MRCpy implements minimax risk classifiers with performance guarantees and distribution shift adaptability.
problem Classical risk minimization approaches are not robust to distribution shifts.
method Robust risk minimization approach for minimax risk classifiers.
result MRCs provide performance guarantees and adapt to distribution shifts.
Efficient learning of minimax risk classifiers in high dimensions.
problem Efficient learning of classifiers in high-dimensional data.
method Iterative algorithm leveraging constraint generation methods for minimax risk classifiers.
result The algorithm provides efficient learning and feature selection in high-dimensional scenarios.
Paper presents an efficient algorithm for learning minimax risk classifiers with large-scale data.
problem Efficient learning of minimax risk classifiers for large-scale data with multiple classes.
method Combination of constraint and column generation for efficient learning.
result 10x speedup for general large-scale data and 100x speedup with many classes.
Paper presents adaptive minimax risk classifiers for multidimensional concept drift.
problem Multidimensional concept drift in supervised classification.
method Adaptive minimax risk classifiers (AMRCs) tracking multivariate and high-order distribution changes.
result AMRCs provide computable tight performance guarantees and improve classification.
Paper develops MRCs for supervised classification using generalized maximum entropy.
problem Developing robust classifiers for decision problems.
method Generalized maximum entropy principle applied to minimax risk classifiers.
result Learning techniques for determining MRCs with performance guarantees.
Study on clustering in high dimensions with anisotropic Gaussian mixtures, showing interpolation can be optimal and robust.
problem Clustering in high-dimensional anisotropic Gaussian mixtures.
method Derive minimax bounds, analyze ℓ 2 \ell_2 ℓ 2 -regularized classifiers, and investigate interpolation's robustness. result Interpolating solutions can be optimal and robust under certain conditions.
Paper introduces MRCs that minimize worst-case 0-1 loss, providing tight performance guarantees.
problem Minimizing worst-case 0-1 loss in classification.
method MRCs that minimize worst-case 0-1 loss with uncertainty sets of distributions.
result MRCs provide tight performance guarantees and are strongly universally consistent.
The paper analyzes kernel classifiers' performance in Sobolev spaces and proves their optimality.
problem Theoretical analysis of kernel classifiers' performance in Sobolev spaces.
method Deriving upper and lower bounds on classification excess risk using kernel regression theory and estimating interpolation smoothness.
result The proposed kernel classifier is optimal in Sobolev spaces, with theoretical bounds confirmed by real data.
This paper analyzes neural network classifiers' performance in binary classification.
problem Performance of neural network classifiers in binary classification problems.
method Plug-in classifiers based on neural networks, considering a more general function class and surrogate loss.
result Dimension-free, uniform rate of convergence for the excess risk of neural networks, showing minimax optimality.
Privacy-preserving binary classification using locally differential private data.
problem Classifying data while protecting individual privacy.
method Locally differential private mechanism followed by a universally consistent classifier.
result Minimax rates of convergence are slower when using private data.
MRCs minimize worst-case expected 0-1 loss and provide performance guarantees.
problem Minimizing expected 0-1 loss in classification.
method Minimizes worst-case expected 0-1 loss over uncertainty sets defined by linear constraints.
result Achieves efficient learning and generalization with performance guarantees.
A novel minimax classifier tackles imbalanced datasets with few minority samples.
problem Imbalanced datasets with limited minority samples.
method Proposes a novel minimax learning algorithm with two steps: minimization and maximization.
result The algorithm improves model performance compared to existing methods.
Proposes a fairness criterion for multi-objective optimization in classification.
problem Ensuring fairness in classification models across different groups.
method Formulates a minimax Pareto fairness criterion and provides an optimization algorithm.
result Demonstrates improved fairness compared to existing methods on various real-world datasets.
Paper presents IMRCs for evolving tasks with forward and backward learning.
problem Incremental learning of evolving tasks with few samples per task.
method Incremental minimax risk classifiers (IMRCs) that exploit forward and backward learning.
result IMRCs provide significant performance improvement, especially with reduced sample sizes.
We consider a standard binary classification problem. The performance of any binary classifier based on the training data is characterized by the excess risk. We study Bahadur's type exponential bounds on the minimax accuracy confidence function based on the excess risk. We study how this quantity depends on the comple…
Study minimax linear regression under quantile risk, improving existing bounds and providing new results.
problem Designing minimax procedures in linear regression under quantile risk.
method Analyzes realizable setting with Gaussian noise, extends to all p-th power error functions, develops new lower and upper bounds.
result Proves minimaxity of a variant of the min-max regression procedure for all p-th power error functions.
New method for multiclass classification reduces error bounds.
problem High-dimensional multiclass classification with sparse coefficients.
method Sparse multinomial logistic regression with convex penalties.
result Plug-in classifiers achieve minimax generalization error bounds.
Study on estimating invertible functions with minimax analysis.
problem Minimizing risk of estimating invertible functions on a plane.
method Introduce two types of L 2 L^2 L 2 -risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator. result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.
Paper improves risk bounds for nonconvex-strongly-concave minimax problems.
problem Achieving sharper risk bounds for nonconvex-strongly-concave minimax problems.
method Using uniform localized convergence to derive high probability generalization error bounds.
result Derives n times faster excess primal risk bounds for popular algorithms.
New estimator achieves minimax optimal risk in transfer learning.
problem Nonparametric regression with transfer learning.
method Confidence thresholding estimator and data-driven adaptive algorithm.
result Adaptive algorithm achieves minimax risk up to a logarithmic factor.
Exact minimax risk derived for linear prediction with sample covariance analysis.
problem Understanding the minimax risk in linear prediction under various covariate distributions.
method Exact minimax risk analysis, leveraging statistical leverage scores and PAC-Bayes techniques.
result The minimax risk is of order d / ( n − d + 1 ) d/(n-d+1) d / ( n − d + 1 ) for any covariate distribution, nearly matching the risk for Gaussian design. A new classifier uses Fermat distance for semi-supervised learning in high dimensions.
problem Semi-supervised classification with limited labeled data in high-dimensional settings.
method Proposes weighted k-NN and MDS classifiers using Fermat distance.
result The weighted k-NN classifier is minimax optimal and outperforms other methods.
The paper optimizes risk-sensitive RL with CVaR, achieving near-minimax-optimal results.
problem Optimizing risk-sensitive reinforcement learning with CVaR objective.
method Developed algorithms for multi-arm bandits and online RL in MDPs, achieving near-minimax-optimal regret.
result Achieved near-minimax-optimal regret of O ( τ − 1 S A K ) O(τ^{-1}\sqrt{SAK}) O ( τ − 1 S A K ) for constant τ τ τ . Minimax defense improves neural network security against gradient-based attacks.
problem Gradient-based adversarial attacks on neural networks.
method Minimax optimization in a GAN framework to create a discriminator that plays a minimax game with the generator.
result Minimax defense significantly reduces adversarial attack success rates compared to standard classifiers.
Develops estimators for near-optimal linear regression under distribution shift.
problem Linear regression under distribution shift with scarce target domain data.
method Minimax linear risk estimators covering various transfer learning settings.
result Achieves near-optimal risk for linear regression problems under distribution shift.
The paper establishes risk bounds for PU learning with label noise.
problem Finding a classifier in PU learning with label noise.
method Establishes risk bounds under the assumption of label selection randomness.
result Proves that the upper bound on minimax risk is almost optimal.
Paper explores generalization of minimax learners, proposing a new metric.
problem Understanding how minimax learners perform on unseen data.
method Proposes a new metric, the primal gap, to study generalization of minimax learners.
result Derives generalization error bounds for the primal gap in nonconvex-concave settings.
Sparse multinomial logistic regression for multiclass classification with feature selection.
problem High-dimensional multiclass classification with a focus on sparse models.
method Penalized maximum likelihood with complexity penalty, feature selection using group Lasso and Slope classifiers.
result Achievement of minimax order in both small and large number of classes regimes.
Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation…
Study tests uniformity of categorical data against missing-ball alternatives, finding chi-squared test outperforms.
problem Testing uniformity of categorical data against missing-ball alternatives.
method Characterizes minimax risk, uses collisions and chi-squared test, reduces to structured subset of alternatives.
result Minimax test outperforms chi-squared test under least favorable alternative.
Develops high-probability minimax quantile bounds for statistical problems.
problem Statistical procedures often lose information about tail behavior when reduced to expectations.
method Introduces minimax quantiles, develops high-probability variants of minimax methods, and converts risk lower bounds to quantile lower bounds.
result Obtains high-probability minimax quantile lower bounds for various statistical problems.
Deep neural network with l_1-regularization achieves nearly optimal risk bounds.
problem Achieving optimal risk bounds in deep learning.
method Empirical risk minimization with l_1-regularization.
result Adaptively nearly-minimax risk bound across various function classes.
Paper proposes ZO-SMD for MERO, achieving optimal convergence rates.
problem Minimizing excess risk across all test distributions.
method Zeroth-order stochastic mirror descent algorithm for both smooth and non-smooth MERO.
result Converges at optimal rates of O ( 1 / t ) \mathcal{O}(1/\sqrt{t}) O ( 1/ t ) for estimates and optimization errors. Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.
We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average L p L_p L p distance between the learned classifier and the true maximum a posteriori classifier, which are well-established surrogates for th…
Study on kernel regression risk in high dimensions using Pinsker bound.
problem Kernel regression risk in high-dimensional inner product spaces.
method Investigation of Pinsker bound for kernel regression on sphere S d \mathbb{S}^{d} S d with sample size n = α d γ ( 1 + o d ( 1 ) ) n = αd^γ(1+o_{d}(1)) n = α d γ ( 1 + o d ( 1 )) . result Exact minimax risk and Pinsker constant identified for kernel regression.
Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial learning problem can be reduced to a minimax statistical learning problem by intr…
Score attack method provides a lower bound on privacy-constrained minimax risk.
problem Characterizing the optimality of privacy-constrained statistical models.
method Score attack based on tracing attack concept.
result Optimally lower bounds the minimax risk of estimating unknown model parameters.
We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution P X Y P_{XY} P X Y . Our result generalizes and provides an alternative proof for the resul…
Paper explores fair classification with bounded disparity using finite datasets.
problem Ensuring fairness in binary classification with protected groups.
method Minimax optimal approach with fairness constraints and demographic disparity control.
result Proposes FairBayes-DDP+ method that achieves minimax lower bound on fairness-aware excess risk.
Improves RL generalization by minimizing adversarial risk.
problem Overfitting to training environments and poor generalization to unseen scenarios.
method Introduces minimax formulation and distributional framework to RL.
result Trained policy shows improved generalization to different environments.
Recently, researchers have discovered that the state-of-the-art object classifiers can be fooled easily by small perturbations in the input unnoticeable to human eyes. It is also known that an attacker can generate strong adversarial examples if she knows the classifier parameters. Conversely, a defender can robustify …
Minimax solutions are weak solutions to Cauchy problems involving Hamilton--Jacobi equations, constructed from generating families quadratic at infinity of their geometric solutions. We give a complete description of minimax solutions and we classify their generic singularities of codimension not greater than 2.
The paper explores the information-theoretic nature of excess risk in machine learning.
problem Understanding the excess risk in machine learning models.
method Formulates the minimax excess risk as a zero-sum game and modifies it to allow swapping of the order of play.
result Proves that under certain conditions, the duality gap is zero, allowing for the application of Bayesian results to provide bounds on minimax excess risk.
An algorithm learns from multiple models to match an oracle's risk.
problem Learning from multiple noisy models to estimate a target parameter.
method Elimination rounds algorithm for adaptive learning.
result Risk of weak-oracle learner matches that of an oracle in multiple source case.
Develops a robust learning method for unknown context distributions.
problem Learning from data in different, unknown contexts.
method Focuses on excess risks, constructs distribution sets with statistical coverage.
result Shows robustness in worst-case scenarios without sacrificing nominal performance.
Paper analyzes minimax risks of personalized federated learning algorithms.
problem Statistical heterogeneity among clients in federated learning.
method Minimax analysis of FedAvg and local training approaches.
result Threshold for optimality between FedAvg and local training depends on data heterogeneity.
The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same underlying population. In this paper, we introduce a general measure of classif…