When deploying a machine learning model in production, it is common to encounter changes in the data distribution, such as shifts in covariates [Shimodaira, 2000], labels [Saerens et al., 2002,

In other cases, the motivation may simply be to train more reliable classifiers.

Accurately evaluating model performance is crucial for deploying machine learning systems in real-world applications. Traditional methods often require a sufficiently large labeled test set to ensure a reliable evaluation. However, in many contexts, a large labeled dataset is costly and labor-intensive. Therefore, we sometimes have to do evaluation by a few labeled samples, which is theoretically challenging. Recent advances in generative models offer a promising alternative by enabling the synthesis of high-quality data. In this work, we make a systematic investigation about the use of synthetic data to estimate the test error of a trained model under limited labeled data conditions. To this end, we develop novel generalization bounds that take synthetic data into account. Those bounds suggest novel ways to optimize synthetic samples for evaluation and theoretically reveal the significant role of the generator's quality. Inspired by those bounds, we propose a theoretically grounded method to generate optimized synthetic data for model evaluation. Experimental results on simulation and tabular datasets demonstrate that, compared to existing baselines, our method achieves accurate and more reliable estimates of the test error.

When deploying a machine learning model in production, it is common to encounter changes in the data distribution, such as shifts in covariates [Shimodaira, 2000], labels [Saerens et al., 2002,

Machine learning models are routinely used to support decisions that affect individuals - be it to screen a patient for a serious illness or to gauge their response to treatment. In these tasks, we are limited to learning models from datasets with noisy labels. In this paper, we study the instance-level impact of learning under label noise. We introduce a notion of regret for this regime which measures the number of unforeseen mistakes due to noisy labels. We show that standard approaches to learning under label noise can return models that perform well at a population level while subjecting individuals to a lottery of mistakes . We present a versatile approach to estimate the likelihood of mistakes at the individual level from a noisy dataset by training models over plausible realizations of datasets without label noise. This is supported by a comprehensive empirical study of label noise in clinical prediction tasks. Our results reveal how failure to anticipate mistakes can compromise model reliability and adoption, and demonstrate how we can address these challenges by anticipating and avoiding regretful decisions. Machine learning models are routinely used to support or automate decisions that affect individuals - be it to screen a patient for a mental illness [47], or assess their risk for an adverse treatment response [3]. In such tasks, we train models with labels that reflect noisy observations of the true outcome we wish to predict. In practice, such noise may arise due to measurement error [e.g., 20, 35], human annotation [26], or inherent ambiguity [35]. In all these cases, label noise can have detrimental effects on model performance [10]. Over the past decade, these issues have led to extensive work on learning from noisy datasets [see e.g., 10, 28, 36, 39, 45].

We introduce a novel approach for detecting distribution shifts that negatively impact the performance of machine learning models in continuous production environments, which requires no access to ground truth data labels. It builds upon the work of Podkopaev and Ramdas [2022], who address scenarios where labels are available for tracking model errors over time. Our solution extends this framework to work in the absence of labels, by employing a proxy for the true error. This proxy is derived using the predictions of a trained error estimator. Experiments show that our method has high power and false alarm control under various distribution shifts, including covariate and label shifts and natural shifts over geography and time.

Robustness and generalization ability of machine learning models are of utmost importance in various application domains. There is a wide interest in efficient ways to analyze those properties. One important direction is to analyze connection between those two properties. Prior theories suggest that a robust learning algorithm can produce trained models with a high generalization ability. However, we show in this work that the existing error bounds are vacuous for the Bayes optimal classifier which is the best among all measurable classifiers for a classification problem with overlapping classes. Those bounds cannot converge to the true error of this ideal classifier. This is undesirable, surprizing, and never known before. We then present a class of novel bounds, which are model-dependent and provably tighter than the existing robustness-based ones. Unlike prior ones, our bounds are guaranteed to converge to the true error of the best classifier, as the number of samples increases. We further provide an extensive experiment and find that two of our bounds are often non-vacuous for a large class of deep neural networks, pretrained from ImageNet.

We introduce a Robust version of the Physics-Informed Neural Networks (RPINNs) to approximate the Partial Differential Equations (PDEs) solution. Standard Physics Informed Neural Networks (PINN) takes into account the governing physical laws described by PDE during the learning process. The network is trained on a data set that consists of randomly selected points in the physical domain and its boundary. PINNs have been successfully applied to solve various problems described by PDEs with boundary conditions. The loss function in traditional PINNs is based on the strong residuals of the PDEs. This loss function in PINNs is generally not robust with respect to the true error. The loss function in PINNs can be far from the true error, which makes the training process more difficult. In particular, we do not know if the training process has already converged to the solution with the required accuracy. This is especially true if we do not know the exact solution, so we cannot estimate the true error during the training. This paper introduces a different way of defining the loss function. It incorporates the residual and the inverse of the Gram matrix, computed using the energy norm. We test our RPINN algorithm on two Laplace problems and one advection-diffusion problem in two spatial dimensions. We conclude that RPINN is a robust method. The proposed loss coincides well with the true error of the solution, as measured in the energy norm. Thus, we know if our training process goes well, and we know when to stop the training to obtain the neural network approximation of the solution of the PDE with the true error of required accuracy.

We study over-parameterized classifiers where Empirical Risk Minimization (ERM) for learning leads to zero training error. In these over-parameterized settings there are many global minima with zero training error, some of which generalize better than others. We show that under certain conditions the fraction of "bad" global minima with a true error larger than {\epsilon} decays to zero exponentially fast with the number of training data n. The bound depends on the distribution of the true error over the set of classifier functions used for the given classification problem, and does not necessarily depend on the size or complexity (e.g. the number of parameters) of the classifier function set. This insight may provide a novel perspective on the unexpectedly good generalization even of highly over-parameterized neural networks. We substantiate our theoretical findings through experiments on synthetic data and a subset of MNIST. Additionally, we assess our hypothesis using VGG19 and ResNet18 on a subset of Caltech101.