Related papers: Optimal PAC Bounds Without Uniform Convergence
Multiclass neural networks are a common tool in modern unsupervised domain adaptation, yet an appropriate theoretical description for their non-uniform sample complexity is lacking in the adaptation literature. To fill this gap, we propose…
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…
In the problem of aggregation, the aim is to combine a given class of base predictors to achieve predictions nearly as accurate as the best one. In this flexible framework, no assumption is made on the structure of the class or the nature…
We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
This paper proposes an easy-to-compute upper bound for the overlap index between two probability distributions without requiring any knowledge of the distribution models. The computation of our bound is time-efficient and memory-efficient…
Binary classification based on predicted probabilities (scores) is a fundamental task in supervised machine learning. While thresholding scores is Bayes-optimal in the unconstrained setting, using a single threshold generally violates…
Recent advances have significantly improved our understanding of the sample complexity of learning in average-reward Markov decision processes (AMDPs) under the generative model. However, much less is known about the constrained…
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…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input…
In the context of supervised learning, meta learning uses features, metadata and other information to learn about the difficulty, behavior, or composition of the problem. Using this knowledge can be useful to contextualize classifier…
When dealing with imbalanced classification data, reweighting the loss function is a standard procedure allowing to equilibrate between the true positive and true negative rates within the risk measure. Despite significant theoretical work…
We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…
Let $f(\theta, X_1),$ $ \dots,$ $ f(\theta, X_n)$ be a sequence of random elements, where $f$ is a fixed scalar function, $X_1, \dots, X_n$ are independent random variables (data), and $\theta$ is a random parameter distributed according to…
The Partial Area Under the ROC Curve (PAUC), typically including One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC), measures the average performance of a binary classifier within a specific false positive rate and/or true positive…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
One of the main open problems in the theory of multi-category margin classification is the form of the optimal dependency of a guaranteed risk on the number C of categories, the sample size m and the margin parameter gamma. From a practical…
Consider the binary classification problem of predicting a target variable $Y$ from a discrete feature vector $X = (X_1,...,X_d)$. When the probability distribution $\mathbb{P}(X,Y)$ is known, the optimal classifier, leading to the minimum…
In many, if not most, machine learning applications the training data is naturally heterogeneous (e.g. federated learning, adversarial attacks and domain adaptation in neural net training). Data heterogeneity is identified as one of the…
We consider the problem of estimating the mean of a sequence of random elements $f(X_1, \theta)$ $, \ldots, $ $f(X_n, \theta)$ where $f$ is a fixed scalar function, $S=(X_1, \ldots, X_n)$ are independent random variables, and $\theta$ is a…