Related papers: Generalization Bounds for Meta-Learning via PAC-Ba…

Generalization bounds for deep learning models are typically vacuous, not computable or restricted to specific model classes. In this paper, we tackle these issues by providing new disagreement-based certificates for the gap between the…

As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…

We present a general approach, based on exponential inequalities, to derive bounds on the generalization error of randomized learning algorithms. Using this approach, we provide bounds on the average generalization error as well as bounds…

Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…

Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning combating distributional uncertainty, e.g., the uncertainty of an empirical distribution compared…

Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation…

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…

We extend PAC-Bayesian theory to generative models and develop generalization bounds for models based on the Wasserstein distance and the total variation distance. Our first result on the Wasserstein distance assumes the instance space is…

Uncertainty quantification is essential in safety-critical settings--from autonomous driving to aviation, finance, and health--where decisions must rely on conservative bounds rather than point estimates. Predictor-level intervals (e.g.,…

Neural Network based controllers hold enormous potential to learn complex, high-dimensional functions. However, they are prone to overfitting and unwarranted extrapolations. PAC Bayes is a generalized framework which is more resistant to…

PAC-Bayesian bounds have proven to be a valuable tool for deriving generalization bounds and for designing new learning algorithms in machine learning. However, it typically focus on providing generalization bounds with respect to a chosen…

We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison…

Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation. However, all these works only provide regret or sample complexity guarantees. It is still an open question if one can achieve…

In robotics, optimizing controller parameters under safety constraints is an important challenge. Safe Bayesian optimization (BO) quantifies uncertainty in the objective and constraints to safely guide exploration in such settings.…

When data are scarce meta-learning can improve a learner's accuracy by harnessing previous experience from related learning tasks. However, existing methods have unreliable uncertainty estimates which are often overconfident. Addressing…

Deep Probabilistic Programming (DPP) allows powerful models based on recursive computation to be learned using efficient deep-learning optimization techniques. Additionally, DPP offers a unified perspective, where inference and learning…

We propose a novel method for closed-form predictive distribution modeling with neural nets. In quantifying prediction uncertainty, we build on Evidential Deep Learning, which has been impactful as being both simple to implement and giving…

PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To overcome this limitation, we introduce a new family of risk measures, called…

Understanding the relationship between generalization and privacy remains a central challenge in modern machine learning theory, particularly for deep networks trained by variants of differentially private stochastic gradient descent…

PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution $\rho$ to its empirical risk and to its Kullback-Leibler divergence with…