CIR method constructs efficient prediction intervals with guaranteed coverage.
problem Efficiently constructing near-minimal prediction intervals with guaranteed coverage.
method Conditional Interquantile Regression (CIR) and CIR+ (enhanced version).
result Optimal balance between predictive accuracy and computational efficiency.
CTI produces efficient prediction intervals with guaranteed coverage.
problem Efficient and reliable uncertainty quantification in regression.
method CTI estimates conditional density for interval length, then thresholds intervals based on this density.
result CTI achieves smaller prediction sets with guaranteed coverage compared to existing methods.
A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Support vector machines (SVMs) are well established to estimate location functions …
Proposes a method to create shorter, more accurate prediction intervals.
problem Challenges in achieving both conditional validity and interval efficiency in complex settings.
method Uses a conformal-style calibration method for neural network responses, adjusting to empirical PIT distribution.
result Demonstrates better conditional calibration and shorter intervals than existing methods.
Study optimality conditions for interval-valued optimization problems on Riemannian manifolds.
problem Optimizing interval-valued functions on Riemannian manifolds under a total order relation.
method Generalized Hukuhara directional differentiability to derive KKT-type optimality conditions.
result Derives optimality conditions for interval-valued optimization problems on Riemannian manifolds.
Boosted conformal procedure improves prediction intervals.
problem Enhancing prediction interval properties like coverage and length.
method Gradient boosting to optimize conformity score function.
result Significant improvements in interval length and coverage.
The paper improves prediction intervals for non-parametric regression using histograms.
problem Computing accurate prediction intervals for non-parametric regression models.
method Uses conditional histograms to estimate conditional distributions and compute shortest prediction intervals.
result The method provides prediction intervals with provable marginal coverage and asymptotic conditional coverage.
Study KKT conditions for multi-objective optimization on Hadamard manifolds.
problem Optimizing multi-objective interval-valued functions on Hadamard manifolds.
method Developed KKT conditions for Pareto optimal solutions under different ordering and convexity notions.
result Results are more general than on Euclidean spaces.
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.
MAPS algorithm creates reliable prediction intervals for high-dimensional data.
problem Computing reliable conditional prediction intervals in high-dimensional settings.
method Lifted predictive model (LPM) and MAPS algorithm for distribution-free intervals.
result MAPS algorithm produces valid prediction intervals for any trained model.
New method narrows prediction intervals for individual treatment effects.
problem Insufficiently conservative prediction intervals for individual treatment effects.
method Conformal inference using conditional density estimates.
result Narrower prediction intervals compared to existing methods.
In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the question under which conditions the orbits yield low-discrepancy sequences. The case o…
Self-calibrating conformal prediction improves interval efficiency and offers a practical alternative.
problem Improving the reliability and uncertainty quantification of machine learning predictions.
method Combines Venn-Abers calibration and conformal prediction for binary and regression problems.
result Improves interval efficiency through model calibration and offers practical alternatives.
The statistical properties of the return intervals τq between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold q are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of τq for different thresholds q. …
This paper improves prediction intervals for heteroskedastic regression.
problem Adaptive prediction intervals for heteroskedastic regression.
method Normalized and Mondrian conformal prediction methods.
result Conditional validity of chosen conformal predictors related to data-generating assumptions.
The spectral flow theorem is applied to operators on finite intervals.
problem Operators on finite intervals without boundary conditions are not Fredholm.
method Interpolation theory is used to define boundary conditions making the operators Fredholm. The spectral flow theorem is applied to find the Fredholm index.
result The Fredholm index is given by the spectral flow of the operator path.
Having a regression model, we are interested in finding two-sided intervals that are guaranteed to contain at least a desired proportion of the conditional distribution of the response variable given a specific combination of predictors. We name such intervals predictive intervals. This work presents a new method to fi…
New model uses interval-valued CVaR for better risk assessment in finance.
problem Measuring tail risk in rapidly changing financial markets.
method Employing random intervals to describe asset returns and using ICVaR as a risk measure.
result Optimal portfolio selection models show better risk assessment in real data.
TA-CQR predicts regression intervals with exact coverage, splitting miscoverage between endpoints.
problem Predicting regression intervals with exact coverage under reporting constraints.
method TA-CQR uses tail allocation to parameterize the oracle, estimating the allocation by searching quantile cores and applying nonnegative additive split-conformal calibration.
result TA-CQR achieves exact finite-sample marginal coverage under exchangeability, with theoretical guarantees on calibration and length.
Energy markets and the associated energy futures markets play a crucial role in global economies. We investigate the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, which are defined as the waiting times τ between consecutive volatilities exceeding a gi…
CoCP optimizes prediction intervals by jointly learning center and radius, improving efficiency and coverage.
problem Inefficient conformal prediction intervals under heteroscedasticity and skewness.
method Co-optimization framework that learns center and radius through alternating optimization steps.
result CoCP yields consistently shorter intervals and state-of-the-art conditional coverage diagnostics.
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least Squares Monte Carlo is the "Regress-Later" method. Unlike conventional methods wher…
This work uses statistical bootstrapping to provide accurate confidence intervals for policy value in reinforcement learning.
problem Bias in estimating policy value using empirical transitions and rewards.
method Statistical bootstrapping to produce calibrated confidence intervals for the true policy value.
result Statistical bootstrapping can yield correct confidence intervals under certain conditions, and mechanisms are proposed to mitigate these conditions.
Posterior conformal prediction improves prediction interval validity for subgroups.
problem Marginal and conditional prediction interval validity for subgroups.
method Modeling conditional nonconformity score distribution as a mixture of cluster distributions.
result PCP produces tighter prediction intervals, especially for well-represented clusters.
New method makes CP intervals locally adaptive using trainable transformations.
problem Making Conformal Prediction intervals locally adaptive.
method Defining a trainable change of variables φX(A) that depends on object attributes X. result Locally adaptive prediction intervals with guaranteed marginal validity and variable sizes.
We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the …
Novel method for time-series prediction with tighter confidence intervals.
problem Improving prediction intervals for time-series data.
method Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI) using adaptive weights.
result KOWCPI achieves narrower confidence intervals with guaranteed coverage.
VBMC+VIQR outperforms noisy models in Bayesian inference.
problem Bayesian inference with noisy likelihoods in complex models.
method Gaussian process surrogates, expected information gain, variational interquantile range.
result VBMC+VIQR achieves state-of-the-art performance in noisy inference benchmarks.
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.
Random forests are stable and provide reliable prediction intervals.
problem Stability and reliability of random forest prediction intervals.
method Established stability under mild conditions and proved coverage bounds.
result Non-asymptotic lower and upper bounds for prediction interval coverage.
This work challenges the assumption that shorter conformal prediction intervals are always better.
problem The conventional evaluation of conformal prediction metrics (coverage and interval length) may not fully capture the quality of predictions.
method The Prejudicial Trick (PT) is introduced, which probabilistically returns either a null interval or a longer one to maintain valid coverage while potentially reducing interval length.
result The Prejudicial Trick can yield deceptively shorter intervals without compromising coverage, but introduces practical vulnerabilities.
ICP improves prediction intervals for continuous outcomes at lower computational cost.
problem Systematic bias in point predictions that undermines their use in decision-making.
method Develops Isotonic Conformal Prediction (ICP) framework to decouple calibration from prediction-set construction.
result SICP and TICP procedures match SC-CP coverage at lower computational cost.
Develops efficient time series prediction intervals.
problem Constructing reliable prediction intervals for time series data.
method Introduces exttt{EnbPI} algorithm for time series data.
result Demonstrates superior performance compared to existing methods.
We investigate the probability distributions of the recurrence intervals τ between consecutive 1-min returns above a positive threshold q>0 or below a negative threshold q<0 of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresho…
We study the return interval τ between price volatilities that are above a certain threshold q for 31 intraday datasets, including the Standard & Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold q, the probability density function Pq(τ) scales with the mean i…
Improved conformalized quantile regression for adaptive prediction intervals.
problem Lack of adaptiveness in the conformal step of conformalized quantile regression.
method Cluster explanatory variables by permutation importance and apply k conformal steps.
result Improved prediction intervals are more adaptive to heteroscedasticity.
A new algorithm reduces inference error in adaptive contextual bandits.
problem Challenges in statistical inference for adaptive contextual bandits.
method Proposes a regularized EXP4 algorithm that satisfies the Lai-Wei stability condition.
result Valid Wald-type confidence intervals for linear functionals can be achieved without the price of adaptivity.
The paper develops a theory for random forests, separating variance components and providing methods for estimating prediction intervals.
problem Understanding the variance and uncertainty in random forest predictions.
method Design-based theory, Monte Carlo averaging, PASR resampling.
result The floor of prediction uncertainty is positive and persists even without observation overlap, providing conservative prediction intervals.
Improved confidence interval estimation with control variates.
problem Estimating confidence intervals with minimal samples.
method Designing an estimation algorithm using control variates and leveraging order statistics.
result Improved asymptotic efficiency compared to existing algorithms.
We introduce a unified framework for random forest prediction error estimation based on a novel estimator of the conditional prediction error distribution function. Our framework enables simple plug-in estimation of key prediction uncertainty metrics, including conditional mean squared prediction errors, conditional bi…
SCIENCE improves prediction intervals for individual causal effects.
problem Wide prediction intervals limit practical utility of causal inference.
method Surrogate-assisted conformal inference for efficient individual causal effects.
result SCIENCE produces more efficient prediction intervals for individual causal effects.
We study the statistical properties of the recurrence intervals τ between successive trading volumes exceeding a certain threshold q. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2…
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.
Study GKM actions on special manifolds with interval orbit spaces.
problem Understanding GKM actions on specific types of manifolds.
method Analyzing group diagrams and orbit spaces; describing GKM graphs.
result Necessary and sufficient conditions for GKM actions on cohomogeneity one manifolds.
Proposes adaptive method for classifying interval-valued time series.
problem Lack of classification methods for interval-valued time series.
method Represent intervals as images, classify using CNN, optimize coefficients with ADMM.
result Validated through simulations and real data, outperforming point-valued methods.
Normalizing Flows improve prediction interval efficiency in CP.
problem Inefficient prediction intervals in CP due to non-uniform error distribution.
method Train a Normalizing Flow to optimize the distance metric between errors and inputs.
result Optimized prediction intervals are more efficient and valid.
A theorem for debiasing machine learning with finite sample guarantees.
problem Calculating confidence intervals for machine learning functionals.
method Debiased machine learning based on bias correction and sample splitting.
result Nonasymptotic debiased machine learning theorem with finite sample guarantees.
Develops a calibration prediction interval for non-parametric regression and neural networks.
problem Lack of accurate conditional prediction in regression settings.
method Calibration Prediction Interval (cPI) using Deep Neural Networks (DNN) or kernel methods.
result Asymptotically valid coverage rate and high probability of coverage rate with large sample sizes.