New calibration measure SSCE ensures truthful prediction, unlike existing measures.
problem Ensuring truthful calibration measures in sequential prediction.
method Introduced a new calibration measure, Subsampled Smooth Calibration Error (SSCE).
result SSCE ensures truthful prediction, while existing measures are far from truthful.
Post-processing predictors reduces calibration errors for decision-making.
problem Predictors with low calibration error for machine learning may have high error for decision-making.
method Post-processing with ε distance to calibration adds noise to make predictions differentially private.
result Post-processing achieves O(√ε) ECE and CDL, asymptotically optimal.
The paper provides a uniform convergence bound for smooth calibration error and its relationship with functional gradient.
problem Limited theoretical understanding of learning algorithms achieving high accuracy and good calibration.
method Focuses on smooth calibration error, providing a uniform convergence bound and proving the relationship with functional gradient.
result Derives conditions for simultaneous classification and calibration guarantees in gradient boosting trees, kernel boosting, and neural networks.
This work proves L2-regularized ERM controls smCE without post-hoc correction.
problem Calibration of predicted probabilities in machine learning models.
method Canonical L2-regularized empirical risk minimization. result Theoretical proof that smCE is controlled by ERM without post-hoc correction.
SGLDiff approximates Bayesian posterior distributions with subsampling error.
problem Approximating Bayesian posterior distributions in large-scale data settings.
method Stochastic Gradient Langevin Diffusion (SGLDiff) with subsampling.
result The Wasserstein distance between the posterior and SGLDiff's limiting distribution is bounded by a fractional power of the mean waiting time.
Estimates convex hulls of smooth function images with error bounds.
problem Estimating the convex hull of the image of a smooth boundary set.
method Using submersion properties and sampling inputs, derive bounds on Hausdorff distance.
result New tighter and more general error bounds for geometric inference.
We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for n observations is estimated from a random subset of m observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smal…
Enhances privacy in federated learning with Laplacian smoothing.
problem Protecting data privacy in federated learning while maintaining model accuracy.
method Laplacian smoothing for differentially private federated learning (DP-Fed-LS).
result Improves model accuracy with differential privacy guarantee and membership privacy.
Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than on subsampling without replacement (SSWR). In this paper we investigate a kind of…
New method for Bayesian inference on large datasets.
problem Scalable sampling for Bayesian generalized linear mixed models on large datasets.
method Mirror Langevin dynamics with data subsampling, post-processing for variance estimation.
result Asymptotic, order-wise correct estimation of posterior variance.
Improved kernel quadrature with convex weights using subsampling.
problem Constructing quadrature rules with small worst-case error.
method Combining spectral properties of the kernel with recombination results.
result Effective algorithms for constructing convex quadrature rules with i.i.d. samples.
T-Cal tests model calibration with a minimax optimal test.
problem Detecting mis-calibration of predictive models using a finite validation dataset.
method T-Cal is a minimax optimal test for calibration based on a debiased plug-in estimator of the ℓ2-Expected Calibration Error (ECE). result T-Cal is a practical tool for testing the calibration of probabilistic classification methods.
Improved DNN estimator with scalable subsampling for efficient inference.
problem Efficient inference for deep neural networks (DNNs).
method Non-random subsampling technique (scalable subsampling) applied to DNNs.
result Subagged DNN estimator offers computational efficiency and accurate point estimation/prediction intervals.
Robust data fusion via subsampling improves model performance for rare data types.
problem Challenges in integrating large, contaminated external data with limited target data.
method Subsampling strategies to reduce biases and minimize variances, combined with error bounds analysis.
result Proposed methods enhance transfer learning performance, especially for rare data types.
New method improves calibration of neural networks by targeting robust margins and local smoothness.
problem Poor calibration of neural networks, leading to unreliable confidence estimates.
method Intervene on training procedure by targeting robust margins and local smoothness.
result Improved out-of-sample calibration without sacrificing accuracy.
A new approach RA improves stochastic optimization by executing multiple steps between subsample updates.
problem Improving the efficiency and effectiveness of stochastic optimization methods.
method Developed Retrospective Approximation (RA) which executes multiple steps between subsample updates using a deterministic solver.
result RA achieves almost sure and L1 consistency under weak conditions and optimizes iteration and oracle complexity. Magnetic particle imaging (MPI) data is commonly reconstructed using a system matrix acquired in a time-consuming calibration measurement. The calibration approach has the important advantage over model-based reconstruction that it takes the complex particle physics as well as system imperfections into account. This be…
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where statistical leverage scores are often used to define subsampling probabilities. In this p…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees on the accuracy of the predictive mean/variance and its generalization ability.…
New method calibrates LV surfaces for exotic derivatives with smoother, more stable Greeks.
problem Challenges in LV calibration leading to spiky surfaces and unstable Greeks.
method Automatic local regression to pre-process market observables and smooth LV surfaces.
result Significantly smoother LV surfaces and greatly improved Greek stability with negligible additional cost.
A new algorithm PBNN improves scalability of Bayesian Neural Networks.
problem Scalability issues in Neural Network posterior sampling with large datasets.
method Penalty Bayesian Neural Networks (PBNN) using subsampled batch data.
result PBNN achieves good predictive performance with small mini-batch sizes.
Subsampled Newton methods approximate Hessian matrices through subsampling techniques, alleviating the cost of forming Hessian matrices but using sufficient curvature information. However, previous results require Ω(d) samples to approximate Hessians, where d is the dimension of data points, making it less practica…
This paper studies a Nyström type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying kernel. This case is less understood, in spite of its practical importance. To model su…
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In this approach, one gets a surrogate dataset by sampling from the full data, and …
Causal discovery can be a powerful tool for investigating causality when a system can be observed but is inaccessible to experiments in practice. Despite this, it is rarely used in any scientific or medical fields. One of the major hurdles preventing the field of causal discovery from having a larger impact is that it …
New truthful calibration errors improve model ranking in multiclass prediction.
problem Non-truthful calibration errors can mislead model comparisons.
method Introduced perfectly truthful calibration errors for multiclass predictions.
result Truthful calibration errors preserve decision-theoretic dominance and stabilize model rankings.
A new perfectly truthful calibration measure improves prediction reliability.
problem Improving the reliability of predictions by ensuring they are conditionally unbiased.
method Designing a simple, perfectly truthful calibration measure called ATB.
result ATB is the first perfectly truthful calibration measure in the batch setting.
Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which usually causes subsampling bias, inflates generalization errors and jeopardizes the r…
Framework for precise recall control in spatial conflation tasks.
problem Precise recall control in large-scale spatial conflation tasks to avoid downstream analytics failures and excessive manual review.
method End-to-end framework using equigrid bounding-box filter, CSR representation, neural ranker, and inverse-variance weighted ensemble of threshold estimators.
result Achieves exact recall with sub-percent variance over tens of millions of geometry pairs, runs on a single TPU v3 core.
The paper analyzes the risk of bagging regularized M-estimators under proportional asymptotics.
problem Characterizing the risk of ensemble estimators trained with subsamples and regularizers.
method Developed a consistent estimator for the risk of ensemble estimators under proportional asymptotics.
result Optimal subsample size k⋆ tends to be in the overparameterized regime for the full-ensemble estimator. Smooth calibration improves forecast reliability even with leaked information.
problem Improving forecast reliability with leaked information.
method Combining nearby forecasts to ensure smooth calibration, which can be guaranteed by deterministic procedures.
result Smooth calibration can be guaranteed by deterministic procedures even with leaked forecasts, and it yields uncoupled finite-memory dynamics in games.
We propose to use nonparametric Bernstein copulas as bivariate pair-copulas in high-dimensional vine models. The resulting smooth and nonparametric vine copulas completely obviate the error-prone need for choosing the pair-copulas from parametric copula families. By means of a simulation study and an empirical analysis…
Optimizes calibration error estimators for better classifier trustworthiness.
problem Lack of guidance on selecting and tuning calibration error estimators.
method Reformulates calibration estimation as a regression problem with i.i.d. input pairs.
result Demonstrates the effectiveness of optimized calibration estimators on image classification tasks.
Paper detects duality obstruction in smooth calibrations.
problem Detecting duality obstruction in smooth calibrations.
method Examine Lawlor cones and calibrations, use gluing results.
result Existence of Lawlor cones without smooth calibrations.
New decision-theoretic calibration error metric improves prediction reliability.
problem Improving the reliability of predictions for decision-making.
method Proposed Calibration Decision Loss (CDL) and an efficient algorithm to achieve near-optimal CDL.
result Near-optimal CDL guarantees vanishing payoff loss from miscalibration.
Nyström subsampling with Tikhonov regularization for covariate shift adaptation under misspecified case
problem Adaptation to misspecified covariate shift
method Regularized Nyström subsampling with Tikhonov regularization
result Upper bounds on excess risk
Overparameterized models can worsen minority group errors even when overall test error improves.
problem Overparameterization exacerbates spurious correlations, harming minority groups.
method Simulations and experiments on image datasets, theoretical analysis of linear models.
result Subsampling the majority group can achieve low minority error in overparameterized models.
Cone structures over minimal products can't be calibrated smoothly.
problem Calibrating cones over minimal products with smooth calibrations.
method Extending a key result from [Zha26], showing obstruction.
result Cone structures over minimal products cannot be calibrated by smooth calibrations.
Proposes a new calibration error estimator for deep neural networks.
problem Improves calibration of deep neural networks, especially for canonical calibration.
method Uses a Dirichlet kernel density estimate to create a low-bias, trainable calibration error estimator.
result Asymptotically converges to true Lp calibration error, enabling efficient estimation and mini-batch updates. Estimates proper calibration errors and refinement terms in probabilistic predictions.
problem Lack of a general estimator for proper calibration errors and refinement terms with known statistical properties.
method Proposes a method for consistent, asymptotically unbiased estimation of proper calibration errors and refinement terms.
result Proves the relation between refinement and f-divergences, implying information monotonicity in neural networks.
New insights into how randomization affects greedy model selection.
problem Understanding the impact of feature subsampling on greedy model selection.
method Investigated greedy forward selection with feature subsampling, proving effects on bias and variance.
result Ensembling with feature subsampling reduces both bias and variance, unlike convex base learners.
Enhances random forest performance with exogenous randomness.
problem Improving random forest performance through exogenous randomness.
method Developed non-asymptotic MSE expansions for individual trees and forests, identified two types of randomness, and conducted simulations.
result Exogenous randomness, particularly feature subsampling, reduces both bias and variance of random forests.
Tree-based models biased when trained on imbalanced data, requiring new calibration methods.
problem Bias in tree-based models trained on imbalanced datasets.
method Analytical calibration of random forest models, demonstrating bias in decision trees.
result Calibrating tree-based models on imbalanced data negatively impacts predictions, especially for the minority class.
We extend a variational framework to estimate calibration errors for Lp divergences.
problem Ensuring predicted probabilities match observed class frequencies in machine learning.
method Extend variational framework to Lp divergences, separating over- and under-confidence. result Avoids overestimation and separates over- and under-confidence.
Optimal multiclass U-calibration error found to be Θ(√KT).
problem Online multiclass U-calibration with low regret for all bounded proper losses.
method Follow-the-Perturbed-Leader algorithm and lower bound construction.
result Optimal U-calibration error is Θ(√KT).
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to …
Simple algorithm achieves distance to calibration error of at most 2√T+1.
problem Achieving distance to calibration error of O(√T) in adversarial setting.
method An extremely simple, efficient, deterministic algorithm.
result Obtains distance to calibration error at most 2√T+1.
Paper develops methods for statistical inference in SGD with infinite variance.
problem Challenges in statistical inference for SGD with infinite variance.
method Model-agnostic methodology based on weak convergence and subsampling calibration.
result Asymptotically valid confidence regions for SGD in both finite and infinite variance regimes.