Related papers: Sample Complexity Result for Multi-category Classi…

We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the…

Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the…

For machine learning models trained with limited labeled training data, validation stands to become the main bottleneck to reducing overall annotation costs. We propose a statistical validation algorithm that accurately estimates the…

Importance sampling (IS) is a technique that enables statistical estimation of output performance at multiple input distributions from a single nominal input distribution. IS is commonly used in Monte Carlo simulation for variance reduction…

In this paper we study the sampling recovery problem for certain relevant multivariate function classes which are not compactly embedded into $L_\infty$. Recent tools relating the sampling numbers to the Kolmogorov widths in the uniform…

We prove an L2 recovery bound for a family of sparse estimators defined as minimizers of some empirical loss functions -- which include hinge loss and logistic loss. More precisely, we achieve an upper-bound for coefficients estimation…

Estimating the prevalence of a category in a population using imperfect measurement devices (diagnostic tests, classifiers, or large language models) is fundamental to science, public health, and online trust and safety. Standard approaches…

One prominent method of evaluating machine learning model trustworthiness is the notion of calibration. In the binary outcome setting, a probabilistic predictor is calibrated if outcomes are realized according to a model's distributional…

The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

In functional data analysis, binary classification with one functional covariate has been extensively studied. We aim to fill in the gap of considering multivariate functional covariates in classification. In particular, we propose an…

Suppose some classifiers are selected from a set of hypothesis classifiers to form an equally-weighted ensemble that selects a member classifier at random for each input example. Then the ensemble has an error bound consisting of the…

We study the optimal scale at which real-valued function classes exhibit uniform convergence and learnability. Our main result establishes a scale-sensitive generalization of the fundamental theorem of PAC learning: for every bounded…

Classifiers are often tested on relatively small data sets, which should lead to uncertain performance metrics. Nevertheless, these metrics are usually taken at face value. We present an approach to quantify the uncertainty of…

The deployment of machine learning classifiers in high-stakes domains requires well-calibrated confidence scores for model predictions. In this paper we introduce the notion of variable-based calibration to characterize calibration…

An important question in constructing Cross Validation (CV) estimators of the generalization error is whether rules can be established that allow "optimal" selection of the size of the training set, for fixed sample size $n$. We define the…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…

Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions.…

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However…

In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between…