The paper improves nonparametric confidence bands for band-limited functions.
problem Constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees.
method Based on Paley-Wiener reproducing kernel Hilbert spaces, the paper relaxes assumptions, improves noise estimation, and tightens constraints.
result Enhanced confidence bands with improved efficiency and tighter constraints.
The paper improves confidence regions for band-limited functions using tighter norm bounds and majority voting.
problem Constructing reliable confidence regions for band-limited functions from noisy data.
method Improved norm bounds using Hoeffding's inequality and empirical Bernstein bound, majority voting to aggregate intervals.
result Confidence intervals retain their simultaneous coverage guarantee even when aggregated from random subsamples.
Confidence bands for tuning curves improve hyperparameter comparison in NLP.
problem Ambiguity in comparing hyperparameter tuning methods.
method Constructs exact, simultaneous, and distribution-free confidence bands for tuning curves.
result Confidence bands provide a robust basis for comparing methods rigorously.
The paper constructs optimal confidence bands for kernel gradient flow estimators.
problem Estimating generalization error and constructing confidence bands for kernel gradient flows.
method Established convergence rates and constructed optimal confidence bands under capacity-source condition.
result Optimal confidence bands for kernel gradient flows have shrinkage rates close to minimax optimal rates.
New method for accurate uncertainty estimation in deep learning predictions.
problem Insufficient methods for assessing prediction uncertainty in deep learning.
method Valid non-parametric bootstrap method for deep neural networks.
result Accurate confidence intervals and simultaneous confidence bands for survival data.
This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the traditional Bahadur representation in parametric models, that is, Bahadur [Ann. Inst. S…
Paper proposes a method to estimate confidence bands for survival random forests.
problem No statistically valid and computationally feasible approach for estimating confidence bands for survival random forests.
method Extending recent developments in infinite-order incomplete U-statistics, the paper proposes an unbiased confidence band estimation.
result The proposed method accurately estimates the confidence band and achieves desired coverage rate.
The paper creates nonparametric confidence bands for band-limited functions.
problem Estimating confidence bands for band-limited functions with finite samples and unknown noise.
method Uses Paley-Wiener reproducing kernel Hilbert spaces and gradient-perturbation methods.
result Non-asymptotic guarantees for confidence regions without assuming a parametric model.
New random forest method provides optimal rates and confidence bands.
problem Improving random forest regression rates and constructing confidence bands.
method Proposed Ehrenfest centered purely random forests achieve optimal rates; used Gaussian approximation for supremum of empirical processes.
result Explicit asymptotic uniform confidence bands constructed for both random forest types.
Develops methods for estimating and providing confidence bands in sparse high-dimensional additive models.
problem Estimating and providing reliable confidence bands for nonparametric components in high-dimensional additive models.
method Integrates sieve estimation into a high-dimensional Z-estimation framework, employing a multiplier bootstrap procedure.
result Constructs uniformly valid confidence bands for the target component f1 in sparse high-dimensional additive models. We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the literature, the kernel regression and the spline method, and is of interest in it…
New method constructs confidence bands for ODE models with unknown regulatory effects.
problem Building confidence bands for ODE models with unknown regulatory relations is challenging.
method Localized kernel learning approach combined with de-biasing method.
result The constructed confidence band has the desired asymptotic coverage probability and accurately recovers the regulatory network.
New calibration bands for various distributions improve testing for auto-calibration.
problem Testing for auto-calibration in finite samples is challenging.
method Construct calibration bands for the exponential dispersion family using finite sample properties.
result Calibration bands allow for various tests for calibration and auto-calibration.
Proposes a Varying-Coefficient MoE model for analyzing dynamic data.
problem Inadequate constant coefficients in MoE models for dynamic settings.
method Varying-Coefficient Mixture of Experts (VCMoE) model with varying coefficients in gating and expert models.
result Established identifiability and consistency of the VCMoE model.
We use PDPs with confidence bands to explain HPO results.
problem Lack of explainable insights into HPO results.
method Use IML techniques, specifically PDPs, with estimated confidence bands.
result Increased quality of PDPs in relevant sub-regions.
New method for predicting paths of unpredictable objects with high confidence.
problem Need for dependable uncertainty estimates in motion planning with diverse unpredictable objects.
method Blend online conformal prediction, multiple time series techniques, and heteroscedasticity addressing.
result Simultaneous forecasting bands that cover entire paths with high probability.
Kernel ridge regression inference for nonstandard data.
problem Inferential theory for kernel ridge regression with nonstandard data.
method Constructs valid and sharp confidence sets using anti-symmetric multipliers.
result Develops a test for match effects in school matching mechanisms.
Many problems that appear in biomedical decision making, such as diagnosing disease and predicting response to treatment, can be expressed as binary classification problems. The costs of false positives and false negatives vary across application domains and receiver operating characteristic (ROC) curves provide a visu…
Electricity production via solar energy is tackled via short-term forecasts and risk management. Our main tool is a new setting on time series. It allows the definition of "confidence bands" where the Gaussian assumption, which is not satisfied by our concrete data, may be abandoned. Those bands are quite convenient an…
Efficiently constructs prediction bands with minimal assumptions.
problem Uncertainty quantification for nonparametric, heteroscedastic data.
method Semi-definite programming for data-adaptive prediction bands.
result Strong non-asymptotic coverage properties with minimal distributional assumptions.
Method provides statistical guarantees for identifying subgroups in ML studies.
problem Bias and noise in estimating conditional average treatment effects (CATE).
method Develops uniform confidence bands (GATES) for estimating group average treatment effects (GATEs).
result Identifies subgroups with statistical guarantees, regardless of effect size.
Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, includi…
New methods for estimating and inferring nonparametric structural functions and elasticities.
problem Estimating and inferring nonparametric structural functions and their derivatives.
method Data-driven sieve dimension choice and uniform confidence bands construction.
result Optimal estimation and inference procedures with minimax rates of convergence.
The paper analyzes LETF option markets using moneyness scaling to find statistical arbitrage opportunities.
problem Statistical discrepancies between levered and unlevered ETF option implied volatility smiles.
method Bootstrap uniform confidence bands, dynamic semiparametric factor model, moneyness scaling, Heston stochastic volatility.
result Trading opportunities exist on LETF market, and a statistical arbitrage strategy generates positive returns.
Gaussian Process Regression and Kernel Ridge Regression are popular nonparametric regression approaches. Unfortunately, they suffer from high computational complexity rendering them inapplicable to the modern massive datasets. To that end a number of approximations have been suggested, some of them allowing for a distr…
Develops local population-risk certificates for model updates
problem Model updates in machine learning
method Certify population-risk increments around a model
result Certified upper endpoint yields a risk-controlled update rule
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.
New method quantifies uncertainty in distributed regression.
problem Large datasets make traditional regression techniques ineffective.
method Data-driven approach to uncertainty quantification for averaged estimator.
result Rigorous theoretical guarantees for sup-norm consistency.
Proposes sparsified intervals for high-dimensional regression coefficients.
problem Challenges of high-dimensional regression coefficient inference.
method Sparsified simultaneous confidence intervals.
result Intervals can shrink some coefficients to zero, indicating unimportance.
As adversarial attacks pose a serious threat to the security of AI system in practice, such attacks have been extensively studied in the context of computer vision applications. However, few attentions have been paid to the adversarial research on automatic path finding. In this paper, we show dominant adversarial exam…
This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees provide prediction sets for the underlying stochastic process with a guaranteed fi…
The paper improves the empirical bootstrap method for non-normal estimators.
problem Theoretical properties of empirical bootstrap for non-asymptotically normal estimators.
method Establishing limiting distribution, deriving consistency conditions, proposing alternative methods.
result The empirical bootstrap method can be asymptotically consistent under stability conditions.
New method improves GP uncertainty quantification for misspecified priors.
problem Uncertainty quantification for GPs under incorrect priors.
method Constructs a confidence sequence using martingale techniques.
result Empirically outperforms standard GP methods in robustness and utility for Bayesian Optimization.
Extend CPS to non-exchangeable settings with observation-specific permutation weights
problem Calibrated predictive bands under distributional shifts
method Encoding distributional shifts through observation-specific permutation weights
result Shift-aware predictive systems remain valid
The study improves life insurance surrender risk modeling using various machine learning techniques.
problem Accurate modeling of surrender risk in life insurance to meet Solvency II directive requirements.
method Extensive experiments with XGBoost, random forest, GLM, and neural networks; resampling analysis; time-dependent confidence bands.
result Models trained on resampled data predict significantly biased event probabilities, highlighting the need for complementary assessments.
This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern machine learning (ML) tools. We represent this structural function as a conditional expec…
Audio source separation is the process of separating a mixture (e.g. a pop band recording) into isolated sounds from individual sources (e.g. just the lead vocals). Deep learning models are the state-of-the-art in source separation, given that the mixture to be separated is similar to the mixtures the deep model was tr…
Every link is shown to be presentable as a boundary of an unknotted flat banded surface. A (flat) banded link is defined as a boundary of an unknotted (flat) banded surface. A link's (flat) band index is defined as the minimum number of bands required to present the link as boundaries of an unknotted (flat) banded surf…
Data-driven method for error estimation without needing class complexity.
problem Constructing confidence intervals for a class of estimates.
method Data-driven approach to derive high-probability upper bounds on maximum error.
result Method naturally adapts to unknown correlation structures and works for finite and infinite classes.
The paper develops methods to accurately locate change points in high-dimensional mean shift models.
problem Locating change points in high-dimensional mean shift models.
method Locally refitted least squares estimator, component-wise and simultaneous rates of estimation.
result Asymptotic validity of component-wise and simultaneous confidence intervals for change point parameters.
We explore the role that random arbitrage opportunities play in hedging financial derivatives. We extend the asymptotic pricing theory presented by Fedotov and Panayides [Stochastic arbitrage return and its implication for option pricing, Physica A 345 (2005), 207-217] for the case of hedging a derivative when arbitrag…
Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and simultaneous Bayesian credible sets in GP regression. As an intermediate result, we develop…
FFCP improves FCP's speed without sacrificing accuracy.
problem Inefficient feature transformation in FCP.
method Introduces FFCP using Taylor expansion for faster computation.
result FFCP achieves a 50x speedup with comparable accuracy.
Satellite knots can be trivialized by a single band move.
problem Satellite knots and their trivialization.
method Infinite family of satellite knots and a single band move.
result No disjoint band unknotting exists for satellite knots.
Paper proves a noncompact version of Gromov's band-width estimate.
problem Proving a precise upper bound for noncompact Riemannian bands.
method Developed a quantitative partitioned manifold index theory.
result Proved a version of Gromov's band-width estimate for noncompact Riemannian bands.
Study shows upper limit for torical band width with spectral curvature bounds.
problem Understanding the band width of torical bands with spectral curvature constraints.
method Used the warped \( μ\)-bubble method with spectral curvature bounds.
result Upper bound for the band width of torical bands is established.
The goal of this study is to explain and examine the statistical underpinnings of the Bollinger Band methodology. We start off by elucidating the rolling regression time series model and deriving its explicit relationship to Bollinger Bands. Next we illustrate the use of Bollinger Bands in pairs trading and prove the e…
Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline techniques by additionally allowing for quantification of uncertainty. The prop…