This work bounds classification error in machine learning for low Bayes error conditions.
problem Understanding the error mismatch between Bayes error and model-based classification error.
method Applying classification error bounds to study the relationship with Kullback-Leibler divergence and proposing a linear approximation for low Bayes error conditions.
result A linear approximation of the classification error bound for low Bayes error conditions is proposed.
A new method estimates Bayes error for deep networks, suggesting they may have reached the limit.
problem Evaluating the performance of deep learning models and detecting overfitting.
method A simple and direct Bayes error estimator based on uncertainty of class assignments.
result Deep networks may have reached the Bayes error limit for benchmark datasets.
We address the problem of learning to benchmark the best achievable classifier performance. In this problem the objective is to establish statistically consistent estimates of the Bayes misclassification error rate without having to learn a Bayes-optimal classifier. Our learning to benchmark framework improves on previ…
Researchers compute Bayes error for classification models using normalizing flows.
problem Evaluating the inherent difficulty of classification problems.
method Invertible transformations and Gaussian base distributions to compute Bayes error.
result State-of-the-art models can achieve near-optimal accuracy but not always.
Study shows how classifiers can approach Bayes error in high-dimensional settings.
problem Generalization error in high-dimensional perceptrons.
method Proved a formula for generalization error using convex optimization and observed that logistic and hinge regression can approach Bayes error closely.
result Logistic and hinge regression can approach Bayes-optimal generalization error closely in high-dimensional settings.
We show how to compute the Bayes error-rate for speaker verifiers.
problem How many errors does a speaker verifier make in a hundred trials?
method We compute the Bayes error-rate using calibrated likelihood ratios and user-supplied prior probabilities.
result The Bayes error-rate is upper bounded by the minimum of EER, P, and 1-P.
New PAC-Bayes bound controls multiple error types simultaneously.
problem Current PAC-Bayes bounds are limited to scalar metrics.
method Bounding KL divergence between empirical and true probabilities of multiple error types.
result First PAC-Bayes bound for rich information-rich certificates.
We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower …
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
Paper introduces ILD algorithm to determine Bayes error for binary classification.
problem Determining the best possible performance in binary classification problems.
method Model-agnostic ILD algorithm to calculate Bayes error.
result Provides intrinsic limits of any binary classification algorithm.
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster than the number of labeled training samples. We show that the Bayes error, namely t…
New work shows limits of certifying neural network robustness.
problem Certified training improves robustness but decreases accuracy.
method Bayes error analysis to investigate robustness limits.
result Upper bound for certified robust accuracy established.
The study analyzes multi-class teacher-student perceptron performance and generalization errors.
problem Analyzing multi-class classification with the teacher-student perceptron.
method Deriving asymptotic expressions for Bayes-optimal and empirical risk minimization (ERM) generalization errors.
result Regularised cross-entropy minimization yields close-to-optimal accuracy for multi-class classification.
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a bridge to connect the estimation error of the mean difference and the misclassificat…
New PAC-Bayes training method improves model generalization for unbounded loss.
problem Improving generalization of complex models under unbounded loss.
method Established new PAC-Bayes bound for unbounded loss, jointly training prior and posterior.
result Outperforms existing PAC-Bayes training algorithms and matches ERM accuracy.
Bayes-optimal learning of a neural network with quadratic activations is achieved with GAMP-RIE.
problem Learning a neural network with quadratic activations from quadratic samples.
method Combining approximate message passing with rotationally invariant matrix denoising.
result Derives a closed-form expression for Bayes-optimal test error.
Optimizes pruning masks for neural networks using probabilistic fine-tuning and PAC-Bayes bounds.
problem Improving neural network performance through adaptive pruning of weights.
method Optimizes stochastic pruning masks by minimizing expected loss, considering data-adaptive regularization and feature alignment.
result Probabilistic fine-tuning leads to improved test error over baseline methods in neural networks.
Meta-learning bounds derived using PAC-Bayes theory for improved generalization.
problem Uncertainty in generalization performance for meta-learning with new tasks.
method PAC-Bayes relative entropy bounds and empirical risk minimization (ERM) method.
result Competitive generalization performance and rapid convergence with data-dependent prior.
Study on conditions for Bayes optimal classifier in adversarial robustness.
problem Existence of Bayes optimal classifier for adversarial robustness.
method General sufficient conditions for existence of Bayes optimal classifier.
result Guaranteed existence of Bayes optimal classifier under certain conditions.
Improved Naive Bayes classifier with neural network models.
problem Limited complexity handling and independence assumption in Naive Bayes.
method Introducing Neural Naive Bayes and Neural Pooled Markov Chain models.
result Error rate reduced by 4.5 on IMDB dataset.
Adversarial consistency depends on the uniqueness of adversarial Bayes classifiers.
problem Consistency of adversarial surrogate losses is not guaranteed.
method Connected consistency of adversarial surrogate losses to the uniqueness of adversarial Bayes classifiers.
result A convex surrogate loss is statistically consistent for adversarial learning if and only if the adversarial Bayes classifier is unique.
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the underlying data distribution setting where connections to maximal marginal diver…
We compare in this paper several feature selection methods for the Naive Bayes Classifier (NBC) when the data under study are described by a large number of redundant binary indicators. Wrapper approaches guided by the NBC estimation of the classification error probability out-perform filter approaches while retaining …
New estimators outperform maximum likelihood without hyper-parameter estimation.
problem Improving system identification performance without hyper-parameter estimation.
method Developed generalized Bayes and closed-form biased estimators using excess MSE.
result New estimators have comparable performance to empirical-Bayes-based regularized estimator.
We explore the family of methods "PAC-Bayes with Backprop" (PBB) to train probabilistic neural networks by minimizing PAC-Bayes bounds. We present two training objectives, one derived from a previously known PAC-Bayes bound, and a second one derived from a novel PAC-Bayes bound. Both training objectives are evaluated o…
A new hyperparameter optimization method reduces overfitting.
problem Overfitting in hyperparameter optimization.
method PAC-Bayes bound minimization using gradient-based algorithm.
result Significant reduction in out-of-sample error.
We propose a new splitting criterion for a meta-learning approach to multiclass classifier design that adaptively merges the classes into a tree-structured hierarchy of increasingly difficult binary classification problems. The classification tree is constructed from empirical estimates of the Henze-Penrose bounds on t…
In many signal detection and classification problems, we have knowledge of the distribution under each hypothesis, but not the prior probabilities. This paper is aimed at providing theory to quantify the performance of detection via estimating prior probabilities from either labeled or unlabeled training data. The erro…
Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we derive the approximation error of VB in terms of mean, mode, variance, predictive den…
Meta learning of optimal classifier error rates allows an experimenter to empirically estimate the intrinsic ability of any estimator to discriminate between two populations, circumventing the difficult problem of estimating the optimal Bayes classifier. To this end we propose a weighted nearest neighbor (WNN) graph es…
New method calibrates machine learning models with theoretical guarantees.
problem Lack of theoretical guarantees for recalibration in multiclass classification.
method PAC-Bayes analysis for generalization error in calibration.
result First optimizable upper bound for generalization error in calibration.
We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k growing appropriately with sample size. We will argue that a margin-regularized 1…
New analysis reveals gaps in selective classifiers, guiding improvements.
problem Improving selective classifiers to match perfect-ordering oracle performance.
method Formalized selective classification gap, decomposed into five sources of looseness.
result Monotone post-hoc calibration has limited impact on closing the gap.
Paper improves PAC-Bayes bounds using a better-than-KL divergence.
problem Estimating the generalization error of stochastic algorithms.
method Developed new PAC-Bayes bounds with a novel divergence.
result Achieved strictly tighter bounds than the KL divergence.
The study sets limits on how robust classifiers can be against adversarial attacks.
problem Understanding the limits of robustness in classification models against adversarial attacks.
method Utilized optimal transport theory to derive variational formulae and explicit lower-bounds on Bayes-optimal error.
result Explicit lower-bounds on the Bayes-optimal error for distance-based attacks, universal in geometry of class-conditional distributions.
We study the statistical performance of semidefinite programming (SDP) relaxations for clustering under random graph models. Under the Z2 Synchronization model, Censored Block Model and Stochastic Block Model, we show that SDP achieves an error rate of the form \[ \exp\Big[-\big(1-o(1)\big)\bar{n} I^* \Bi…
AIM models explain deep learning in attention layers, offering solvable insights.
problem Understanding how deep learning models learn in attention layers.
method Statistical mechanics and random matrix theory.
result Closed-form predictions for Bayes-optimal generalization error and gradient descent performance.
Unified derivation of PAC-Bayes and MI bounds for general VC classes with fast rates.
problem Generalization bounds for machine learning models with VC classes.
method Unified derivation of conditional PAC-Bayesian and mutual information bounds, including MAC-Bayesian bounds.
result Nontrivial bounds for general VC classes and faster rates for specific conditions.
The cold posterior effect is explored through PAC-Bayes bounds for small sample sizes.
problem The cold posterior effect in approximate Bayesian inference for small datasets.
method Investigation through PAC-Bayes generalization bounds, focusing on temperature parameter λ.
result The temperature parameter λ in PAC-Bayes bounds captures the cold posterior effect.
New PAC-Bayes meta-learning method improves few-shot learning accuracy and calibration.
problem Few-shot learning with limited data.
method PAC-Bayes framework extended to meta-learning, estimating task-specific posteriors.
result State-of-the-art calibration and classification results on benchmarks.
Bayes Error Rate estimators are evaluated for accuracy and sample requirements.
problem Evaluating the accuracy and sample requirements of Bayes Error Rate estimators.
method Monte Carlo simulations with synthetic data and real-world scenarios.
result k-Nearest Neighbor (kNN) is the most accurate non-parametric estimator.
New algorithm optimizes PAC-Bayes bound without surrogate loss.
problem Mismatch between optimisation objective and generalisation bound in stochastic neural networks.
method Proposes a novel training algorithm that optimizes the PAC-Bayesian bound directly.
result Empirical results show improved performance over existing PAC-Bayesian training methods.
The VAE's reconstruction ability is studied using PAC-Bayes theory.
problem Understanding the performance of VAEs for unseen data.
method PAC-Bayes theory is applied to analyze VAE's reconstruction error.
result Generalization bounds on VAE's reconstruction error are provided.
Study of loss functions for learning to defer, proving consistency.
problem Learning to defer in machine learning.
method Introduced a family of surrogate losses parameterized by Ψ and proved their consistency. result Proved realizable H-consistency and Bayes-consistency of specific surrogate losses. We show that Entropy-SGD (Chaudhari et al., 2017), when viewed as a learning algorithm, optimizes a PAC-Bayes bound on the risk of a Gibbs (posterior) classifier, i.e., a randomized classifier obtained by a risk-sensitive perturbation of the weights of a learned classifier. Entropy-SGD works by optimizing the bound's p…
Paper tightens PAC-Bayes bounds using coin-betting for better estimates.
problem Estimating mean of random elements with possibly S-dependent parameters.
method Refined PAC-Bayes proof strategy based on coin-betting framework.
result Derives tighter concentration inequalities for all sample sizes.
Lower bounds on Bayes risk for realizable models derived using information theory.
problem Deriving lower bounds on Bayes risk for realizable machine learning models.
method Information-theoretic analysis using rate-distortion theory and mutual information.
result Lower bounds on Bayes risk for realizable models, matching known bounds up to logarithmic factors.
Paper estimates optimal classification error with soft labels and calibration.
problem Estimating the optimal classification error with soft labels and calibration.
method Extends previous work on soft labels to estimate Bayes error, addressing bias and corrupted labels.
result The method provides a statistically consistent estimator of the Bayes error, even with imperfectly calibrated soft labels.