Study on error probability for classification of heavy-tailed renewal processes.
problem Error probability in classification of heavy-tailed renewal processes.
method Asymptotic expressions for Bhattacharyya bound on misclassification error probabilities.
result Obtained asymptotic expressions for misclassification error probabilities.
This note provides an error bound for the Hartman-Watson integral's leading term.
problem Bounding the error of the leading term of the Hartman-Watson integral.
method Asymptotic expansion analysis focusing on the regime rt=ρ constant. result The error term is bounded uniformly as ∣ϑ(t,ρ)∣≤701t. Study efficient rebalancing strategies for portfolio tracking error.
problem Optimizing portfolio rebalancing under high-frequency asset price models.
method Discrete-time rebalancing strategies derived from continuous model.
result Asymptotically efficient sequence of simple strategies.
Optimizes prediction error method for time-varying models.
problem Achieving optimal prediction error rates for time-varying models.
method Nonlinear least squares method for time-varying parametric models.
result First rate-optimal non-asymptotic analysis for time-varying models.
Dynamic hedging of an European option under a general local volatility model with small linear transaction costs is studied. A continuous control version of Leland's strategy that asymptotically replicates the payoff is constructed. An associated central limit theorem of hedging error is proved. The asymptotic error va…
In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails o…
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are …
This paper analyzes error bounds for biased SMC samplers in conditional sampling.
problem Analyzing error bounds for biased SMC samplers in conditional sampling.
method Develops a non-asymptotic error analysis for SMC samplers with biased mutation kernels.
result Derives the first non-asymptotic error bound for conditional sampling with score-based diffusion models.
Double Q-learning has the same mean-squared error as Q-learning under certain conditions.
problem Comparing the mean-squared error of Double Q-learning and Q-learning.
method Theoretical analysis based on Lyapunov equations for both tabular and linear function approximation settings.
result The asymptotic mean-squared error of Double Q-learning is exactly equal to that of Q-learning under specific conditions.
Study GLS estimator properties in multivariate regression with heteroskedastic and autocorrelated errors.
problem Asymptotic properties of GLS estimator in multivariate regression with specific error structures.
method Derive Wald statistics for linear restrictions and assess their performance.
result Wald statistics remain robust to heteroskedasticity and autocorrelation.
This paper analyzes hedge errors in Black-Scholes models using finite difference techniques.
problem Accurate hedging strategies in dynamic market environments.
method Asymptotic approach and finite difference techniques.
result Reduction of hedge errors and enhancement of option pricing model robustness.
We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error pr…
New weighted Lasso estimates improve logistic regression performance with measurement error.
problem Improper Lasso estimates in sparse logistic regression with equal penalties.
method Proposed weighted Lasso estimates using McDiarmid inequality for non-asymptotic oracle inequalities.
result Finite sample behavior illustrated by non-asymptotic oracle inequalities for estimation and prediction errors.
The paper proves a non-asymptotic test error approximation for KRR.
problem Understanding the test error of Kernel Ridge Regression.
method Established a non-asymptotic deterministic approximation for test error of KRR.
result The test error of KRR can be approximated by a closed-form estimate derived from the spectrum of the kernel operator.
The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been…
Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide conditions under which an appropriate scaling allows to improve the error bounds in…
New method calibrates asynchronous, error-prone covariates for longitudinal data.
problem Estimation biases and slow convergence in analyzing time-varying covariates with measurement error.
method Functional calibration approach based on functional principal component analysis.
result Asymptotically unbiased and consistent estimators for time-invariant coefficients; optimal convergence rate for time-varying coefficients.
The paper improves confidence intervals for test error using cross-validation.
problem Improving confidence intervals for test error in machine learning.
method Develops central limit theorems and consistent estimators for cross-validation.
result Provides asymptotically-exact confidence intervals and hypothesis tests.
New metric explains neural network performance, simplifying generalization error calculation.
problem Precise characterization of neural network generalization error.
method Introducing Representation Gap, linking to intrinsic dimension and equivariant diffusion models.
result Asymptotic equivalent of Representation Gap is governed by intrinsic dimension, easy to estimate.
Study stability thresholds of big line bundles, proving bounds and generalizing results.
problem Stability thresholds of big line bundles and their asymptotic behavior.
method Explicit bounds on error terms, using quasi-monomial valuations to compute stability thresholds.
result Proves Jin--Rubinstein--Tian's questions affirmatively.
We derive formulas for F measures' standard error and confidence intervals.
problem Estimating F measures' accuracy with confidence.
method Analytic formulas based on asymptotic normality.
result Valid formulas for sample size planning.
The paper analyzes methods for estimating linear functionals from observational data, proving upper bounds and showing optimal procedures.
problem Estimating linear functionals from observational data in causal inference and bandit literature.
method Two-stage procedures that first estimate treatment effect function, then use it to estimate the linear functional.
result Proves non-asymptotic upper bounds on mean-squared error for two-stage procedures and shows instance-dependent optimality.
This paper corrects an error in [Keller-Ressel, M. and Steiner T. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models." Finance and Stochastics 12.2 (2008): 149-172]. The error concerns the correct expression for the boundary between normal and humped yield curve behavior in affin…
Study non-asymptotic bounds for robust estimators under misspecified models.
problem Evaluate performance of robust estimators under adversarial conditions.
method Propose a general approach to adversarial risk analysis, including investigations on generalization and approximation errors.
result Establish non-asymptotic upper bounds for adversarial excess risk under Lipschitz loss functions.
This study analyzes LTS in sparse models with finite sample error bounds.
problem Robust regression in high-dimensional sparse models with limited data.
method Non-asymptotic analysis of LTS error bounds.
result Established finite sample error bounds for LTS in sparse models.
Study optimizes prediction error for growing-dimensional PFLM models.
problem Optimizing prediction error for growing-dimensional PFLM models.
method Penalized least-squares approach in RKHS with effective dimension consideration.
result Shows exact upper bound for excess prediction risk in non-asymptotic form.
In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data point to be estimated or predicted given the side information or p…
Paper calculates the exact error of LDA models.
problem Bayesian generalization error in Latent Dirichlet Allocation (LDA).
method Theoretical analysis of learning coefficient using algebraic geometry.
result Exact asymptotic form of LDA's generalization error.
Derives error formula for convex regression in high dimensions.
problem Asymptotic mean squared error in convex regression.
method Oracle-VAMP and state evolution analysis.
result Explicit formula for asymptotic MSE in convex regression.
In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhäuser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize…
Develops confidence intervals for ECE, a measure of model calibration.
problem Ensuring the calibration of probabilistic predictions in machine learning models.
method Develops confidence intervals for the ℓ2 Expected Calibration Error (ECE), considering top-1-to-k calibration. result Shows asymptotic normality and different convergence rates for calibrated and miscalibrated models, developing methods to construct valid confidence intervals.
In this paper we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving-average (SARMA) models under the assumption that the errors are uncorrelated but not necessarily independent.We relax the standard independence assumption on the error term in order to extend the range …
Study on error probabilities of machine learning classification techniques using large deviations theory.
problem Performance analysis of machine learning binary classification techniques.
method Large deviations theory applied to Data-Driven Decision Function (D3F) for error probability analysis.
result Classification error probabilities vanish exponentially, with an asymptotic formula providing precise error rate estimates.
DALMC provides non-asymptotic error bounds for generative models.
problem Efficiently generating samples from complex data distributions.
method Analysis of diffusion paths and Langevin Monte Carlo.
result Theoretical guarantees for a class of generative models.
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has minimal variance among all unbiased estimators and is asymptotically normally dis…
Estimates error for robust M-estimators with convex penalties.
problem Estimating out-of-sample error for robust M-estimators in high-dimensional linear regression.
method Proposes a generic out-of-sample error estimate for robust M-estimators with convex penalties, using observed data and derivatives. result The out-of-sample error estimate has a relative error of order n−1/2 under certain conditions. Curiosity-Critic improves world model training by focusing on cumulative prediction error.
problem Training world models with intrinsic rewards that consider cumulative prediction error.
method Curiosity-Critic uses a surrogate reward based on the difference between current and asymptotic prediction errors, estimated online by a co-trained critic.
result Curiosity-Critic outperforms other methods in training speed and final world model accuracy.
GAAVI offers anytime-valid tests for CMF global null and contrasts.
problem Inference on the conditional mean function for high confidence decisions.
method Asymptotic anytime-valid tests for CMF global null and contrasts.
result Achieves asymptotic type-I error guarantees, power one, and optimal sample complexity.
The paper analyzes how data augmentation affects the test error in regression models.
problem Understanding the impact of data augmentation on the test error in regression models.
method Characterizes the test error in terms of population quantities and augmentation statistics.
result Provides a tight characterization of the test error in mean squared error.
New bounds show current methods overestimate system parameter errors.
problem Current bounds overestimate parameter errors in system identification.
method Utilized asymptotic normality and second-order decomposition.
result Obtained finite-sample bounds matching optimal rates up to constants.
Study robust linear regression with outliers, providing exact asymptotics for ERM performance.
problem Robust linear regression in high-dimension with outliers.
method Analyzes ℓ2, ℓ1, and Huber losses, providing asymptotic performance metrics. result Optimally-regularised ERM is asymptotically consistent with simple calibration, but Huber loss requires norm calibration.
Study tightens bounds for interpolating noisy data using minimum l1-norm.
problem Predicting noisy data with minimum l1-norm interpolation.
method Provided matching upper and lower bounds for prediction error.
result Tight consistency up to negligible terms for d≫n. We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3^(2l+1)/sqrt(8πl);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2πl)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.
Estimates proper calibration errors and refinement terms in probabilistic predictions.
problem Lack of a general estimator for proper calibration errors and refinement terms with known statistical properties.
method Proposes a method for consistent, asymptotically unbiased estimation of proper calibration errors and refinement terms.
result Proves the relation between refinement and f-divergences, implying information monotonicity in neural networks.
Sharp bounds derived for test error of finite-rank kernel ridge regression.
problem Loose bounds on test error for finite-rank kernels in machine learning.
method Sharp non-asymptotic upper and lower bounds for KRR test error.
result Tighter bounds on finite-rank KRR test error, valid for any regularization parameters.
Study on linear regression with dependent covariates, proving universality and error characterization.
problem Linear regression with dependent covariates in high-dimensional settings.
method Analysis of ridge regression performance, Gaussian universality theorem, spectral properties of covariance matrices.
result Asymptotic performance of ridge regression is invariant under non-Gaussian covariates with preserved mean and covariance.
Characterizes test error in learning with deep, structured feature maps.
problem Characterizing test error in learning with deep, structured feature maps.
method Asymptotic analysis of feature covariance and population covariance.
result Closed-form formula for feature covariance in Gaussian rainbow neural networks.
We study how the round-off (or discretization) error changes the statistical properties of a Gaussian long memory process. We show that the autocovariance and the spectral density of the discretized process are asymptotically rescaled by a factor smaller than one, and we compute exactly this scaling factor. Consequentl…