Study reveals pervasive label errors in test sets, affecting machine learning benchmarks.
problem Label errors in test sets destabilize machine learning benchmarks.
method Identified label errors in 10 common datasets using confident learning algorithms and human validation.
result Lower capacity models may be more useful in real-world datasets with high proportions of erroneously labeled data.
The paper improves confidence intervals for test error using cross-validation.
problem Improving confidence intervals for test error in machine learning.
method Develops central limit theorems and consistent estimators for cross-validation.
result Provides asymptotically-exact confidence intervals and hypothesis tests.
Study controls error rates of binary classifiers using hypothesis testing.
problem Traditional binary classifiers have uncontrolled error rates.
method Combines binary classification with statistical hypothesis testing.
result Trained classifiers can be made to meet target error rate thresholds.
This work improves confidence intervals for Cox model test error using nested CV.
problem Insufficient understanding of confidence intervals for cross-validation in Cox model.
method Generalized nested cross-validation to Cox proportional hazards model.
result Improved coverage of confidence intervals for Cox model test error.
We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error pr…
Proposes a new test for validating multivariate dynamic regression models.
problem Inadequate exogeneity conditions for conventional model specification tests in dynamic systems.
method Develops a generalized Durbin estimator for multiple-equation systems with dynamic dependencies, and constructs Wald tests.
result Bootstrap-based Wald tests improve finite-sample size control and validate the null hypothesis in multifactor models.
The repeated community-wide reuse of test sets in popular benchmark problems raises doubts about the credibility of reported test-error rates. Verifying whether a learned model is overfitted to a test set is challenging as independent test sets drawn from the same data distribution are usually unavailable, while other …
TCE measures calibration error with a test-based approach.
problem Measuring calibration error of probabilistic binary classifiers.
method TCE uses a novel loss function based on a statistical test.
result TCE offers clear interpretation, consistent scale, and enhanced visual representation.
Study loop corrections in random feature models affecting training and test errors.
problem Analyzing loop corrections in random feature models to understand training and test errors.
method Statistical physics and effective field theory approach to study loop corrections.
result Derived loop corrections to training error, test error, and generalization gap.
DD algorithm tracks test error from train error without validation data.
problem Systematic generalization gap between train and test errors in modern model training.
method Decoupled descent (DD) algorithm that cancels data reuse biases via approximate message passing.
result DD algorithm rigorously demonstrates zero-cost validation and 100% data utilization.
This work identifies redundant tests in conditional-independence-based discovery that can improve graphical model accuracy.
problem Reliability and sensitivity of conditional-independence-based discovery algorithms.
method Analysis of redundant tests and their impact on error detection and correction.
result Redundant tests can improve graphical model accuracy but not all are beneficial.
Efficient tests achieve best error rates in high-dimensional hypothesis testing.
problem Achieving optimal error rates in computationally efficient hypothesis testing.
method Linear spectral statistics and low-degree likelihood ratio analysis.
result An efficient test achieves the best possible error rates among all computationally efficient tests.
New methods for CI testing under model misspecification.
problem Challenges in CI testing with misspecified models.
method Proposes new approximations and upper bounds for testing errors of regression-based CI tests.
result Introduces the Rao-Blackwellized Predictor Test (RBPT) robust against misspecified inductive biases.
We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing …
Selective inference controls Type I error in k-means clustering tests.
problem Inflated Type I error in classical hypothesis tests for k-means clusters.
method Selective inference approach to control Type I error.
result Proposes a computable finite-sample p-value for selective inference.
SGD-trained models' disagreement predicts test error.
problem Estimating test error of deep networks.
method Empirical testing and theoretical analysis of SGD ensembles.
result SGD ensembles' disagreement correlates with test error.
Adversarial training achieves optimal test error for shallow networks.
problem Achieving optimal adversarial test error for general data distributions.
method Applying new Rademacher complexity bounds and properties of optimal adversarial predictors.
result Adversarial training can achieve optimal adversarial test error for general data distributions.
New insights into CI tests reveal key factors for practical performance.
problem Understanding and improving CI tests in practical applications.
method Investigation of the Kernel-based Conditional Independence (KCI) test and analysis of its practical behavior.
result Errors in conditional mean embedding estimates and appropriate conditioning kernel selection are crucial for CI tests.
We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.
problem Understanding the generalization performance of random feature ridge regression.
method We derive a deterministic equivalent for the test error of RFRR under a concentration property, showing it can be approximated by a closed-form expression dependent on feature map eigenvalues.
result Our approximation guarantee is non-asymptotic, multiplicative, and independent of the feature map dimension, providing a tight result for the smallest number of features achieving optimal minimax error rate.
SGD reduces test error by decorrelating updates.
problem Improving generalization error in machine learning models.
method Derive a formula for generalization gap change due to SGD updates, compare to GD, and show decorrelation effect.
result SGD implicitly regularizes generalization error by decorrelating updates.
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, F measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures simultaneously. For example, error is the sum of false positives and false negatives…
Recent theoretical work has guaranteed that overparameterized networks trained by gradient descent achieve arbitrarily low training error, and sometimes even low test error. The required width, however, is always polynomial in at least one of the sample size n, the (inverse) target error 1/ε, and the (inverse) fail…
Study shows gap between uniform convergence and test error in random feature models.
problem Understanding the gap between uniform convergence and test error in random feature models.
method Analytical expressions for uniform convergence over norm balls, interpolators, and minimum norm interpolator risk derived and proved.
result Uniform convergence over interpolators still gives a non-trivial bound of test error even when classical uniform convergence is vacuous.
DP synthetic data may inflate statistical test results, caution advised.
problem Inflated Type I errors in statistical tests on DP-synthetic data.
method Evaluation of Mann-Whitney U test, t-test, chi-squared test, and median test on DP-synthetic data generated from real-world and simulated datasets using various DP-synthetic data generation methods.
result A large portion of evaluation results showed inflated Type I errors, especially at low privacy levels.
Optimal AFs minimize RFR test error and sensitivity.
problem Finding optimal AFs for RFR to minimize test error and sensitivity.
method Closed-form solution for AFs minimizing test error and sensitivity under different functional parsimony.
result Optimal AFs can be linear, saturated linear, or Hermite polynomial expressions.
DP-SPRT improves privacy in sequential tests with near-optimal error rates.
problem Privacy constraints in sequential probability ratio tests.
method A wrapper for SPRT that uses a private mechanism to determine when to stop based on predefined intervals.
result DP-SPRT achieves near-optimal error rates and privacy guarantees.
Max-rank improves multiple testing in conformal prediction.
problem Simultaneous testing of multiple hypotheses in scientific inquiries.
method Introduces max-rank, a novel correction for positive dependencies in simultaneous testing.
result Max-rank efficiently controls family-wise error rate and improves predictive uncertainty estimates.
Diffusion models generate data with Gaussian Universality, matching linear model test errors.
problem Analyzing the performance of models trained on synthetic data generated by diffusion models.
method Investigates Gaussian Universality for data distributions generated via diffusion models, matching test errors of linear models trained on synthetic data to Gaussian Mixture models.
result The test error of a linear model trained on diffusion-generated data matches the test error of a linear model trained on Gaussian Mixture data with matching means and covariances per class.
Kernel tests assess equivalence between distributions without assuming specific moments.
problem Traditional goodness-of-fit tests fail to detect meaningful distributional differences.
method Proposes kernel-based tests using kernel Stein discrepancy and Maximum Mean Discrepancy.
result Tests assess the absence of meaningful distributional differences under controlled error rates.
Sharp bounds derived for test error of finite-rank kernel ridge regression.
problem Loose bounds on test error for finite-rank kernels in machine learning.
method Sharp non-asymptotic upper and lower bounds for KRR test error.
result Tighter bounds on finite-rank KRR test error, valid for any regularization parameters.
Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic for use in the permutation tests of worst likely assignments that improves error b…
Neural network accuracy improves with denser training samples.
problem Improving neural network accuracy on unseen test samples.
method Bounding empirical training error smoothed across activation regions and using it to discard high-risk test samples.
result Discarding high-risk test samples based on error bounds improves prediction accuracy by up to 20%.
This work finds a point with small test error in polynomial time for mildly overparameterized neural nets.
problem Achieving small test error in mildly overparameterized neural networks.
method The work shows that the landscape of loss functions with explicit regularization has a property that all local minima and certain stationary points achieve small test error. It also proves the existence of polynomial time algorithms for finding such points in convolutional and fully connected neural nets.
result Polynomial time algorithms exist for finding points with small test error in mildly overparameterized neural nets.
A method for safe online classification reduces test costs while maintaining low error rates.
problem Sequential testing for binary disease outcomes with unknown logistic model parameters.
method Joint estimation of logistic parameter and feature distribution with a conservative threshold.
result Achieves target error with high probability and requires minimal excess tests.
New method for group testing robust to errors in group membership specifications.
problem Errors in specifying group memberships during group testing.
method Debiased Robust Lasso Test Method (DRLT) based on Lasso debiasing.
result Extends LASSO bias mitigation to handle group membership specification errors.
Proposes selective inference for testing differences in means between clusters.
problem Inflated type I error rate when testing differences in means between clusters.
method Selective inference approach to control selective type I error rate.
result Controls selective type I error rate by accounting for data-driven cluster definition.
FactTest assesses LLM factuality with Type I error control.
problem Lack of rigorous factuality verification for LLMs.
method Formulates factuality testing as hypothesis testing, ensuring Type I and II error control.
result Improves model accuracy by over 40% in abstaining from unknown questions.
Sequential Kernel-based Conditional Independence Testing via Adaptive Betting
problem Testing conditional independence
method Testing-by-betting on an adaptively optimized Kernel Conditional Independence statistic
result Significantly reduces Type I error inflation while preserving high power
In this paper, we bound the error induced by using a weighted skeletonization of two data sets for computing a two sample test with kernel maximum mean discrepancy. The error is quantified in terms of the speed in which heat diffuses from those points to the rest of the data, as well as how at the weights on the refere…
New method uses CDMs to improve CI testing without distributional assumptions.
problem Testing conditional independence when the conditional distribution is unknown.
method Uses conditional diffusion models (CDMs) to approximate X∣Z and a classifier-based CMI estimator. result Proposed method performs better than GAN-based CI tests and controls type I and II errors.
New method reveals good classifiers are common in over-parameterized models.
problem Understanding how over-parameterized models generalize well.
method Developed a methodology to compute the full distribution of test errors.
result Test errors concentrate around a small typical value ε* rather than the worst-case model.
Paper shows how gradient concentration helps in learning from inexact data.
problem Learning from inexact and stochastic training data.
method Combines probabilistic gradient concentration with inexact optimization techniques.
result Derives sharp test error guarantees for learning.
Study on error probabilities of machine learning classification techniques using large deviations theory.
problem Performance analysis of machine learning binary classification techniques.
method Large deviations theory applied to Data-Driven Decision Function (D3F) for error probability analysis.
result Classification error probabilities vanish exponentially, with an asymptotic formula providing precise error rate estimates.
This article analyzes the weak error of SGD optimization schemes.
problem Analyzing the error in SGD optimization schemes with respect to a test function.
method Weak error analysis for SGD type optimization schemes.
result The weak error decays at the same speed as in the strong sense.
New TTP framework fuses control arms while controlling Type-I error.
problem Bias in borrowing control data from previous trials.
method Kernel two-sample testing via MMD and equivalence testing.
result Higher power than standard TTP methods while maintaining error control.
The paper proves a non-asymptotic test error approximation for KRR.
problem Understanding the test error of Kernel Ridge Regression.
method Established a non-asymptotic deterministic approximation for test error of KRR.
result The test error of KRR can be approximated by a closed-form estimate derived from the spectrum of the kernel operator.
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.
Improves test set performance and reduces out-of-sample disappointment for unstable models.
problem Ensuring strong test set performance via cross-validation for unstable models.
method Nested k-fold cross-validation with hyperparameter selection based on a weighted sum of cross-validation metric and model stability measure.
result Improves out-of-sample MSE for sparse ridge regression and CART by 4% and 2% respectively, compared to k-fold cross-validation.