相关论文: A Theory of Universal Agnostic Learning

The universal learning framework has been developed to obtain guarantees on the learning rates that hold for any fixed distribution, which can be much faster than the ones uniformly hold over all the distributions. Given that the Empirical…

How quickly can a given class of concepts be learned from examples? It is common to measure the performance of a supervised machine learning algorithm by plotting its "learning curve", that is, the decay of the error rate as a function of…

We provide a full characterization of the concept classes that are optimistically universally online learnable with $\{0, 1\}$ labels. The notion of optimistically universal online learning was defined in [Hanneke, 2021] in order to…

In this paper we study the problem of multiclass classification with a bounded number of different labels $k$, in the realizable setting. We extend the traditional PAC model to a) distribution-dependent learning rates, and b) learning rates…

We consider the classical problem of learning rates for classes with finite VC dimension. It is well known that fast learning rates up to $O\left(\frac{d}{n}\right)$ are achievable by the empirical risk minimization algorithm (ERM) if low…

The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…

The vast majority of statistical theory on binary classification characterizes performance in terms of accuracy. However, accuracy is known in many cases to poorly reflect the practical consequences of classification error, most famously in…

We propose a universal classifier for binary Neyman-Pearson classification where null distribution is known while only a training sequence is available for the alternative distribution. The proposed classifier interpolates between…

We study the problem of learning in the presence of an adversary that can corrupt an $\eta$ fraction of the training examples with the goal of causing failure on a specific test point. In the realizable setting, prior work established that…

The well-known empirical risk minimization (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is…

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…

We study universal consistency of non-i.i.d. processes in the context of online learning. A stochastic process is said to admit universal consistency if there exists a learner that achieves vanishing average loss for any measurable response…

Statistical learning theory and the Probably Approximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to analyze learning problems and algorithms, and have been studied thoroughly.…

We study a localized notion of uniform convergence known as an "optimistic rate" (Panchenko 2002; Srebro et al. 2010) for linear regression with Gaussian data. Our refined analysis avoids the hidden constant and logarithmic factor in…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

Binary classification in the classic PAC model exhibits a curious phenomenon: Empirical Risk Minimization (ERM) learners are suboptimal in the realizable case yet optimal in the agnostic case. Roughly speaking, this owes itself to the fact…

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…

We establish a tight characterization of the worst-case rates for the excess risk of agnostic learning with sample compression schemes and for uniform convergence for agnostic sample compression schemes. In particular, we find that the…

We study distribution-free nonparametric regression following a notion of average smoothness initiated by Ashlagi et al. (2021), which measures the "effective" smoothness of a function with respect to an arbitrary unknown underlying…

A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…