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.
We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter θ, i.e. we want to construct a confidence set for theta that contains theta with high probability, and that is as small as possible. The l_2 diameter of a …
New method constructs confidence sets for GLMs via game theory.
problem Developing reliable confidence intervals for GLM parameters.
method Reduction to sequential prediction games with low regret.
result Online-to-confidence-set conversions provide new types of intervals.
New methods improve confidence set calibration in complex models.
problem Challenges in maintaining confidence set coverage in complex models.
method TRUST and TRUST++ methods using simulated data for calibration.
result Methods achieve distribution-free conditional coverage and robust inference.
We propose an algorithm combining calibrated prediction and generalization bounds from learning theory to construct confidence sets for deep neural networks with PAC guarantees---i.e., the confidence set for a given input contains the true label with high probability. We demonstrate how our approach can be used to cons…
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.
New method optimizes offline linear bandits using different confidence sets.
problem Optimizing offline learning for linear contextual bandits.
method Introduces a family of pessimistic learning rules based on ℓ p \ell_p ℓ p confidence sets. result The π ^ ∞ \hatπ_\infty π ^ ∞ rule achieves minimax performance and strictly dominates other predictors. Novel confidence sets improve linear bandit performance by adapting to unknown noise levels.
problem Adapting to unknown noise levels in sequential decision-making.
method Proposed semi-adaptive and variance-adaptive confidence sets.
result Improved regret bounds and better performance in Bayesian optimization tasks.
The age of big data has produced data sets that are computationally expensive to analyze and store. Algorithmic leveraging proposes that we sample observations from the original data set to generate a representative data set and then perform analysis on the representative data set. In this paper, we present efficient a…
Improved regret bounds for logistic bandits via novel confidence set construction.
problem Dependencies in parameter space for logistic bandits, especially when S ≥ d S \geq d S ≥ d . method Regret-to-confidence-set conversion (R2CS) to construct convex confidence sets.
result Strict improvement in regret bound w.r.t. S S S in logistic bandits. We shrink confidence sets for equivalent discrete distributions using permutation equivalence.
problem Building high-probability confidence sets for equivalent discrete distributions.
method Exploiting permutation-equivalence to refine confidence sets.
result Confidence sets shrink at asymptotic rates of O ( 1 / ∑ k ∈ K n k ) O(1/\sqrt{\sum_{k\in \mathcal K} n_k}) O ( 1/ ∑ k ∈ K n k ) and O ( 1 / max k ∈ K n k ) O(1/\max_{k\in K} n_{k}) O ( 1/ max k ∈ K n k ) . Develops methods for valid and validated confidence sets in multiclass and multilabel prediction.
problem Challenges of typical conformal prediction methods in multiclass and multilabel problems, especially uneven coverage.
method Leverages quantile regression to build methods that always guarantee correct coverage and asymptotically optimal conditional coverage, addressing label interactions with tree-structured classifiers.
result Empirical evaluation suggests more robust coverage of confidence sets.
Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator follows a known distribution to form a confidence set [Kohavi 1995, Martin 1996,Yang…
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…
Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. To this end, we show joint asymptotic normality in the spectral calibration method for the estimators of the volatility, the drift, the jump intensity and the …
Deep learning architectures have proved versatile in a number of drug discovery applications, including the modelling of in vitro compound activity. While controlling for prediction confidence is essential to increase the trust, interpretability and usefulness of virtual screening models in drug discovery, techniques t…
A universal framework for constructing confidence sets using sequential likelihood mixing.
problem Constructing reliable confidence sets for realizable likelihood functions.
method Sequential likelihood mixing, integrating Bayesian inference and regret inequalities.
result Establishes fundamental connections and provable coverage guarantees for various inference techniques.
The paper finds a fundamental trade-off between confidence and efficiency in transductive conformal prediction.
problem The challenge is to balance confidence and efficiency in predicting multiple data points.
method The authors derive a strict finite-sample bound and introduce a practical algorithm to approach this bound.
result Any non-trivial confidence level leads to exponential growth in prediction set size, with a linear scaling in the number of samples.
Confidence-based deferral works well in many scenarios but fails in specific cases.
problem Understanding when confidence-based deferral fails and when other strategies are better.
method Theoretical analysis and post-hoc deferral mechanisms were studied.
result Theoretical analysis characterizes settings where confidence-based deferral may fail.
Study three types of uncertainty quantification for binary classification without distributional assumptions.
problem Uncertainty quantification for binary classification in a distribution-free setting.
method Established theorems connecting calibration, confidence intervals, and prediction sets for score-based classifiers.
result Distribution-free calibration is only possible using scoring functions that partition feature space into countably many sets.
Paper presents methods to create stock price confidence intervals using LSTM models.
problem Creating accurate confidence intervals for LSTM-estimated stock prices.
method Three bootstrap methods for dependent data, optimal block length selection, and benchmark comparison.
result Illustrated through stock price data, different bootstrap strategies provide varying confidence intervals.
The paper addresses the gap between theoretical and practical confidence set widths in universal inference.
problem Inference procedures can be overly conservative, leading to wider confidence sets than expected.
method The authors identify the source of asymptotic conservativeness and propose a remedy based on studentization and bias correction.
result The proposed method achieves exact asymptotic coverage at the nominal 1 − α 1-α 1 − α level, even under model misspecification. New algorithm for precise changepoint localization without assumptions.
problem Offline changepoint localization in arbitrary distributions.
method Distribution-free algorithm CONformal CHangepoint localization (CONCH) using exchangeability arguments.
result Derives principled score functions for informative and small confidence sets with normalized length shrinking to zero.
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.
Develops spatial uncertainty guarantees for image segmentation models.
problem Ensuring reliable segmentation predictions for biomedical images.
method Adapting conformal inference to imaging, using transformed logit scores and calibration datasets.
result Confidence sets provide spatial uncertainty guarantees with desired probability.
Algorithm finds small confidence sets for arbitrary distributions.
problem Learning high-density regions in arbitrary distributions.
method Competitive with sets from a concept class with bounded VC-dimension.
result Algorithm finds a confidence set with volume exp ( i l d e O ( d 1 / 2 ) ) \exp( ilde{O}(d^{1/2})) exp ( i l d e O ( d 1/2 )) competitive with optimal ball. Paper certifies intersection of minimum-volume confidence sets for multinomial outcomes.
problem Certifying intersection of minimum-volume confidence sets for multinomial outcomes.
method Exploits likelihood ordering to induce halfspace constraints, enabling adaptive geometric partitioning and computable bounds on p-values.
result Efficient and provably sound algorithm for certifying intersection, disjointness, or indeterminate result.
A new method for predicting with confidence for complex models.
problem Lack of reliable confidence in high-stake decision-making models.
method Developed a full-CP for sparse high-order interaction model using homotopy mining.
result SHIM achieves comparable accuracy to complex models and superior statistical power.
The paper extends confidence sequences for infinite variance data.
problem Addressing confidence sequences for distributions with infinite variance.
method Establishing lower bounds and deriving tight confidence sequences for relaxed bounded p t h p^{th} p t h -moment distributions. result Derived confidence sequences are tighter than those using Dubins-Savage inequality.
New algorithm improves best arm identification in Bayesian settings.
problem Finding the arm with the highest mean in unknown distributions.
method Developed a variant of successive elimination algorithm.
result Achieved optimal performance in Bayesian setting with logarithmic gap.
Develops statistical confidence sets for multidimensional scaling.
problem Statistical uncertainty in multidimensional scaling of noisy data.
method Formal statistical framework, distributional convergence results, uniform confidence sets, bootstrap procedures.
result Construction of reliable confidence sets for latent configurations in multidimensional scaling.
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.
Develops confidence bounds for off-policy evaluation in contextual bandits.
problem Evaluating policies that were not used to collect data.
method Martingale analysis for non-asymptotic, non-parametric, and valid confidence sequences.
result Empirically tight bounds on failure probability and width.
New method HNCI for evaluating treatment effects in network interference.
problem Evaluating the effectiveness of treatments or policies under network interference.
method High-dimensional network causal inference (HNCI) using linear regression with latent homogeneity.
result Valid confidence intervals and sets for average direct treatment effect and neighborhood size.
New tighter confidence bounds for sequential kernel regression.
problem Quantifying uncertainty in sequential learning algorithms.
method Martingale tail inequalities and conic programming.
result New confidence bounds are tighter than existing ones.
Study shows NCCP can replace CP for ACI in non-exchangeable data.
problem Ensuring reliable prediction under non-exchangeability.
method Demonstrates NCCP as a valid alternative to CP for ACI.
result NCCP offers computational advantages and comparable predictive efficiency.
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…
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.
New method uses weak labels to create valid confidence sets for predictions.
problem Lack of labeled data in machine learning models.
method Developed a conformal prediction framework to provide valid predictive confidence sets using weakly labeled data.
result New coverage definition allows for tighter and more informative (but valid) confidence sets.
Improved algorithms for stochastic linear bandits using tighter confidence sequences.
problem Stochastic linear bandits with improved worst-case regret guarantees.
method Novel tail bound for adaptive martingale mixtures to construct tighter confidence sequences.
result Linear bandit algorithm achieves competitive worst-case regret.
This paper introduces a new method for uncertainty quantification in prediction models.
problem Quantifying uncertainty in high-stakes applications like medicine and finance.
method Confidence sets for outcome excursions, focusing on identifying subsets of features where outcomes exceed a threshold.
result Theoretical guarantees for the probability that confidence sets contain the true feature subset, both asymptotically and for finite sample sizes.
We provide a pointwise confidence bound for non-linear least-squares with fixed design.
problem Confidence estimation in non-linear ℓ 2 \ell^2 ℓ 2 -regularized least squares. method Pointwise confidence bound for local minimizers, using weighted norm involving inverse-Hessian.
result The proposed confidence bound scales with the test input's similarity to the training data.
Paper presents robust confidence sequences for means with known moment bounds and arbitrary corruption.
problem Tackles robustness to outliers and adversarial corruptions in mean estimation.
method Designs new robust exponential supermartingales to create confidence sequences.
result Achieves optimal width and shows smaller margin of error compared to fixed-time robust methods.
New method predicts sets under unknown covariate shift with high confidence.
problem Adapting to unknown covariate shift in prediction sets.
method PredSet-1Step, a flexible distribution-free method.
result Achieves asymptotic probably approximately correct coverage.
Paper improves confidence intervals and variance estimation for deep learning models.
problem Improving confidence intervals and variance estimation in deep learning models.
method Residual-based framework for conditional variance estimation; robust bootstrap procedure for confidence intervals.
result First non-asymptotic bounds for variance estimation using ReLU networks.
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.
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.
Fuzzy prediction sets generalize binary predictions to include elements at varying confidence levels.
problem Binary prediction sets are limited; fuzzy prediction sets offer richer guarantees.
method Generalize prediction sets to fuzzy sets, showing they are e-values with merging properties.
result Optimal e-values lead to optimal fuzzy prediction sets, including optimal conformal prediction.