive time-uniform confidence sphere sequences (CSSs) for various types of random vectors.
result Optimal CSSs for log-concave, sub-Gaussian, and sub-ψ random vectors. Develops anytime-valid stopping rules for SGD based on observed trajectory.
problem Stopping stochastic gradient descent (SGD) based on observed trajectory.
method Develops anytime-valid confidence sequences for stochastic gradient methods.
result Statistically valid, time-uniform stopping rules for SGD across convex and nonconvex settings.
Paper improves CI and CS for bounded means using betting and mixtures.
problem Estimating means of bounded random variables.
method Composite nonnegative martingales, testing by betting, method of mixtures.
result Empirically outperforms existing CI and CS methods.
The paper develops time-uniform inference methods for stochastic approximation parameters.
problem Statistical inference for parameters in stochastic approximation problems.
method Analysis of averaged iterates convergence rates and construction of asymptotic confidence sequences.
result Valid asymptotic confidence sequences for parameters in stochastic approximation problems.
The paper introduces methods to quantify uncertainty in sampling without replacement.
problem Accurately estimating parameters from finite populations sampled without replacement.
method Develops confidence sequences using Bayesian and empirical methods.
result Improved confidence intervals and sequences for sampling without replacement.
Bayes-assisted confidence sequences improve efficiency for bounded means.
problem Efficient uncertainty quantification for bounded IID means without parametric assumptions.
method Bayesian working predictive model selects adaptive martingale updates maximizing predictive log-growth.
result Asymptotically log-optimal performance with informative priors reducing width and sampling effort.
Efficient inference method for adaptive experiments with tighter confidence sequences.
problem Efficient inference of Average Treatment Effect in a changing policy sequential experiment.
method Semiparametric efficient inference using Adaptive Augmented Inverse-Probability Weighted estimator and asymptotic confidence sequences.
result Derives tighter confidence sequences for adaptive experiments under data-dependent stopping times.
This work creates a CS for non-negative heavy-tailed data with bounded mean.
problem Constructing a confidence sequence for non-negative heavy-tailed data with bounded mean.
method Non-parametric, non-asymptotic lower confidence sequence construction.
result The constructed CS is efficient and can be converted into a closed-interval CS.
Detects harmful distribution shifts in deployed models without false alarms.
problem Detecting harmful distribution shifts in deployed models without false alarms.
method Sequential tools for testing if the difference between source and target distributions leads to a significant increase in a risk function.
result Demonstrated the efficacy of the proposed framework through extensive empirical studies.
The paper provides bounds on the CDF of a variable under nonstationary conditions.
problem Estimating the complete distribution of a random variable under nonstationary conditions.
method Time-uniform and value-uniform bounds on the CDF of the running averaged conditional distribution.
result Presented computationally efficient bounds that are always valid and sometimes trivial.
Unified technique for sequential estimation of convex divergences.
problem Estimating convex divergences between distributions.
method Martingale methods and maximal inequalities for reverse submartingales.
result Valid time-uniform confidence sequences for arbitrary stopping times.
Unified CS for GLMs improves bandit regret bounds.
problem Improving regret bounds for GLMs in bandit settings.
method Unified likelihood ratio-based CS with PAC-Bayesian bound.
result Unified CS attains poly(S)-free regret for Bernoulli.
The betting CI outperforms classical methods in constructing confidence intervals for bounded means.
problem Constructing nonasymptotic confidence intervals for bounded means.
method A betting-based approach to define and time-uniform variants of confidence intervals (CSs).
result The betting CI matches the fundamental limits, outperforming existing empirical Bernstein CIs.
UCRL3 improves UCRL2's efficiency in reinforcement learning by reducing exploration.
problem Long burn-in phases in numerical experiments of UCRL2.
method UCRL3 uses state-of-the-art time-uniform concentration inequalities and adaptive support computation to tighten exploration.
result UCRL3 achieves a better numerical improvement over UCRL2 in standard environments.
This study uses neural networks to approximate Bayesian filtering problems.
problem Estimating latent time-series signal statistics from observation sequences.
method Formulated a generic recurrent neural network framework to learn recursive mappings directly.
result Approximation error bounds for filtering in non-compact domains and strong time-uniform bounds.
The paper extends confidence sequences for infinite variance data.
problem Addressing confidence sequences for distributions with infinite variance.
method Establishing lower bounds and deriving tight confidence sequences for relaxed bounded pth-moment distributions. result Derived confidence sequences are tighter than those using Dubins-Savage inequality.
Improved algorithms for stochastic linear bandits using tighter confidence sequences.
problem Stochastic linear bandits with improved worst-case regret guarantees.
method Novel tail bound for adaptive martingale mixtures to construct tighter confidence sequences.
result Linear bandit algorithm achieves competitive worst-case regret.
Unified framework for anytime-valid PAC-Bayes bounds.
problem Deriving time-uniform PAC-Bayes bounds for stochastic processes.
method Combines four tools: nonnegative supermartingales, method of mixtures, Donsker-Varadhan formula, and Ville's inequality.
result Unified PAC-Bayes theorem for a wide class of discrete stochastic processes.
Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.
problem Tackles robustness to outliers and adversarial corruptions in mean estimation.
method Designs new robust exponential supermartingales to create confidence sequences.
result Achieves optimal width and shows smaller margin of error compared to fixed-time robust methods.
Paper tightens PAC-Bayes bounds using coin-betting for better estimates.
problem Estimating mean of random elements with possibly S-dependent parameters.
method Refined PAC-Bayes proof strategy based on coin-betting framework.
result Derives tighter concentration inequalities for all sample sizes.
Develops confidence bounds for off-policy evaluation in contextual bandits.
problem Evaluating policies that were not used to collect data.
method Martingale analysis for non-asymptotic, non-parametric, and valid confidence sequences.
result Empirically tight bounds on failure probability and width.
Near-optimal confidence intervals for bounded data.
problem Online inference for sequential decision problems like A/B testing.
method Utilizing Bentkus' concentration results to improve on existing methods.
result Near-optimal confidence intervals confirmed favorable in synthetic and practical applications.
Reduces change detection to estimation using confidence sequences.
problem Detecting changes in data streams with minimal delay and false alarms.
method Reduction from sequential change detection to sequential estimation using confidence sequences.
result Change detection scheme with minimal structural assumptions and strong guarantees.
A new method detects changes in data sequences by comparing backward and forward confidence sequences.
problem Detecting changes in data sequences over time.
method Constructing and comparing backward and forward confidence sequences.
result The method successfully detects changes with strong nonasymptotic guarantees.
Develops new e-processes and confidence sequences for Gaussian means with unknown variance.
problem Constructing valid t-tests and confidence sequences for Gaussian means with unknown variance.
method Explores generalized nonintegrable martingales and extended Ville's inequality, developing two new e-processes and confidence sequences.
result Analyzes the width of resulting confidence sequences with a polynomial dependence on error probability, proving it to be unavoidable and even better than classical fixed-sample t-tests.
Develops hypothesis tests for conditional distributions using learning-theoretic bounds.
problem Testing differences in conditional distributions and functionals.
method Transforming learning-theoretic bounds into hypothesis tests for conditional expectations.
result Establishes comprehensive foundation for conditional testing, including theoretical guarantees and practical implementations.
Recurrent neural networks' hidden state can be reconstructed from its past, providing a theoretical framework for stability and tracking.
problem Hidden-state stability in RNNs
method Backward coherence analysis
result Almost-sure convergence, rates under mixing, interpretable limiting representation, finite pathwise stopping times, and theoretical framework for time-uniform confidence sequences.
Near-optimal tests and confidence sequences for non-parametric data.
problem Flexible statistical inference and decision-making with non-parametric data.
method Classic delayed-start normal-mixture sequential probability ratio tests with asymptotic guarantees.
result Asymptotically optimal type-I error and expected rejection time guarantees.
The paper provides Gaussian approximations for decentralized Federated Learning.
problem Lack of asymptotic statistical guarantees for local SGD in Federated Learning.
method Two generalized Gaussian approximation results for local SGD trajectories.
result Valid multiplier bootstrap procedures and Gaussian bootstrap-based tests for detecting adversarial attacks.
The paper proposes a method to construct confidence sets using likelihood ratios for sequential decision-making.
problem Constructing valid uncertainty estimates for unknown quantities in sequential decision-making.
method The method uses likelihood ratios to create any-time valid confidence sequences without specialized treatment for each application.
result The proposed confidence sets maintain the prescribed coverage in a model-agnostic manner and their size depends on the choice of estimator sequence.
Confidence-based deferral works well in many scenarios but fails in specific cases.
problem Understanding when confidence-based deferral fails and when other strategies are better.
method Theoretical analysis and post-hoc deferral mechanisms were studied.
result Theoretical analysis characterizes settings where confidence-based deferral may fail.
Bayesian sequence prediction is a simple technique for predicting future symbols sampled from an unknown measure on infinite sequences over a countable alphabet. While strong bounds on the expected cumulative error are known, there are only limited results on the distribution of this error. We prove tight high-probabil…
SMURF-THP improves Transformer Hawkes process models by providing uncertainty quantification.
problem Uncertainty quantification for Transformer Hawkes process predictions.
method Score matching for learning the score function of event arrival times.
result SMURF-THP outperforms likelihood-based methods in confidence calibration.
BestChanID identifies the channel with maximal capacity using training sequences.
problem Identifying the channel with maximal capacity among several discrete memoryless channels.
method Formulated as a multi-armed bandit problem, proposed a capacity estimator, and developed gap-elimination algorithms.
result Guaranteed to output the DMC with the largest capacity with a desired confidence.
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.
The paper develops statistical inference for gradient flows in optimization.
problem Uncertainty quantification along the entire optimization path.
method Uniform central limit theorem and algorithm-aware covariance estimator.
result Asymptotically valid confidence intervals for target parameter.
Paper compares two forecasters using novel online inference methods.
problem How to compare forecasters without distributional assumptions.
method Confidence sequences and game-theoretic statistical framework for sequential testing.
result Valid methods for comparing forecasters without distributional assumptions.
Paper offers anytime-valid inference for causal parameters using DML.
problem Classic DML is only valid asymptotically for a fixed sample size.
method Time-uniform DML results for anytime-valid inference.
result Valid inference at any arbitrary stopping time.
Unified high-probability regret bounds for online convex optimisation with randomised gradient estimators.
problem Online convex optimisation with randomised gradient estimators for ℓq-Lipschitz losses. method FTRL with randomised two-point finite-difference gradient estimators based on cone-measure sampling from ℓr-spheres. result Unified high-probability regret bounds for all p,q,r∈[1,∞]. Paper optimizes change-point detection using learned distributions from training sequences.
problem Optimal change-point detection with unknown pre- and post-change distributions.
method Designs a change-point estimator using training sequences and test sequences.
result Optimal confidence width characterized as a function of undetected error.
Note improves confidence bounds for random variables.
problem Improving confidence bounds for random variables with unbounded ranges and different distributions.
method PAC-Bayes-ification of a derived confidence bound.
result Streamlined proofs for existing results.
EENNs improve inference efficiency but need nested prediction sets for reliable uncertainty estimates.
problem Non-nested prediction sets from standard uncertainty quantification methods in EENNs.
method Introduced anytime-valid confidence sequences (AVCSs) tailored for EENNs.
result AVCSs generate nested prediction sets across EENN exits, addressing the issue of non-nested sets.
We present a new method for computing ASR word confidences that effectively mitigates the effect of ASR errors for diverse downstream applications, improves the word error rate of the 1-best result, and allows better comparison of scores across different models. We propose 1) a new method for modeling word confidence u…
GPT learns a causal world model from token predictions, validated in game sequences.
problem Does GPT implicitly learn a causal world model from token predictions?
method Derived a causal interpretation of GPT's attention mechanism and proposed zero-shot causal structure learning.
result GPT can generate legal next moves with high confidence for sequences with encoded causal structures, but fails for illegal moves.