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…
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48 results for “interval”
Prediction intervals are a valuable way of quantifying uncertainty in regression problems. Good prediction intervals should be both correct, containing the actual value between the lower and upper bound at least a target percentage of the time; and tight, having a small mean width of the bounds. Many prior techniques f…
New methods for ordinal classification of interval-valued data and functional data.
problem Ordinal classification of interval-valued data and functional data.
method Six ordinal classifiers are proposed, including parametric, binary decomposition, logistic regression, distance-based, k-nearest-neighbor, kernel PCA, and random forest methods.
result Considering ordering and interval-valued information improves the accuracy of ordinal classification.
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.
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…
Proposes a method to create prediction intervals for neural networks using cross-validation.
problem Lack of prediction intervals for neural networks.
method k-fold cross-validation to construct conformal prediction intervals.
result Proposed method produces narrower intervals with similar coverage compared to SC method.
The statistical properties of the return intervals between successive 1-min volatilities of 30 liquid Chinese stocks exceeding a certain threshold are carefully studied. The Kolmogorov-Smirnov (KS) test shows that 12 stocks exhibit scaling behaviors in the distributions of for different thresholds . …
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.
The paper presents a method for generating well-calibrated prediction intervals using quality-driven deep ensembles.
problem Generating reliable prediction intervals for regression analysis.
method A multi-objective loss function combining quality measures for prediction intervals and point estimates, with a penalty function to ensure semantic integrity and stability.
result The method produces well-calibrated prediction intervals and point estimates, capturing both aleatoric and epistemic uncertainty.
Constructs tail-specific prediction intervals for financial applications
problem Financial applications require strict control on the left tail
method Extends classical conformal frameworks to provide explicit tail-specific guarantees
result Improved directional calibration in skewed data
Analyzes biased random walks and corrupted intervals in adversarial settings.
problem Learning thresholds and intervals in adversarial conditions.
method Analyzes biased random walks and corrupted intervals under adversarial design.
result Analyzes the expected behavior of biased random walks and corrupted intervals.
Paper introduces a new method for classifying interval-valued time series.
problem Classification of interval-valued time series.
method Extends point-valued time series imaging methods to interval-valued scenarios using -distance and employs deep learning for classification.
result Proposed method achieves superior classification performance compared to existing methods.
Extends Fisher's Discriminant Analysis for interval-valued data.
problem Classifying entities represented by intervals and histograms.
method Adapts Fisher's Discriminant Analysis using Moore's interval arithmetic and Mallows' distance.
result Discriminant directions for interval-valued data are numerically maximized.
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 between consecutive volatilities exceeding a gi…
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.
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.
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.
We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold 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 …
Paper simulates LR fuzzy intervals with interval-valued cores.
problem Generating random fuzzy intervals with interval-valued cores.
method Developed algorithms for simulating LR fuzzy numbers with interval-valued cores.
result Numerically efficient algorithm for simulating fuzzy values.
New confidence intervals improve treatment effect estimation in randomized experiments.
problem Improving confidence intervals for treatment effects in randomized experiments.
method Systematic exploitation of negative dependence or variance adaptivity.
result Achieved nonasymptotic confidence intervals with the same effective sample size as asymptotic ones.
Practical or scientific considerations often lead to selecting a subset of parameters as ``important.'' Inferences about those parameters often are based on the same data used to select them in the first place. That can make the reported uncertainties deceptively optimistic: confidence intervals that ignore selection g…
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.
RQR improves prediction intervals for skewed data.
problem Invalid prediction intervals for skewed noise.
method Relaxed Quantile Regression (RQR) for asymmetric noise.
result Improved prediction intervals with desirable qualities.
In this paper we consider an interval portfolio selection problem with uncertain returns and introduce an inclusive concept of satisfaction index for interval inequality relation. Based on the satisfaction index, we propose an approach to reduce the interval programming problem with uncertain objective and constraints …
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.
RFpredInterval: An R Package for Prediction Intervals with Random Forests and Boosted Forestsstat.ML
RFpredInterval package builds prediction intervals for random forests and boosted forests.
problem Quantifying uncertainty in random forest and boosted forest point predictions.
method 16 methods to build prediction intervals with random forests and boosted forests.
result The proposed method outperforms existing methods in building prediction intervals.
In the present paper we study interval identification systems of order three. We prove that the Rauzy induction preserves symmetry: for any symmetric interval identification system of order three after finitely many iterations of the Rauzy induction we always obtain a symmetric system. We also provide an example of sym…
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.
Proposes sparsified intervals for high-dimensional regression coefficients.
problem Challenges of high-dimensional regression coefficient inference.
method Sparsified simultaneous confidence intervals.
result Intervals can shrink some coefficients to zero, indicating unimportance.
Methods for prediction and tolerance intervals in non-normal models.
problem Constructing prediction and tolerance intervals for non-normal data.
method Two approaches: pivotal quantity approximation and confidence interval for mean.
result Intuitive, simple, efficient methods with proper operating characteristics.
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.
CoinDICE estimates confidence intervals for unknown behavior policies in reinforcement learning.
problem Estimating value of a target policy using only behavior policy data.
method Function space embedding, generalized empirical likelihood method, Lagrangian optimization.
result Valid confidence intervals with tighter and more accurate estimates than existing methods.
New method estimates optimal dose intervals for personalized treatment.
problem Learning optimal dose intervals from observational data.
method Probability dose interval (PDI) method using DC algorithm.
result Consistent policy with risk converging to best-in-class at root-n rate.
Study compares Interval Regression models and their performance.
problem Regression models struggle with interval target values.
method Comprehensive review and comparative analysis of existing Interval Regression models.
result No single model is universally optimal for all scenarios.
This work reviews and evaluates methods for predicting prediction intervals in regression problems.
problem Calibration of prediction intervals in regression problems.
method Four classes of methods: Bayesian, ensemble, direct interval estimation, and conformal prediction.
result Conformal prediction can be used as a general calibration procedure.
Paper tackles online learning with interval regret, achieving adaptive bounds.
problem Non-stationary online learning over time intervals.
method Two-layer online ensemble structure with gradient variation.
result Achieves strong theoretical guarantees with adaptive bounds.
Power law for the calm-time interval of price changescond-mat.stat-mech
In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We conducted quantitative investigation of the {\it calm-time intervals} of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index over a 27-year period from January …
Responds to critiques on tests for causal parameter confidence intervals.
problem Testing nominal confidence interval coverage for causal parameters estimated by machine learning.
method Rejoinder to critiques on nearly assumption-free tests.
result Clarifies and supports the original research's approach.
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for interval-valued datasets. We propose a geometrical approach in the determination of s…
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long range correlations. Hence, in the last few year…
Developing an explainable outlier detection method for interval-valued data using Shapley value-based approach.
problem Outlier detection in interval-valued data.
method Proposed a novel approach based on Shapley value for interval-valued data.
result Fine-grained interpretation of outliers with variable contributions.
INNs produce interval-valued uncertainty scores for DNNs.
problem Uncertainty quantification in deep neural networks.
method Data-driven interval propagating network using interval arithmetic.
result INNs produce sensible lower and upper bounds for prediction error.
New method combines HQR and WACI for better time series prediction intervals.
problem Challenges in creating reliable prediction intervals for time series forecasting.
method Combining Heteroscedastic Quantile Regression (HQR) with Width-Adaptive Conformal Inference (WACI).
result Combined approach meets or surpasses typical benchmarks for validity and efficiency.
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'.
Interval bankruptcy problems arise in situations where an estate has to be liquidated among a fixed number of creditors and uncertainty about the amounts of the claims is modeled by intervals. We extend in the interval setting the classical results by Curiel, Maschler and Tijs (1987) that characterize division rules wh…
Improved neural network predicts tropical storm trajectories and Bayesian intervals.
problem Accurately predicting the trajectories of tropical storms to prevent damage.
method Developed an improved RNN model with dropout to predict Bayesian intervals.
result Neural network dropout values significantly affect prediction accuracy and intervals.
Certainty in Uncertainty: Reasoning over Uncertain Knowledge Graphs with Statistical Guaranteesstat.ML
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.
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.