Extends Infinitesimal Jackknife for model covariance, enhancing ensemble model analysis.
problem Estimating uncertainty in combinations of models.
method Extends Infinitesimal Jackknife to estimate covariance between models.
result Theoretical consistency of Infinitesimal Jackknife covariance estimate demonstrated.
We study the variability of predictions made by bagged learners and random forests, and show how to estimate standard errors for these methods. Our work builds on variance estimates for bagging proposed by Efron (1992, 2012) that are based on the jackknife and the infinitesimal jackknife (IJ). In practice, bagged predi…
Cross validation (CV) and the bootstrap are ubiquitous model-agnostic tools for assessing the error or variability of machine learning and statistical estimators. However, these methods require repeatedly re-fitting the model with different weighted versions of the original dataset, which can be prohibitively time-cons…
The paper proposes a method to improve fairness in machine learning models without refitting.
problem Mitigating biases in machine learning models that disadvantage certain groups.
method Infinitesimal jackknife-based approach to drop selected training data points.
result The intervention improves fairness without significantly reducing predictive performance.
The infinitesimal jackknife (IJ) has recently been applied to the random forest to estimate its prediction variance. These theorems were verified under a traditional random forest framework which uses classification and regression trees (CART) and bootstrap resampling. However, random forests using conditional inferenc…
The network jackknife provides conservative variance estimates for network statistics.
problem Estimating the variance of network statistics.
method Leave-node-out jackknife procedure for network data under the sparse graphon model.
result The network jackknife leads to conservative estimates of the variance for network functionals invariant to node permutation.
MAGIC method optimally estimates model predictions changes.
problem Estimating how training data affects model predictions in large-scale settings.
method Combines classical methods and recent advances in metadifferentiation.
result MAGIC method nearly optimally estimates model predictions changes.
Study evaluates posterior covariance matrix W for frequentist evaluation of Bayesian estimators.
problem Evaluating variability of posterior estimates in Bayesian models.
method Use of Bayesian Infinitesimal Jackknife approximation and W-kernel.
result Principal space of W is central to frequentist evaluation of Bayesian models.
Proposes a new jackknife method for time series hyperparameter selection.
problem Hyperparameter selection for time series models.
method Artificial delete-d jackknife approach.
result Asymptotic and finite-sample advantages demonstrated.
A new method reduces bootstrap simulation cost and improves accuracy.
problem Efficiently simulating input uncertainty with large sample sizes.
method Orthogonal Bootstrap: Decomposes into Infinitesimal Jackknife and orthogonal parts.
result Significantly reduces computational cost and maintains accuracy.
Jackknife variance estimation validated for generalized U-statistics.
problem Uncertainty quantification for subsampling-based estimators.
method Jackknife variance estimation for generalized U-statistics with row-wise Lr weak law. result Jackknife and delete-d variance estimators are ratio-consistent for generalized U-statistics. Cluster jackknife improves inference for staggered DID methods.
problem Over-rejection of CSDID in small clusters or treated clusters.
method Cluster jackknife for CSDID inference.
result Cluster jackknife greatly improves inference for CSDID.
Assessing heterogeneous treatment effects has become a growing interest in advancing precision medicine. Individualized treatment effects (ITE) play a critical role in such an endeavor. Concerning experimental data collected from randomized trials, we put forward a method, termed random forests of interaction trees (RF…
Discriminative jackknife estimates deep learning uncertainty.
problem Quantifying uncertainty in deep learning models.
method Discriminative jackknife using influence functions of loss.
result DJ satisfies frequentist coverage and discriminative accuracy.
Modified jackknife method improves predictive inference for time series data.
problem Lack of exchangeability and temporal dependence in time series data.
method Leave-a-window-out (LWO) method modification of the jackknife.
result LWO method achieves valid coverage in time series models with mild temporal dependence.
Random forests have proven to be reliable predictive algorithms in many application areas. Not much is known, however, about the statistical properties of random forests. Several authors have established conditions under which their predictions are consistent, but these results do not provide practical estimates of ran…
Enhances polynomial chaos models with uncertainty intervals.
problem Uncertainty quantification in surrogate models.
method Jackknife-based conformal prediction integrated into polynomial chaos expansions.
result Produces accurate predictive intervals for low-accuracy models.
We provide additional statistical background for the methodology developed in the clinical analysis of knee osteoarthritis in "A Precision Medicine Approach to Develop and Internally Validate Optimal Exercise and Weight Loss Treatments for Overweight and Obese Adults with Knee Osteoarthritis" (Jiang et al. 2020). Jiang…
Adaptive method improves prediction intervals with global coverage guarantees and local error distribution.
problem Global coverage guarantees of conformal regression are often violated by local error distributions.
method Adaptive Conformal Regression with Jackknife+ Rescaled Scores
result Improves local coverage without sacrificing global coverage, especially in low-data regimes.
New algorithms delete user data from machine learning models efficiently.
problem Deleting user data from machine learning models trained with empirical risk minimization.
method Developed an online unlearning algorithm using the infinitesimal jackknife, targeting non-smooth regularizers.
result Empirically improved runtime while maintaining memory requirements and test accuracy.
Frequentist method estimates uncertainty in RNNs without altering architecture.
problem Uncertainty quantification in RNNs for decision-making.
method Jackknife resampling and influence functions to estimate variability.
result The method provides theoretical coverage guarantees on uncertainty intervals.
JAWS audits predictive uncertainty under covariate shift using jackknife+ weighted methods.
problem Auditing predictive uncertainty under data distribution shifts.
method JAW and JAWA methods for distribution-free uncertainty quantification.
result JAW relaxes the jackknife+'s assumption of data exchangeability for covariate shift.
Paper proposes diagnostics for error and variance estimation in randomized matrix computations.
problem Safe use of randomized matrix algorithms in applications.
method Leave-one-out error estimator and jackknife resampling method.
result Provides rapid diagnostics to assess quality of randomized matrix computations.
Adaptive classification methods ensure correct prediction intervals.
problem Developing methods to ensure correct prediction intervals for classification problems.
method Specialized conformal inference techniques combining cross-validation+, jackknife+, and a novel conformity score.
result The methods provide guaranteed approximate conditional coverage for complex data distributions.
New methods improve prediction intervals across multiple environments.
problem Valid confidence intervals and sets in multi-environment prediction.
method Extended jackknife and split-conformal methods, with resizing for problem difficulty.
result Distribution-free coverage achieved in non-traditional data scenarios.
In this paper we propose using the principle of boosting to reduce the bias of a random forest prediction in the regression setting. From the original random forest fit we extract the residuals and then fit another random forest to these residuals. We call the sum of these two random forests a \textit{one-step boosted …
The paper derives uniform stability-based coverage bounds for conformal prediction methods.
problem Establishing theoretical guarantees for conformal prediction methods.
method Uniform stability perspective applied to full-conformal, jackknife+, and CV+ prediction regions.
result Coverage bounds for finite-dimensional models derived using a concentration argument.
Paper accelerates conformal prediction by using approximate leave-one-out estimators.
problem Limited computational cost for conformal prediction.
method Incorporates approximate leave-one-out estimators to accelerate conformal prediction.
result ALO-based methods achieve comparable coverage and efficiency to exact methods but with significantly reduced runtime.
Data-OOB efficiently estimates data value using out-of-bag estimates.
problem Efficiently estimating the value of data in large datasets.
method Data-OOB method using out-of-bag estimates for bagging models.
result Significantly outperforms existing data valuation methods in identifying mislabeled data.
A new method for uncertainty estimation in neural networks using Gaussian-softmax integration.
problem Quantifying uncertainty in neural network predictions.
method Proposes a single-model approach integrating Gaussian distribution with softmax outputs, using mean-field approximation.
result Competitive performance on uncertainty estimation tasks and outperforms many methods on out-of-distribution detection.
Develops asymptotic theory for deep Cox models to enable valid inference.
problem Theoretical gaps in deep neural network estimators for Cox models.
method Asymptotic distribution theory linking in-sample optimization error to population risk.
result Pointwise and multivariate asymptotic normality for subsampled ensemble estimators.
The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra of polyvector fields as its non-linear cohomology.
A hybrid algorithm fuses significance-based splitting with honest sample-splitting for estimating heterogeneous treatment effects.
problem Estimating heterogeneous treatment effects while maintaining valid inference.
method Significance-first splitting using a squared t-statistic for treatment imes side interaction. result Achieves approximately 90% CI coverage at the 90% nominal level across various synthetic designs and datasets.
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.
Study on bending knots and energy changes in 3D space.
problem Understanding energy changes in knots under small deformations.
method Analyzes infinitesimal bending of knots and energy changes using Willmore and Mobius energies.
result Changes in energy under small deformations of knots have been quantified.
In this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. We define infinitesimal equivariant eta cochains, prove their regul…
Cauchy used infinitesimals in differential geometry and integral geometry.
problem Applying infinitesimals in differential and integral geometry.
method Using infinitesimals as numbers in differential and integral geometry.
result Valid application of infinitesimals in geometric probability, differential geometry, elasticity, and Dirac delta functions.
Metric spaces with certain curvature properties are universally infinitesimally Hilbertian.
problem Analyzing the infinitesimal geometry of metric spaces with curvature bounds.
method Proving a metric space with a Gromov-Hausdorff tangent splitting property is universally infinitesimally Hilbertian.
result Metric spaces with curvature bounds are universally infinitesimally Hilbertian.
Weiss and, independently, Mazzeo and Montcouquiol recently proved that a 3--dimensional hyperbolic cone-manifold (possibly with vertices) with all cone angles less than 2π is infinitesimally rigid. On the other hand, Casson provided 1998 an example of an infinitesimally flexible cone-manifold with some of the cone an…
coverforest speeds up conformal predictions for random forests.
problem Efficient uncertainty quantification for random forest predictions.
method Optimized Python package leveraging random forest's out-of-bag scores for cross-conformal predictions.
result coverforest achieves desired coverage with faster training and prediction times.
In this paper, we prove that infinitesimal equivariant Chern-Connes characters are well-defined. We decompose an equivariant index as a pairing of infinitesimal equivariant Chern-Connes characters with the Chern character of an idempotent matrix. We compute the limit of infinitesimal equivariant Chern- Connes character…
Paper generalizes connections between Lie groups and affine connections.
problem Exploring properties of infinitesimal groups and affine connections.
method Introducing second-order infinitesimal groups and using them to define Lie brackets and connections.
result Generalized correspondence between symmetric and non-symmetric affine connections.
Ancient formula connects volume forms and infinitesimal square volumes in manifolds.
problem Relating volume forms and infinitesimal square volumes in Riemannian manifolds.
method Uses Heron's formula to link these concepts.
result Established a connection between volume forms and infinitesimal square volumes.
New examples of rigid Lie foliations with dense leaves found.
problem Infinitesimal rigidity of Lie foliations with dense leaves.
method Construction of specific Lie foliations.
result First examples of infinitesimally rigid Riemannian foliations with dense leaves.
Smooth manifolds have been always understood intuitively as spaces with an affine geometry on the infinitesimal scale. In Synthetic Differential Geometry this can be made precise by showing that a smooth manifold carries a natural structure of an infinitesimally affine space. This structure is comprised of two pieces o…
Lie algebroids are like infinitesimal Lie groupoids.
problem None explicitly stated in the abstract.
method Overview article.
result Lie algebroids are infinitesimal counterparts of Lie groupoids.
New classification of hypersurfaces with conformal variations.
problem Classifying hypersurfaces with conformal infinitesimal variations.
method Analyzing hypersurfaces in conformal geometry, extending previous work by Cartan and Sbrana.
result The class of hypersurfaces with conformal infinitesimal variations is larger than previously known.
Using standard analysis only, we present an extension ∙R of the real field containing nilpotent infinitesimals. On the one hand we want to present a very simple setting to formalize infinitesimal methods in Differential Geometry, Analysis and Physics. On the other hand we want to show that these infinitesim…