Related papers: On Medians of (Randomized) Pairwise Means
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…
With the deluge of digitized information in the Big Data era, massive datasets are becoming increasingly available for learning predictive models. However, in many practical situations, the poor control of the data acquisition processes may…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of Large Language Models (LLMs), which aim to identify and mitigate intermediate errors in the reasoning processes. However, the…
In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by $U$-statistics of degree $d\geq 1$, i.e. functionals of the training data with low variance…
Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…
We study the task of learning from non-i.i.d. data. In particular, we aim at learning predictors that minimize the conditional risk for a stochastic process, i.e. the expected loss of the predictor on the next point conditioned on the set…
Machine learning models are often evaluated using point estimates of performance metrics such as accuracy, F1 score, or mean squared error. Such summaries fail to capture the inherent variability induced by stochastic elements of the…
The generalization ability of minimizers of the empirical risk in the context of binary classification has been investigated under a wide variety of complexity assumptions for the collection of classifiers over which optimization is…
The empirical risk minimization approach to data-driven decision making requires access to training data drawn under the same conditions as those that will be faced when the decision rule is deployed. However, in a number of settings, we…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain…
The development of state-of-the-art systems in different applied areas of machine learning (ML) is driven by benchmarks, which have shaped the paradigm of evaluating generalisation capabilities from multiple perspectives. Although the…
In order to circumvent statistical and computational hardness results in sequential decision-making, recent work has considered smoothed online learning, where the distribution of data at each time is assumed to have bounded likeliehood…
Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this…
Many applied settings in empirical economics involve simultaneous estimation of a large number of parameters. In particular, applied economists are often interested in estimating the effects of many-valued treatments (like teacher effects…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…