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.
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.
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.
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…
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 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.
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. 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.
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.
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.
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.
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.
In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method. The main idea is to cancel out the covariance matrix which is hard/costly to estimate. In the process of developing the algorithm, we establish process-level functional cent…
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.
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.
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…
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.
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…
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.
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.
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).
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.
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.
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…
Clarifies the confidence interval approach for bioequivalence testing.
problem Ensuring the reliability of bioequivalence testing methods.
method Clarifies the conditions under which a 100(1-2α)% confidence interval yields a size-α test.
result A 100(1-2α)% confidence interval approach for bioequivalence testing yields a size-α test only when the two one-sided tests are 'equal-tailed'.
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.
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.
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
problem Determining if minimum-volume confidence sets for multinomial outcomes are disjoint.
method Enumerating and covering the continuous regions of the exact p-value function to study the geometry of minimum-volume confidence sets.
result The geometry of minimum-volume confidence sets for multinomial parameters is studied, providing insights into their structure and properties.
The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of the two classes, while the overlap is an ambiguity region which could belong to e…
New method to assess uncertainty in Bayesian optimization.
problem Uncertainty quantification in Bayesian optimization.
method Constructing confidence regions of the maximum point or value of the objective function.
result Unified uncertainty quantification framework for various sampling policies and stopping criteria.
The paper provides a method to find optimal machine learning model parameters with confidence.
problem Finding optimal machine learning model parameters that generalize well to the entire population.
method Constructs valid confidence sets for the optimal parameter using only training data.
result Valid confidence sets for optimal machine learning model parameters can be generated using bootstrapping techniques.
Discriminatively trained neural classifiers can be trusted, only when the input data comes from the training distribution (in-distribution). Therefore, detecting out-of-distribution (OOD) samples is very important to avoid classification errors. In the context of OOD detection for image classification, one of the recen…
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.
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 …
DeepLR constructs confidence intervals for neural networks with asymmetric expansions.
problem Uncertainty estimation for neural network predictions.
method Likelihood-ratio-based approach for constructing asymmetric confidence intervals.
result DeepLR offers asymmetric intervals expanding in regions with limited data.
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.
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…
An automatic machine learning (AutoML) task is to select the best algorithm and its hyper-parameters simultaneously. Previously, the hyper-parameters of all algorithms are joint as a single search space, which is not only huge but also redundant, because many dimensions of hyper-parameters are irrelevant with the selec…