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.
Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.
problem Estimating low-rank matrices from noisy, non-linear observations.
method Proves strong universality result with equivalent Gaussian model and effective prior parameters.
result Signal-to-noise ratio requirement grows as $N^{ rac 12 (1-1/k_F)}$ for accurate reconstruction.
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.
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 …
New method predicts binary matrix entries using empirical Bayes and low-rank structure.
problem Predicting unobserved entries in binary matrices.
method Empirical Bayes method motivated by Efron--Morris estimator, exploiting low-rank structure.
result Superior performance in predictive accuracy, calibration, and efficiency compared to existing methods.
A scalable method for accurate inference of low-dimensional parameters in high-dimensional linear regression.
problem Statistical inference for low-dimensional parameters in high-dimensional linear regression models.
method Mean-field variational Bayes approach, focusing on nuisance parameters and conditional distributions.
result Competitive numerical performance and theoretical guarantees for estimation and uncertainty quantification.
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.
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
Study improves theoretical understanding of Bayesian deep learning for classification tasks.
problem Theoretical gap in understanding Bayesian approaches in deep learning for classification.
method PAC-Bayes bounds techniques and Spike-and-Slab priors for sparse deep learning.
result Established non-asymptotic results for prediction error, achieving minimax optimal rates.
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…
Regularization helps improve classification of noisy high-dimensional data.
problem Classifying high-dimensional noisy Gaussian mixture with limited oracle knowledge.
method Analysis of regularized convex classifiers including ridge, hinge, and logistic regression.
result Regularization can reach Bayes-optimal performance under certain conditions.
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix calibration, sparse principal component analysis, blind source separation, low rank matrix …
LDA-GO improves LDA for high-dimensional data via gradient optimization.
problem LDA struggles in high-dimensional settings due to unreliable covariance matrix estimation.
method LDA-GO learns a low-rank precision matrix via gradient optimization, automatically selecting between Gaussian likelihood and cross-entropy loss.
result LDA-GO outperforms other LDA variants in sparse-signal high-dimensional regimes.
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.
Improved IVON boosts LoRA model accuracy and calibration.
problem Improving the accuracy and calibration of large language models.
method Replaced AdamW with IVON for finetuning Llama-2.
result IVON improves Llama-2 accuracy by 2.8% and calibration error by 4.6%.
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.
Empirical Bayes rates via variational approximations and prior decomposition.
problem Nonparametric and high-dimensional inference convergence rates.
method Variational perspective and prior decomposition.
result Empirical Bayes posterior rates derived from variational Bayes.
This paper proposes an efficient method for calculating Shapley values in Naive Bayes classifiers.
problem The need for explaining machine learning model decisions.
method An exact analytic expression of Shapley values for Naive Bayes classifiers.
result The proposed Shapley values provide informative results with low complexity and low computation time.
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.
Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially outperform simple spectral approaches. Recent work characterizes the asymptotic acc…
Develops methods for fair classification under linear disparity constraints.
problem Disparate impacts of machine learning algorithms on protected groups.
method Bayes-optimal fair classification methods via pre-, in-, and post-processing.
result Explicit forms of Bayes-optimal fair classifiers under linear disparity measures.
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.
This work addresses privacy in Bayesian estimation, achieving near-optimal error rates.
problem Preserving privacy in Bayesian estimation while maintaining optimal estimation accuracy.
method Developed efficient algorithms for Gaussian mean estimation and linear regression with near-optimal error rates, leveraging sum-of-squares techniques.
result Achieved near-optimal mean-squared error rates for Bayesian mean estimation and linear regression, with computational-statistical gaps.
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.
Optimal graph classification uses message-passing neural networks.
problem Node classification on sparse graphs with fixed feature dimensions.
method Asymptotic local Bayes optimality, message-passing graph neural networks.
result Optimal message-passing architecture interpolates between MLP and convolution.
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…
Random projections improve classifier generalization without needing to choose the best threshold.
problem Improving classifier generalization without choosing the best threshold.
method Thresholding a random one-dimensional feature after random projection of data.
result Generalization gap is significantly smaller than linear classifiers.
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.
Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this algorithm as the approximate survey propagation (ASP) and derive it for a class of low-…
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…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover, we show that our al…