Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
Proposes isotonic recalibration for insurance pricing to ensure auto-calibration under low signal-to-noise ratio.
problem Ensuring auto-calibration in insurance pricing models to prevent cross-financing.
method Applies isotonic recalibration to regression models to achieve auto-calibration.
result Isotonically recalibrated regression functions have low complexity under low signal-to-noise ratio.
Paper corrects GIRP algorithm to ensure isotonic models.
problem GIRP algorithm fails to produce isotonic models.
method Modified GIRP algorithm with binary partitioning.
result Correct solution exists and can be found.
Proposes stabilized weights for causal inference using isotonic calibration.
problem Stability and bias issues in inverse propensity weighting.
method Post-hoc isotonic calibration of inverse propensity weights.
result Improves performance of doubly robust estimators of average treatment effect.
Additive isotonic regression attempts to determine the relationship between a multi-dimensional observation variable and a response, under the constraint that the estimate is the additive sum of univariate component effects that are monotonically increasing. In this article, we present a new method for such regression …
New method tackles adversarial sign-corrupted isotonic regression, estimating monotonic signals under heavy dependence.
problem Estimating monotonic signals when responses are sign-corrupted and adversarially designed to violate monotonicity.
method Developed ASCIFIT, a three-step estimation procedure using PAVA with pre- and post-processing corrections.
result Theoretical guarantees of sharp high probability upper bounds and minimax lower bounds for ASCIFIT.
Proposes new method for calibrating treatment effect predictors.
problem Calibrating predictors of heterogeneous treatment effects.
method Causal isotonic calibration and cross-calibration.
result Achieves fast calibration rates under weak conditions.
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
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.
Isotonic regression binning affects calibration statistics of machine learning models.
problem Isotonic regression binning introduces aleatoric uncertainty in calibration statistics.
method Calibration error statistics are recalibrated using isotonic regression, which produces stratified uncertainties.
result Stratified uncertainties lead to significant differences in bin-based calibration statistics.
We consider the online version of the isotonic regression problem. Given a set of linearly ordered points (e.g., on the real line), the learner must predict labels sequentially at adversarially chosen positions and is evaluated by her total squared loss compared against the best isotonic (non-decreasing) function in hi…
Paper develops DP algorithms for isotonic regression over posets.
problem Differential privacy in isotonic regression over partially ordered sets.
method Developed pure-DP and near-matching lower bound algorithms for isotonic regression.
result Achieved near-matching bounds for isotonic regression with and without poset structure.
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints corresponding to first-order stochastic dominance. We propose new discretization sch…
Proposes isotonic regression for calibrating Deep Cox models' survival probabilities.
problem Poor calibration of Deep Cox models' survival probabilities.
method Isotonic regression for post hoc calibration of Deep Cox models.
result Establishes favorable theoretical guarantees and demonstrates empirical effectiveness.
Estimates isotonic functions under unknown permutations, achieving optimal statistical and computational efficiency.
problem Estimating isotonic functions with unknown permutations in multiway comparison data.
method Mirsky partition estimator for minimax optimal and adaptive estimation.
result Achieves optimal worst-case statistical performance and computational efficiency.
Paper proposes a shape-constrained approach to distributionally robust learning.
problem Challenges in statistical learning under distribution shift.
method Shape-constrained approach to distributionally robust learning (DRL). Assumes isotonic density ratio.
result Improved accuracy demonstrated in empirical studies.
Learning accurate probabilistic models from data is crucial in many practical tasks in data mining. In this paper we present a new non-parametric calibration method called \textit{ensemble of near isotonic regression} (ENIR). The method can be considered as an extension of BBQ, a recently proposed calibration method, a…
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider the response to be a summation of unknown transformations applied on the predict…
Calibrated Prediction-Powered Inference improves semisupervised mean estimation by calibrating prediction scores.
problem Semisupervised mean estimation with a small labeled sample and a large unlabeled sample, and miscalibrated prediction models.
method Calibrated Prediction-Powered Inference (Calibeating) post-hoc calibrates the prediction score on the labeled sample before using it for semisupervised estimation.
result Calibrated Prediction-Powered Inference can improve the original score both as a predictor of the outcome and as a regression adjustment for semisupervised inference.
Experiment shows author rankings can improve peer review scores.
problem Improving accuracy in machine learning conference peer review.
method Used Isotonic Mechanism to calibrate review scores using author rankings.
result Calibrated scores outperform raw scores in estimating ground truth review scores.
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and constrained single index model. We review some of the theoretical properties of the least …
Boosted decision trees typically yield good accuracy, precision, and ROC area. However, because the outputs from boosting are not well calibrated posterior probabilities, boosting yields poor squared error and cross-entropy. We empirically demonstrate why AdaBoost predicts distorted probabilities and examine three cali…
Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating an unknown matrix in this class, based on noisy observations of (possibly, a su…
iQRA improves probabilistic forecasts of electricity prices.
problem Lack of uncertainty estimates in machine learning forecasts for volatile markets.
method Isotonic Quantile Regression Averaging (iQRA) with stochastic order constraints.
result iQRA outperforms state-of-the-art methods in reliability and sharpness.
Corrects mismatch in consistency of nuisance estimators for doubly robust methods.
problem Mismatch in consistency of nuisance estimators in doubly robust methods.
method Calibrated debiased machine learning (calibrated DML) with isotonic regression adjustment.
result Calibrated DML yields doubly robust asymptotic normality with slower convergence of nuisance estimators.
Proposes differentiable and sparse top-k operators for neural networks.
problem Discontinuity of top-k operator makes it unsuitable for end-to-end training with backpropagation.
method Formulates top-k as a linear program over permutahedron, introduces p-norm regularization, and uses isotonic optimization.
result Successfully applied to neural network pruning, fine-tuning, and routing.
Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function f from independent pairs (xi,yi) where E[yi]=f(xi),i=1,…n. While this problem is well understood both statistically and computationally, much l…
Paper introduces Isotonic Mechanism for better item scoring.
problem Noisy reviewer scores; owner prefers not to disclose true scores.
method Uses owner's ranking of items and raw scores to adjust and improve accuracy.
result Adjusted scores are significantly more accurate than raw scores.
New neural network with RePU activation approximates smooth functions and their derivatives.
problem Approximating smooth functions and their derivatives with neural networks.
method Differentiable neural networks with RePU activation functions.
result Improved approximation error bounds for RePU-activated neural networks.
SISR improves feature attribution in complex payoff schemes.
problem Distorted feature attributions due to non-additive payoff functions and high-dimensional feature spaces.
method Sparse Isotonic Shapley Regression (SISR) learns a monotonic transformation to restore additivity and enforces L0 sparsity.
result SISR achieves strong support recovery and stable attributions across various payoff schemes.
Paper quantifies distortion risk measures' robustness to distributional uncertainty.
problem Quantifying risk measures' robustness to distributional uncertainty.
method Employing isotonic projections, the paper derives bounds on distortion risk measures' values.
result Sharp bounds on distortion risk measures' values are provided, especially for Value-at-Risk and Range-Value-at-Risk.
New method improves probabilistic electricity price predictions.
problem Improving point forecasts to probabilistic distributions for better decision-making.
method Isotonic Distributional Regression combined with other postprocessing methods.
result Isotonic Distributional Regression outperforms other methods in combining probabilistic distributions.
Proposes a tuning-free dynamic pricing method for linear valuation models.
problem Dynamic pricing in linear valuation models with unknown market noise distribution.
method Shape-constrained isotonic regression under weaker Hölder continuity assumptions.
result Demonstrates lower empirical regret compared to existing methods.
Binary classification is highly used in credit scoring in the estimation of probability of default. The validation of such predictive models is based both on rank ability, and also on calibration (i.e. how accurately the probabilities output by the model map to the observed probabilities). In this study we cover the cu…
The paper tackles ranking experts based on their answers to questions, considering statistical and computational challenges.
problem Ranking experts based on their answers to questions, considering isotonic constraints.
method Investigates the existence of statistically optimal and computationally efficient procedures for ranking experts under isotonic constraints.
result Disproves the existence of computational-statistical gaps for the problem.
Study improves survival analysis for credit risk by accounting for data drift.
problem Survival analysis in credit risk assumes a stationary data-generating process, but real-world data drift affects model performance.
method Proposes a dynamic joint modelling framework integrating longitudinal behavioural markers and hazard formulations, combined with drift-adaptive techniques.
result Proposed model outperforms classical survival models and drift-adaptive learners in various data drift scenarios.
Stacked regressions improve predictive accuracy by combining estimators.
problem Improve predictive accuracy in regression models.
method Analogous to least-squares, learn combination weights by minimizing regularized empirical risk with nonnegativity constraint.
result The stacked estimator has strictly smaller population risk than the best single estimator, especially when signal-to-noise ratio is small.
Paper introduces differentiable sorting and ranking with O(nlogn) time complexity.
problem Non-differentiability of sorting and ranking operations in machine learning.
method Differentiable proxies constructed as projections onto the permutahedron and reduction to isotonic optimization.
result First differentiable sorting and ranking operators with O(nlogn) time and O(n) space complexity. In many real-world applications of machine learning classifiers, it is essential to predict the probability of an example belonging to a particular class. This paper proposes a simple technique for predicting probabilities based on optimizing a ranking loss, followed by isotonic regression. This semi-parametric techniq…
We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our a…
This paper continues study, both theoretical and empirical, of the method of Venn prediction, concentrating on binary prediction problems. Venn predictors produce probability-type predictions for the labels of test objects which are guaranteed to be well calibrated under the standard assumption that the observations ar…
This paper studies the addition of linear constraints to the Support Vector Regression (SVR) when the kernel is linear. Adding those constraints into the problem allows to add prior knowledge on the estimator obtained, such as finding probability vector or monotone data. We propose a generalization of the Sequential Mi…
We consider the problem of nonparametric regression when the covariate is d-dimensional, where d≥1. In this paper we introduce and study two nonparametric least squares estimators (LSEs) in this setting---the entirely monotonic LSE and the constrained Hardy-Krause variation LSE. We show that these two LSEs are…
Implied posterior probability of a given model (say, Support Vector Machines (SVM)) at a point x is an estimate of the class posterior probability pertaining to the class of functions of the model applied to a given dataset. It can be regarded as a score (or estimate) for the true posterior probability, which ca…
Obtaining accurate and well calibrated probability estimates from classifiers is useful in many applications, for example, when minimising the expected cost of classifications. Existing methods of calibrating probability estimates are applied globally, ignoring the potential for improvements by applying a more fine-gra…
A new measure PC allows fair comparison of AIWP and NWP models.
problem Fair comparison of AIWP and NWP model outputs.
method Postprocessing deterministic model outputs with isotonic distributional regression (IDR) and calculating PC as mean CRPS of postprocessed forecasts.
result The GraphCast model outperforms the ECMWF HRES model in WeatherBench 2 data.
Study compares various calibration methods for binary classification tasks.
problem Improving probabilistic predictions in binary classification models.
method Benchmarked 21 classifiers using 5 calibration methods on real data.
result Venn-Abers predictors and Beta calibration show the largest log-loss reductions.
The study establishes risk bounds for distributional regression estimators.
problem Estimating distributional regression models with nonparametric methods.
method Theoretical bounds for CRPS and MSE are derived for convex and non-convex constraints.
result Theoretical risk bounds are validated through experiments on simulated and real data.