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.
Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined and it is shown that symmetric intervals are the shortest. The length of the sho…
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.
BCI provides calibrated prediction intervals for time series forecasts.
problem Calibration of prediction intervals for time series forecasts.
method BCI wraps around any time series forecasting models and optimizes interval lengths using dynamic programming.
result BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence.
Study finds saddle connections on random surfaces follow Poisson distribution.
problem Distribution of saddle connections on random translation surfaces.
method Analysis of saddle connections on surfaces of large genus.
result Number of saddle connections in given lengths converges to Poisson distribution.
Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance. Specifically, we construct confidence intervals for the Sliced Wasserstein distanc…
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.
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.
New online conformal prediction methods minimize strongly adaptive regret and achieve near-optimal coverage.
problem Uncertainty quantification in online settings with changing data distributions.
method Developed new online conformal prediction methods that minimize strongly adaptive regret.
result Achieve near-optimal strongly adaptive regret and approximately valid coverage.
An online framework optimizes efficiency in conformal prediction with a target miscoverage rate.
problem Achieving coverage and minimizing interval length in a sequential, online setting.
method Optimizes efficiency by directly optimizing the average length of intervals while maintaining coverage.
result Shows a gap between optimal performance for exchangeable and arbitrary sequences, and provides a matching algorithm for the Pareto-optimal settings.
Study optimizes prediction intervals in conformal regression.
problem Optimizing the length of prediction intervals in conformal regression.
method Introduces EffOrt and Ad-EffOrt methodologies to minimize interval length.
result Demonstrates theoretical and empirical improvements over classical methods.
The nonparametric problem of detecting existence of an anomalous interval over a one dimensional line network is studied. Nodes corresponding to an anomalous interval (if exists) receive samples generated by a distribution q, which is different from the distribution p that generates samples for other nodes. If anomalou…
Paper proposes new method for time series confidence intervals using LSTM.
problem Constructing accurate confidence intervals for multivariate time series.
method Uses Long Short Term Memory Network (LSTM) and novel block bootstrap techniques.
result Demonstrates improved accuracy in constructing confidence intervals.
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.
The paper develops adaptive confidence intervals for Efron's Gaussian two-groups model with unknown contamination.
problem Developing robust uncertainty quantification for Efron's Gaussian two-groups model with unknown contamination fraction.
method The approach involves Fourier-based certification procedures to find minimax-optimal adaptive confidence intervals.
result The minimax-optimal length of adaptive confidence intervals is polynomially worse than when contamination fraction is known.
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.
Optimizes data splitting for shorter conformal prediction intervals.
problem Minimizing prediction interval length while maintaining coverage.
method Theoretical framework for optimal data splitting in split conformal prediction.
result Analytical characterizations of length-optimal split ratios in various settings.
We study metric and analytic properties of generalized lemniscates E_t(f)={z:ln|f(z)|=t}, where f is an analytic function. Our main result states that the length function |E_t(f)| is a bilateral Laplace transform of a certain positive measure. In particular, the function ln|E_t(f)| is convex on any interval free of cri…
Develops active intervals for geodesics in Teichmüller space.
problem Understanding geodesics in Teichmüller space with no backtracking.
method Defines active intervals for subsurfaces along geodesics in Thurston metric.
result Active intervals represent reparametrized quasi-geodesics in curve graphs with bounded movement outside.
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.
This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time tmix of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require t…
We consider the problem of undirected graphical model inference. In many applications, instead of perfectly recovering the unknown graph structure, a more realistic goal is to infer some graph invariants (e.g., the maximum degree, the number of connected subgraphs, the number of isolated nodes). In this paper, we propo…
A rope is a non-singular embedding of a closed interval into R^3, which sends the ends of the interval to some fixed points A and B such that |AB|=1. A rope is short if its length is less than 3. The main result of the paper is that the fundamental group of the space of short ropes is naturally isomorphic to the group …
AutoCP automates the construction of accurate prediction intervals.
problem Creating valid and accurate prediction intervals for machine learning models.
method AutoML framework that optimizes prediction interval length for better accuracy and less conservatism.
result AutoCP significantly outperforms benchmark algorithms in constructing accurate prediction intervals.
Random Forests provide interpretable prediction intervals with theoretical guarantees.
problem Lack of uncertainty estimates in machine learning point predictions.
method Out-of-Bag procedure for generating parametric and non-parametric prediction intervals.
result Proposed prediction intervals deliver correct coverage rates and narrow lengths.
UnKGCP generates prediction intervals for uncertain knowledge graphs with statistical guarantees.
problem Lack of quantified predictive uncertainty in existing UnKGE methods.
method Proposes extsc{UnKGCP} framework using conformal prediction with a novel nonconformity measure.
result Sharp prediction intervals effectively capture predictive uncertainty in diverse UnKGE methods.
Conformal prediction is a technique for constructing prediction intervals that attain valid coverage in finite samples, without making distributional assumptions. Despite this appeal, existing conformal methods can be unnecessarily conservative because they form intervals of constant or weakly varying length across the…
Private statistical inference methods improve confidence interval lengths.
problem Constructing private confidence intervals with differential privacy.
method Proposed two private variants of non-parametric bootstrap.
result Achieve similar coverage accuracy to non-private methods with shorter intervals.
We present the first treatment of the arc length of the Gaussian Process (GP) with more than a single output dimension. GPs are commonly used for tasks such as trajectory modelling, where path length is a crucial quantity of interest. Previously, only paths in one dimension have been considered, with no theoretical con…
Proposes SCD-split for CP to balance interpretability and efficiency.
problem Difficult interpretation of disconnected subintervals in CP prediction sets.
method Incorporates smoothing operations into CP framework.
result SCD-split balances interval length and subinterval number, theoretically provable.
Study counts geodesics on hyperbolic 3-manifolds, proving prime theorems.
problem Counting primitive closed geodesics on compact hyperbolic 3-manifolds.
method Proves prime geodesic theorems with symmetric error terms in length and holonomy.
result Effective equidistribution of holonomy and symmetric error terms.
New auction design uses statistical learning to reduce costs and improve fairness.
problem Designing efficient multi-item auctions with reduced implementation costs and fairness.
method Nonparametric density estimation for credible intervals, two new strategies.
result Strategies consistently outperform alternative methods in revenue maximization and cost reduction.
CONTINA provides adaptive confidence intervals for traffic demand prediction.
problem Uncertainty in future traffic demand predictions and the need for valid confidence intervals.
method Adaptive confidence interval method that adjusts based on deployment errors.
result Valid confidence intervals with shorter lengths and theoretical coverage guarantee.
Develops confidence intervals for ECE, a measure of model calibration.
problem Ensuring the calibration of probabilistic predictions in machine learning models.
method Develops confidence intervals for the ℓ2 Expected Calibration Error (ECE), considering top-1-to-k calibration. result Shows asymptotic normality and different convergence rates for calibrated and miscalibrated models, developing methods to construct valid confidence intervals.
A new framework for mining high utility patterns in interval-based sequences.
problem Mining patterns in events that persist over varying time intervals and considering event utility.
method Integrates utility into interval-based sequences and proposes HUIPMiner algorithm with pruning strategy.
result HUIPMiner efficiently finds high utility patterns in real datasets.
This paper extends the existing literature on empirical estimation of the confidence intervals associated to the Detrended Fluctuation Analysis (DFA). We used Montecarlo simulation to evaluate the confidence intervals. Varying the parameters in DFA technique, we point out the relationship between those and the standard…
The study constructs a Lorentzian length space and explores its properties and relationships with metric and causal geometry.
problem Understanding the relationship between metric and causal geometry in Lorentzian spaces.
method Constructing a Lorentzian length space with an orthogonal splitting on a product of an interval and a metric space, and using synthetic time-like Ricci curvature bounds.
result Established sufficient conditions for global hyperbolicity and formulated time-like Ricci curvature bounds without push-up and regularity assumptions.
Consider the classical problem of predicting the next bit in a sequence of bits. A standard performance measure is {\em regret} (loss in payoff) with respect to a set of experts. For example if we measure performance with respect to two constant experts one that always predicts 0's and another that always predicts 1's …
The spectral gap γ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix P may be unknown, yet one sample of the chain up to a fixed time n may be observed. We consider here the problem of estimating γ fro…
In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of L. Polterovich and M. Schwarz, we study the role of the fixed global extrema in the Floer complex of the generating Hamiltonian. Our…
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.
In 1992, Reid asked whether hyperbolic 3-manifolds with the same geodesic length spectra are necessarily commensurable. While this is known to be true for arithmetic hyperbolic 3-manifolds, the non-arithmetic case is still open. Building towards a negative answer to this question, Futer and Millichap recently construct…
Unified minimax value interval for off-policy evaluation and optimization.
problem Overcoming the exponential variance in off-policy evaluation and policy optimization.
method Unified minimax value interval using marginalized importance weights.
result Unified value interval with double robustness, valid when either value-function or importance-weight class is well specified.
New method calibrates diffusion models for image regression tasks.
problem Ensuring reliability of diffusion models for critical applications.
method Risk-Controlling Prediction Sets (RCPS) with convex optimization.
result Calibrated entrywise intervals and risk control with minimal mean interval length.
Study improves confidence measures in medical imaging pipelines by addressing bias.
problem Bias in metric-based imaging pipelines compromises the efficiency of prediction intervals.
method Formalized symmetric and asymmetric CP formulations, analyzed bias effects, and validated empirically.
result Symmetric intervals are inflated by bias, while asymmetric intervals remain unaffected.
In this study, we introduce a new approach to combine multi-classifiers in an ensemble system. Instead of using numeric membership values encountered in fixed combining rules, we construct interval membership values associated with each class prediction at the level of meta-data of observation by using concepts of info…
The stochastic block model (SBM) is a flexible probabilistic tool that can be used to model interactions between clusters of nodes in a network. However, it does not account for interactions of time varying intensity between clusters. The extension of the SBM developed in this paper addresses this shortcoming through a…
lCARE improves EVaR model for time-varying tail risk by localizing parameters.
problem Time-varying tail risk in financial portfolios.
method Local parametric approach to fit expectile models, optimizing interval length.
result Optimal interval lengths for tail risk capture (3-6 months) improve risk assessment.