Proposes a new framework for deep learning conditional mean estimation with confidence regions.
problem Lack of asymptotic properties in deep nonparametric regression models.
method Transforms deep estimation into conditional diffusion model for conditional mean estimation.
result Developed end-to-end convergence rate and asymptotic normality for conditional diffusion model.
DRF improves confidence and uncertainty assessment for multivariate conditional distributions.
problem Estimating multivariate conditional distributions with confidence and uncertainty.
method Developed a bootstrap approximation of the asymptotic distribution of DRF to derive inferential tools.
result Asymptotic coverage guarantees for confidence regions and hypothesis testing.
Framework for confidence estimation in deep CT reconstructions.
problem Uncertainty in deep learning-based CT reconstructions.
method Sequential likelihood mixing framework with log-linear forward model.
result Deep models yield tighter confidence regions than classical methods.
Waldo method constructs valid confidence regions for simulator-based inference.
problem Constructing valid confidence regions for simulator-based inference with high-dimensional data.
method Reframes Wald test statistic and uses regression-based machinery for Neyman inversion.
result Waldo method produces conditionally valid and precise confidence regions.
The paper develops optimal confidence regions for categorical data.
problem Constructing tight confidence regions for categorical data.
method Develops new theory for minimum average volume confidence regions.
result Shows optimality of the regions for categorical data and its implications for machine learning.
The paper develops methods for constructing confidence regions for regression functions in binary classification.
problem Building distribution-free confidence regions for regression functions in binary classification.
method Resampling test and empirical risk minimization approach for model classes with finite pseudo-dimensions and inverse Lipschitz parameterizations.
result Strong uniform consistency and exponential probably approximately correct bounds on the L2 sizes of the regions. Method constructs confidence regions for linear models with arbitrary predictors.
problem Constructing confidence regions for linear models with non-linear predictors.
method Mixed Integer Linear Programming for constraints.
result Empty confidence regions for hypothesis testing.
Introduces CCR for constructing confidence regions from conformal predictions.
problem Challenges in constructing confidence regions for model parameters.
method Combines conformal prediction intervals for model outputs to establish confidence regions for parameters under minimal assumptions.
result Valid coverage guarantees for finite sample regime, applicable to various model types.
NCP uses neural networks to efficiently learn conditional distributions.
problem Learning conditional distributions for statistical inference.
method Neural Conditional Probability (NCP) approach.
result NCP efficiently handles complex probability distributions and matches leading methods.
Constructs non-asymptotic confidence regions for unknown functions in RKHS.
problem Global probabilistic confidence regions for unknown functions in RKHS.
method Reduces confidence region construction to estimating RKHS norm.
result Valid confidence regions can be constructed non-asymptotically.
The SPS method constructs confidence regions for true parameters with optimal sample complexity.
problem Constructing exact, non-asymptotic confidence regions for true system parameters.
method Sign-Perturbed Sums (SPS) method, generalized to various types of problems.
result High probability upper bounds for SPS confidence regions show optimal shrinkage rate.
Paper develops a method to construct confidence regions for model parameters using batch means method.
problem Constructing confidence regions for model parameters in stochastic gradient descent.
method Batch means method to cancel out covariance matrix, using Polyak-Ruppert averaging.
result Established process-level functional central limit theorem for stochastic gradient descent estimators.
Develops an efficient approximation for full conformal prediction regions.
problem Computing exact full conformal prediction regions is computationally infeasible.
method Generates an approximate confidence region that can be efficiently computed.
result Introduces a new notion of thickness to quantify approximation tightness.
General predictive models do not provide a measure of confidence in predictions without Bayesian assumptions. A way to circumvent potential restrictions is to use conformal methods for constructing non-parametric confidence regions, that offer guarantees regarding validity. In this paper we provide a detailed descripti…
Robust MDPs (RMDPs) can be used to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution are determined by the ambiguity set---the set of plausible transition probabilities---which is usually constructed as a multi-dimensional confidence region. E…
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.
A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum …
Proposes a method to accelerate safe sequential learning using offline data.
problem Limited exploration due to disconnected safe regions and slow task learning.
method Safe transfer sequential learning using Gaussian processes and offline data.
result Enhances global exploration across multiple disjoint safe regions with lower data consumption.
A new method, Residual-Permuted Sums, improves confidence region construction for linear regression models.
problem Constructing reliable confidence regions for linear regression models with non-symmetric noise.
method Residual-Permuted Sums (RPS) method, which permutes residuals instead of perturbing their signs.
result RPS provides exact finite sample coverage probabilities and is uniformly strongly consistent.
Spatially weighted conformal prediction improves uncertainty quantification in house price models.
problem Uncertainty quantification in automated valuation models with spatial dependencies.
method Survey and demonstration of various spatially weighted approaches to adjust conformal prediction confidence sets.
result Spatially weighted CP makes confidence sets more consistently calibrated across geographical regions.
ACORE improves hypothesis testing and confidence sets in likelihood-free inference.
problem Constructing hypothesis tests and confidence sets in likelihood-free inference settings.
method Formulates classical LRT as a classification problem, uses machine learning to improve estimates.
result Demonstrates improved accuracy in hypothesis testing and confidence sets.
The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess t…
Paper develops methods for PCA inference with missing data and heteroskedastic noise.
problem Constructing confidence regions for PCA in high dimensions with missing data and heteroskedastic noise.
method Proposes HeteroPCA and develops non-asymptotic distributional guarantees for valid inference.
result Valid inference on principal subspace and spiked covariance matrix with missing data.
DO-IQS recovers optimal stopping region from expert trajectories, addressing specific challenges.
problem Recovering optimal stopping region from expert trajectories with unknown gain functions.
method Dynamics-Aware Offline Inverse Q-Learning incorporating temporal information and confidence-based oversampling.
result Demonstrated performance on real and artificial data, including optimal intervention for critical events.
Paper develops inference methods for low-rank tensors without debiasing.
problem Statistical inference for low-rank tensor models.
method Two-iteration alternating minimization for asymptotic distribution.
result Asymptotic distributions and confidence regions for singular subspaces.
PaRCE estimates model confidence for CNNs across various uncertainties.
problem Limited holistic approach to estimating perception model confidence in CNNs.
method Probabilistic and reconstruction-based competency estimation.
result PaRCE best distinguishes between various types of samples and regions.
The paper proposes a method to identify model uncertainty in mechanical presses using optimal design of experiments.
problem Model uncertainties in forming machines impair controller performance.
method Parameter identification, optimal design of experiments, and hypothesis testing.
result Identifies inconsistencies in parameter estimates as indicators of model uncertainty.
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.
AUCRSS detects change points in partially observed multivariate autocorrelated data.
problem Detecting change points in multivariate autocorrelated data with limited sensing resources.
method Adaptive Upper Confidence Region (AUCRSS) with state space model (SSM), adaptive sampling policy, and generalized likelihood ratio test.
result The method outperforms existing approaches in detecting change points efficiently.
Proposes CPO framework for robust decision-making with explainable uncertainty regions.
problem Overly conservative uncertainty regions in data-driven optimization lead to suboptimal decisions.
method Conformal-Predict-Then-Optimize (CPO) framework using conditional generative models and visual summaries.
result Demonstrates improved robustness and explainability in decision-making.
We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the fitted estimating equations to a sparse direction obtained by solving a large-scale…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance (in a Wasserstein sense) from the underlying empirical measure. While motivated by…
Optimizes private statistics with noisy methods.
problem Private inference in statistical models.
method Noisy optimization for M-estimators and confidence regions.
result Private estimators converge to non-private ones with high probability.
Biondi et al. (2012) develop an analytical model to examine the emergent dynamic properties of share market price formation over time, capable to capture important stylized facts. These latter properties prove to be sensitive to regulatory regimes for fundamental information provision, as well as to market confidence c…
The paper improves confidence ellipsoids for ridge regression with PAC bounds.
problem Uncertainty quantification in ridge regression for insufficiently exciting inputs.
method Extension of SPS EOA algorithm to ridge regression with PAC bounds.
result Explicitly shows how regularization parameter affects region sizes and provides tighter bounds.
Low-rank matrix regression refers to the instances of recovering a low-rank matrix based on specially designed measurements and the corresponding noisy outcomes. In the last decade, numerous statistical methodologies have been developed for efficiently recovering the unknown low-rank matrices. However, in some applicat…
This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for conf…
Trust is a collective, self-fulfilling phenomenon that suggests analogies with phase transitions. We introduce a stylized model for the build-up and collapse of trust in networks, which generically displays a first order transition. The basic assumption of our model is that whereas trust begets trust, panic also begets…
Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure t…
FreB protocol uses AI to infer hidden parameters with valid confidence regions.
problem Generating biased or overconfident conclusions from AI-generated posterior distributions.
method Frequentist-Bayes (FreB) protocol reshapes AI-generated posterior distributions into valid confidence regions.
result FreB provides valid confidence regions that consistently include true parameters with expected probability.
BALLET filters a high-confidence region of interest for Bayesian optimization.
problem High-dimensional and non-stationary Bayesian optimization challenges.
method Adaptive level-set estimation using two probabilistic models.
result Ballets can efficiently shrink the search space and exhibit tighter regret bounds.
Improved AI lung ultrasound segmentation using expert confidence values.
problem Label uncertainty in lung ultrasound due to subjective interpretation by radiologists.
method Designing a data annotation protocol capturing expert confidence, training AI on binarized labels with confidence thresholds.
result Improved AI segmentation and better clinical outcomes (e.g., S/F oxygenation ratio estimation, patient readmission prediction).
A new method uses SVM classification to efficiently compute confidence sets.
problem Computing confidence sets for moment inequalities is computationally intensive.
method Converts confidence set construction into a classification problem using SVM.
result Asymptotically reproduces the test in the confidence set using SVM classification.
This paper analyzes the sample complexity of SPS method for scalar linear regression.
problem Analyzing the sample complexity of the Sign-Perturbed Sums (SPS) identification method.
method The paper provides high probability upper bounds for the sizes of SPS confidence intervals under different sets of assumptions.
result The sizes of SPS confidence intervals shrink at a geometric rate around the true parameter, if observation noises are subgaussian.
The research proposes a stopping rule for reinforcement learning algorithms based on instance-dependent confidence.
problem Dramatic variation in convergence rates of reinforcement learning algorithms due to problem structure.
method Develops instance-dependent confidence regions and a data-dependent stopping rule for MDP policy evaluation and optimal value estimation.
result Proposes a stopping rule that adapts to the instance-specific difficulty of the problem, allowing for early termination.
New rule reduces exploration regret to logarithmic, improving bad episode handling.
problem Improving exploration regret in average reward MDPs.
method Replacing Doubling Trick with Vanishing Multiplicative rule in EVI-based algorithms.
result Regret is logarithmic under the new rule, significantly better than linear.
We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. U…
Study on inventory management under uncertainty using smooth ambiguity preference.
problem Managing inventory under Knightian uncertainty with smooth ambiguity preference.
method Demonstrates continuous-time smooth ambiguity as the infinitesimal limit of Kalman-Bucy filtering with recursive robust utility. Solves forward-backward stochastic differential equations with quadratic growth to determine cost function. Derives value function and optimal control policy using variational inequalities and viscosity solutions. Transforms problem into two-dimensional singular control.
result Ambiguity drives decision-makers to act earlier, reducing the continuation region.