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.
Neural network learns kernel functions for survival analysis and prediction intervals.
problem Predicting survival times for individuals based on similar training subjects.
method Develops a neural network framework to learn kernel functions for kernel survival analysis and uses these to construct valid prediction intervals.
result Neural network survival estimators are competitive with existing methods and provide valid prediction intervals.
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 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…
This paper reviews methods for constructing confidence intervals for error rates in 1:1 matching tasks.
problem Challenges in assessing uncertainty of error rates in matching algorithms, especially when data are dependent and error rates are low.
method Derives and examines statistical properties of methods for constructing confidence intervals for error rates in 1:1 matching tasks.
result Coverage and interval width vary with sample size, error rates, and data dependence.
Introduces neural network for interval-censored survival analysis.
problem Lack of non-linear regression algorithms for interval-censored data.
method Sparse neural network architecture for feature selection and AFT model for prediction.
result Outperforms traditional AFT algorithms in non-linear scenarios.
Boosting methods for interval-censored data improve predictive accuracy in survival analysis.
problem Handling interval-censored data in survival analysis and time-to-event studies.
method Nonparametric boosting methods using censoring unbiased transformations and functional gradient descent.
result Effective boosting methods for regression and classification with interval-censored data, offering robust performance.
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…
Research aims to improve confidence intervals for RKHS elements in online learning.
problem Improper confidence intervals lead to suboptimal regret bounds in kernel-based bandit and reinforcement learning.
method Formalizes the open problem of online confidence intervals in RKHS and reviews existing results.
result Identifies the online nature of observation points as the main challenge for tight confidence intervals.
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincaré inequalities. Typically two kind of sensitivity indices are linked by a Poincaré type inequality, which provide upper bounds of the most interpretable index by using the other one, cheaper …
Study improves traffic prediction intervals for minor roads.
problem Uncertainty in traffic data for underrepresented minor roads.
method Quantile Random Forest with PCA for interval prediction.
result Achieved 88.22% interval coverage and Winkler Score of 7,468.47.
We present new methods for batch anomaly detection in multivariate time series. Our methods are based on maximizing the Kullback-Leibler divergence between the data distribution within and outside an interval of the time series. An empirical analysis shows the benefits of our algorithms compared to methods that treat e…
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.
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 …
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.
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 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. …
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…
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 DK-distance and employs deep learning for classification. result Proposed method achieves superior classification performance compared to existing methods.
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.
We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling behavior and memory effect of the return intervals between successive realized vola…
New method assesses prediction intervals across different operating points.
problem Difficulty in comparing prediction intervals across studies.
method Operating characteristics curves and gain over a simple reference.
result A novel operating point agnostic assessment methodology for prediction intervals.
We investigate the probability distribution of the return intervals τ between successive 1-min volatilities of two Chinese indices exceeding a certain threshold q. The Kolmogorov-Smirnov (KS) tests show that the two indices exhibit multiscaling behavior in the distribution of τ, which follows a stretched exponent…
We study confidence intervals based on hard-thresholding, soft-thresholding, and adaptive soft-thresholding in a linear regression model where the number of regressors k may depend on and diverge with sample size n. In addition to the case of known error variance, we define and study versions of the estimators when…
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.
ICODEN models survival data with interval-censored times using neural networks and ODEs.
problem Predicting time-to-event outcomes with interval-censored data, especially when models require strong assumptions or cannot handle high-dimensional predictors.
method ICODEN uses ordinary differential equations and deep neural networks to model the hazard function and cumulative hazard without proportional hazards assumption.
result ICODEN achieves satisfactory predictive accuracy across various simulation and real-world applications, handling high-dimensional predictors robustly.
Proposes a deep learning framework for interval-censored survival data.
problem Lack of deep learning methods for interval-censored survival data.
method Partially linear transformation models with DNN approximations for nonlinear effects.
result DNN estimator achieves minimax-optimal convergence and superior performance.
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.
Being able to forcast extreme volatility is a central issue in financial risk management. We present a large volatility predicting method based on the distribution of recurrence intervals between volatilities exceeding a certain threshold Q for a fixed expected recurrence time τQ. We find that the recurrence inter…
Study analyzes derivative-free loss method for solving PDEs and fluid problems.
problem Solving elliptic PDEs and fluid problems using neural networks.
method Derivative-free loss method with Feynman-Kac formulation and stochastic walkers.
result Training loss bias scales with time interval and spatial gradient, inversely with walker size.
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.
We rebias estimates to improve interval calibration and prediction accuracy.
problem Constructing accurate intervals for noisy and biased estimates.
method Empirical Bayes rebiasing strategy that learns bias distribution from data.
result Substantial precision gains in prediction-powered inference.
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.
Paper bridges statistical inference for DP-SGD, a privacy-preserving machine learning method.
problem Asymptotic statistical inference for Differentially Private Stochastic Gradient Descent (DP-SGD).
method Established asymptotic properties of SGD under randomized subsampling, extended to DP-SGD, proposed methods for constructing valid confidence intervals.
result Valid confidence intervals for DP-SGD output achieve nominal coverage rates while maintaining privacy.
BC-ACI corrects time series forecast bias, improving prediction intervals.
problem Persistent bias in time series forecasts leads to overly conservative prediction intervals.
method Augments ACI with an EWM estimate of forecast bias to correct nonconformity scores and re-center intervals.
result Reduces Winkler interval scores by 13-17% under distribution shifts, improving calibration.
This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the quality distribution function estimator of random variables using integrated mean sq…
The method learns to partition event time space for better prediction.
problem Improving event time prediction in clinical settings with limited data.
method Develops a method to learn cut points for partitioning event time space.
result Improved prediction performance on real-world datasets.
Accurate models of patient survival probabilities provide important information to clinicians prescribing care for life-threatening and terminal ailments. A recently developed class of models - known as individual survival distributions (ISDs) - produces patient-specific survival functions that offer greater descriptiv…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals represent the "topological signal" and the short intervals represent "noise". We give ev…
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.
PyDTS analyzes survival data with discrete intervals and competing risks.
problem Discrete-time survival analysis with competing risks and optional penalization.
method Regularized estimation methods, model evaluation metrics, variable screening tools, and simulation module.
result Supports research and development in discrete-time survival analysis.
For analysis of a high-dimensional dataset, a common approach is to test a null hypothesis of statistical independence on all variable pairs using a non-parametric measure of dependence. However, because this approach attempts to identify any non-trivial relationship no matter how weak, it often identifies too many rel…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting uncertainty. Any one theory of inference is neither right nor wrong, but merely an axiom t…
Paper derives convergence rates and confidence intervals for LSA with Markovian noise.
problem Analyzing convergence rates and constructing confidence intervals for LSA with Markovian noise.
method Derives non-asymptotic Berry-Esseen bounds and multiplier block bootstrap procedure.
result Provides O(n−1/4) convergence rates and guarantees consistent inference. Paper proves neural networks can be approximated using interval bounds.
problem Verifying safety and robustness of neural networks.
method Introduces interval universal approximation (IUA) theorem for neural networks.
result Neural networks can be approximated using interval bounds for any continuous function and squashable activation functions.
We propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution which is a good candidate to describe the first passage time of foreign exchange rate. The analytical expression of the…
A new method for estimating uncertainty intervals in regression.
problem Lack of effective methods to estimate uncertainty intervals in regression.
method Collaborating Networks (CN) approach using two neural networks with distinct loss functions.
result CN method improves performance on various real-world datasets, including forecasting A1c values in diabetic patients.
This paper improves conformal prediction for robust interval estimation under distribution shifts.
problem Robustness of conformal prediction under distribution shifts.
method Modeling distribution shifts using Levy-Prokhorov (LP) ambiguity sets, which capture both local and global perturbations.
result Constructs robust conformal prediction intervals that remain valid under distribution shifts.