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This paper deals with the speed of convergence of the learning curve in a Gaussian process regression framework. The learning curve describes the average generalization error of the Gaussian process used for the regression. More…

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…

For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a…

Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…

Overfitting data is a well-known phenomenon related with the generation of a model that mimics too closely (or exactly) a particular instance of data, and may therefore fail to predict future observations reliably. In practice, this…

Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding…

This paper discusses the estimation of the generalization gap, the difference between generalization performance and training performance, for overparameterized models including neural networks. We first show that a functional variance, a…

The primary objective of learning methods is generalization. Classic uniform generalization bounds, which rely on VC-dimension or Rademacher complexity, fail to explain the significant attribute that over-parameterized models in deep…

Model-based neural networks provide unparalleled performance for various tasks, such as sparse coding and compressed sensing problems. Due to the strong connection with the sensing model, these networks are interpretable and inherit prior…

As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…

Machine learning systems often do not share the same inductive biases as humans and, as a result, extrapolate or generalize in ways that are inconsistent with our expectations. The trade-off between exemplar- and rule-based generalization…

Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…

Quantifying the data uncertainty in learning tasks is often done by learning a prediction interval or prediction set of the label given the input. Two commonly desired properties for learned prediction sets are \emph{valid coverage} and…

Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…

We discuss the prediction accuracy of assumed statistical models in terms of prediction errors for the generalized linear model and penalized maximum likelihood methods. We derive the forms of estimators for the prediction errors, such as…

We propose self-adaptive training---a new training algorithm that dynamically corrects problematic training labels by model predictions without incurring extra computational cost---to improve generalization of deep learning for potentially…

Group imbalance has been a known problem in empirical risk minimization (ERM), where the achieved high average accuracy is accompanied by low accuracy in a minority group. Despite algorithmic efforts to improve the minority group accuracy,…

Are there still barriers to generalization once all of the relevant variables are known? We address this question via a framework that casts compositional generalization as a variational inference problem over latent variables with…

Machine learning models are often susceptible to adversarial perturbations of their inputs. Even small perturbations can cause state-of-the-art classifiers with high "standard" accuracy to produce an incorrect prediction with high…