Study improves weak error estimates for rough volatility models.
problem Efficient numerical schemes for non-Markovian stochastic processes with rough volatility.
method Analyzes weak rates for a class of stochastic processes with rough stochastic volatility.
result Weak rate is of order min{3H+0.5, 1} for a large class of test functions.
We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error f…
Unified approach for multicalibration in weakly supervised learning.
problem Existing multicalibration methods require clean input-label pairs, which are unavailable in weakly supervised learning.
method Developed estimators and post-hoc correction methods for multicalibration under weak supervision.
result Unified framework for estimating and correcting multicalibration under weak supervision with finite-sample guarantees.
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…
WENDy now estimates nonlinear ODEs with noisy data.
problem Estimating parameters of nonlinear ODEs with noisy data.
method WENDy-MLE algorithm for maximum likelihood estimation of nonlinear-in-parameters ODEs.
result WENDy-MLE outperforms other methods in accuracy, speed, and domain of convergence.
Weak supervision is a popular method for building machine learning models without relying on ground truth annotations. Instead, it generates probabilistic training labels by estimating the accuracies of multiple noisy labeling sources (e.g., heuristics, crowd workers). Existing approaches use latent variable estimation…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The method is based on linear programming only, so that its numerical implementation is…
Formalizes weak and strong verification for LLMs, controlling errors without assumptions.
problem Balancing cost and reliability in reasoning with LLMs.
method Formalizes weak-strong verification policies, introduces metrics, develops online algorithm.
result Optimal policies admit a two-threshold structure, and calibration and sharpness govern value of weak verifiers.
The study explores the strengths and weaknesses of models that generalize from weak to strong supervision.
problem Understanding the limitations and capabilities of models that generalize from weak to strong supervision.
method Theoretical analysis and experimental validation in both classification and regression settings.
result Theoretical bounds reveal the importance of strong generalization and calibration of the weak model and a careful balance in the training process.
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
method Used Euler type scheme with integrated kernels to study weak convergence rate.
result Obtained weak convergence rate of min(3α−1,1) for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model. Study on error rates for approximating rough volatility models.
problem Simulation of rough volatility models with fractional Brownian motion.
method Analysis of weak error rates for numerical schemes, focusing on fBm and cubic test functions.
result Convergence rates for approximations are (3H+21)∧1 for exact left-point discretization and H+21 for hybrid schemes. New method preserves unitarity for Schrödinger equation learning, reducing errors and improving time generalization.
problem Learning the evolution operator for time-dependent Schrödinger equation with varying Hamiltonians.
method Linear estimator preserving weak unitarity, with theoretical error bounds and time generalization.
result Achieves up to two orders of magnitude smaller relative errors than existing methods.
We present online boosting algorithms for multiclass classification with bandit feedback, where the learner only receives feedback about the correctness of its prediction. We propose an unbiased estimate of the loss using a randomized prediction, allowing the model to update its weak learners with limited information. …
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.
Optimal spectral estimators and AMP combine for efficient weak recovery in orthogonally invariant GLMs.
problem Parameter estimation from generalized linear models with complex correlation structures.
method Spectral initialization and approximate message passing (AMP) algorithm.
result Established rigorous performance guarantees for spectral initialization and AMP.
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moment, we show that iteratively reweighted $\ell_1…
This work considers the problem of modified portmanteau tests for testing the adequacy of FARIMA models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak FARIMA). We first study the joint distribution of the least squares estimator and the noise empirical autocovariances. …
This work improves trace norm regularization for multi-task learning with limited data.
problem Learning from few samples across multiple tasks.
method Trace norm regularization for a linear shared representation model.
result First estimation error bound for trace norm regularized estimator with scarce data.
Existing deep active learning algorithms achieve impressive sampling efficiency on natural language processing tasks. However, they exhibit several weaknesses in practice, including (a) inability to use uncertainty sampling with black-box models, (b) lack of robustness to labeling noise, and (c) lack of transparency. I…
This article analyzes the weak error of SGD optimization schemes.
problem Analyzing the error in SGD optimization schemes with respect to a test function.
method Weak error analysis for SGD type optimization schemes.
result The weak error decays at the same speed as in the strong sense.
Improved multi-class AdaBoost algorithm with stronger weak learnability condition.
problem Multi-class classification problem with at least two labels.
method Recursive ensemble algorithm inspired by SAMME, strengthening weak learnability condition.
result Final hypothesis converges to correct label with probability 1 and generalization error bounds exponentially.
Proposes a constrained labeling method for weakly supervised learning.
problem Combining weak supervision signals while navigating misleading correlations.
method Randomized constrained labeling within a defined space.
result Randomized constrained labeling converges after few iterations and outperforms other methods.
Improved machine learning models outperform their simpler counterparts by using imperfect labels.
problem Improving model performance using imperfect labels.
method Random feature ridge regression (RFRR) with a deterministic equivalent for excess test error.
result The student model can outperform the teacher model regardless of the teacher's scaling law, achieving the minimax optimal rate.
Simple private estimators for mean and covariance outperform existing methods.
problem Private estimation of mean and covariance at small sample sizes.
method Differentially private estimators for multivariate sub-Gaussian data.
result Asymptotic error rates match theoretical bounds and outperform previous methods.
We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method - within the best …
Study improves robust nonparametric regression in heavy-tailed noise.
problem Robust nonparametric regression with heavy-tailed noise and unbounded functions.
method Huber regression in reproducing kernel Hilbert spaces (RKHS), probabilistic effective hypothesis space, new comparison theorems.
result Explicit finite-sample error bounds and convergence rates for Huber regression in RKHS under heavy-tailed noise.
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential equations into the theoretical framework of diffusion approximation, extending the …
New theory explains how strong models can learn from weak ones.
problem Learning from weak, incomplete, or incorrect labels.
method New bounds based on data distribution and student hypothesis class.
result Existing weak supervision theory fails to account for pseudolabel correction and coverage expansion.
Study on consistency of ML methods for moving objects in non-stationary environments.
problem Consistency of machine learning methods for moving objects in non-stationary environments.
method Least squares, ridge regression, and ℓs-penalized least squares methods under non-stationary spatial-temporal sampling. result Consistency and asymptotic normality of the estimates under weak conditions.
Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at least one or both associated main effects to be present in the model. Lately, thi…
Improved approximations for rough Heston model reduce errors.
problem Lack of Markov and semimartingale properties in rough Heston model.
method Markovian approximations with weak error analysis.
result Super-polynomial convergence of new approximations.
In this paper, we are interested in the strong convergence properties of the Ninomiya-Victoir scheme which is known to exhibit weak convergence with order 2. We prove strong convergence with order 1/2. This study is aimed at analysing the use of this scheme either at each level or only at the finest level of a multil…
Unified framework for error quantification in off-policy evaluation with distributional shift.
problem Establishing high-confidence CI for target policy value from offline data.
method Unified error analysis quantifying misspecification and sampling errors.
result Achieves tightest possible CI and robustness against distributional shifts.
PULSE estimator improves prediction in causal inference with bounded interventions.
problem Optimizing causal models for bounded interventions.
method Relates K-class estimators to anchor regression, introduces PULSE estimator for minimization of mean squared prediction error with bounded constraints.
result PULSE estimator outperforms other estimators in real data and simulation experiments, especially in weak instrument settings.
Establishes a microstructural foundation for a rough log-normal volatility model.
problem Developing a robust model for financial volatility under microstructural effects.
method Introduced a sequence of order-driven financial market models with Poisson process arrivals and analyzed their convergence to a log-normal rough volatility model.
result Weak convergence of price-volatility process to a log-normal rough volatility model with established weak error rates.
New method improves Euler approximation for local stochastic volatility models.
problem Well-posedness of Euler approximation for local stochastic volatility models.
method Start with a well-defined Euler approximation to the formal McKean-Vlasov equation, followed by a half-step scheme.
result Showed weak order one for the Euler discretization, plus error terms.
Estimates classifier errors without ground truth using algebraic geometry.
problem Lack of ground truth in real-world production systems.
method Non-parametric estimation using algebraic geometry to solve the self-assessment problem.
result Accuracy estimators are better than one part in a hundred.
Improves label propagation for weakly supervised learning.
problem Reducing the need for labeled data in machine learning.
method Label Propagation with Weak Supervision (LPA) analysis.
result Demonstrated improvements over existing methods on weakly supervised classification tasks.
A new method calibrates value predictions in offline RL to improve reliability.
problem Difficulty in long-horizon value prediction in offline reinforcement learning.
method Bellman calibration, a weak reliability criterion, and Iterated Bellman Calibration.
result Finite-sample guarantees show that Bellman calibration error is controlled at nonparametric rates.
Gradient estimates for solutions to a p-Laplacian equation on Riemannian manifolds.
problem Gradient estimates for positive weak solutions to a p-Laplacian equation on Riemannian manifolds.
method Morser iteration technique
result Gradient estimates show that positive weak solutions do not exist under certain conditions on manifolds with nonnegative Ricci curvature.
The rough Heston model emerges from scaling bivariate INAR processes, linking microstructure to option pricing.
problem Modeling and pricing financial options with heavy-tailed and cumulative processes.
method Scaling limit of bivariate INAR processes converging to rough Heston model, explicit formulas linking asymmetry parameters to volatility.
result Weak-error estimates and FFT-accelerated simulation for European and path-dependent options.
New theory for PCA under weak latent factors, improving inference and testing.
problem Statistical inference for PCA with weak latent factors and cross-sectional dependence.
method Comprehensive estimation and inference theory for PCA under nearly minimal factor strength, non-asymptotic.
result Asymptotic normality of PCA-based estimator for N≍T with SNR growth rate. Conformal C2ST turns weak classifiers into reliable two-sample tests.
problem Determining if two distributions are identical using weak classifiers.
method Developed conformal variants of the C2ST to convert any classifier scores into reliable p-values.
result Even weak classifiers can yield powerful and reliable two-sample tests.
Study shows how weak inverse anisotropic mean curvature flow behaves at infinity.
problem Understanding the asymptotic behavior of anisotropic mean curvature flow.
method Established local gradient estimates for anisotropic p-harmonic functions and weak solutions of IAMCF. result Weak IAMCF is asymptotic to the expanding Wulff shape solution at infinity.
Estimates long-term effects using past experiments as instruments with many weak instruments.
problem Estimating long-term causal effects with limited short-term outcomes and many weak instruments.
method Nonparametric instrumental variable inference with many weak instruments, using past experiments as instruments.
result Automatic debiased machine learning estimators for linear functionals of the structural function and its minimum-norm projection are efficient in the many-weak-instruments regime.
New research shows label refinement and weak training have limitations for aligning LLMs.
problem Limitations of refinement methods for aligning large language models.
method Analyzed probabilistic assumptions and alternative approaches to label refinement and weak training.
result Label refinement and weak training suffer from irreducible error, leaving a performance gap.
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.
In this paper we consider the cluster estimation problem under the Stochastic Block Model. We show that the semidefinite programming (SDP) formulation for this problem achieves an error rate that decays exponentially in the signal-to-noise ratio. The error bound implies weak recovery in the sparse graph regime with bou…