Many forms of sensitive data, such as web traffic, mobility data, or hospital occupancy, are inherently sequential. The standard method for training machine learning models while ensuring privacy for units of sensitive information, such as individual hospital visits, is differentially private stochastic gradient descent (DP-SGD). However, we observe in this work that the formal guarantees of DP-SGD are incompatible with time series specific tasks like forecasting, since they rely on the *privacy amplification* attained by training on small, unstructured batches sampled from an unstructured dataset. In contrast, batches for forecasting are generated by (1) sampling sequentially structured time series from a dataset, (2) sampling contiguous subsequences from these series, and (3) partitioning them into context and ground-truth forecast windows. We theoretically analyze the privacy amplification attained by this *structured subsampling* to enable the training of forecasting models with sound and tight event- and user-level privacy guarantees. Towards more private models, we additionally prove how data augmentation amplifies privacy in self-supervised training of sequence models. Our empirical evaluation demonstrates that amplification by structured subsampling enables the training of forecasting models with strong formal privacy guarantees.

Amplification by subsampling is one of the main primitives in machine learning with differential privacy (DP): Training a model on random batches instead of complete datasets results in stronger privacy. This is traditionally formalized via mechanism-agnostic subsampling guarantees that express the privacy parameters of a subsampled mechanism as a function of the original mechanism's privacy parameters. We propose the first general framework for deriving mechanism-specific guarantees, which leverage additional information beyond these parameters to more tightly characterize the subsampled mechanism's privacy. Such guarantees are of particular importance for privacy accounting, i.e., tracking privacy over multiple iterations. Overall, our framework based on conditional optimal transport lets us derive existing and novel guarantees for approximate DP, accounting with Renyi DP, and accounting with dominating pairs in a unified, principled manner. As an application, we analyze how subsampling affects the privacy of groups of multiple users. Our tight mechanism-specific bounds outperform tight mechanism-agnostic bounds and classic group privacy results.

Real-world data is complex and often consists of objects that can be decomposed into multiple entities (e.g. images into pixels, graphs into interconnected nodes). Randomized smoothing is a powerful framework for making models provably robust against small changes to their inputs - by guaranteeing robustness of the majority vote when randomly adding noise before classification. Yet, certifying robustness on such complex data via randomized smoothing is challenging when adversaries do not arbitrarily perturb entire objects (e.g. images) but only a subset of their entities (e.g. pixels). As a solution, we introduce hierarchical randomized smoothing: We partially smooth objects by adding random noise only on a randomly selected subset of their entities. By adding noise in a more targeted manner than existing methods we obtain stronger robustness guarantees while maintaining high accuracy. We initialize hierarchical smoothing using different noising distributions, yielding novel robustness certificates for discrete and continuous domains. We experimentally demonstrate the importance of hierarchical smoothing in image and node classification, where it yields superior robustness-accuracy trade-offs. Overall, hierarchical smoothing is an important contribution towards models that are both - certifiably robust to perturbations and accurate.

A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have inherent equivariances, such as rotation or permutation equivariance. In such tasks, even perturbations with large norm do not necessarily change an input's semantic content. Furthermore, there are perturbations for which a model's prediction explicitly needs to change. For the first time, we propose a sound notion of adversarial robustness that accounts for task equivariance. We then demonstrate that provable robustness can be achieved by (1) choosing a model that matches the task's equivariances (2) certifying traditional adversarial robustness. Certification methods are, however, unavailable for many models, such as those with continuous equivariances. We close this gap by developing the framework of equivariance-preserving randomized smoothing, which enables architecture-agnostic certification. We additionally derive the first architecture-specific graph edit distance certificates, i.e. sound robustness guarantees for isomorphism equivariant tasks like node classification. Overall, a sound notion of robustness is an important prerequisite for future work at the intersection of robust and geometric machine learning.

Randomized smoothing is one of the most promising frameworks for certifying the adversarial robustness of machine learning models, including Graph Neural Networks (GNNs). Yet, existing randomized smoothing certificates for GNNs are overly pessimistic since they treat the model as a black box, ignoring the underlying architecture. To remedy this, we propose novel gray-box certificates that exploit the message-passing principle of GNNs: We randomly intercept messages and carefully analyze the probability that messages from adversarially controlled nodes reach their target nodes. Compared to existing certificates, we certify robustness to much stronger adversaries that control entire nodes in the graph and can arbitrarily manipulate node features. Our certificates provide stronger guarantees for attacks at larger distances, as messages from farther-away nodes are more likely to get intercepted. We demonstrate the effectiveness of our method on various models and datasets. Since our gray-box certificates consider the underlying graph structure, we can significantly improve certifiable robustness by applying graph sparsification.

Building models that comply with the invariances inherent to different domains, such as invariance under translation or rotation, is a key aspect of applying machine learning to real world problems like molecular property prediction, medical imaging, protein folding or LiDAR classification. For the first time, we study how the invariances of a model can be leveraged to provably guarantee the robustness of its predictions. We propose a gray-box approach, enhancing the powerful black-box randomized smoothing technique with white-box knowledge about invariances. First, we develop gray-box certificates based on group orbits, which can be applied to arbitrary models with invariance under permutation and Euclidean isometries. Then, we derive provably tight gray-box certificates. We experimentally demonstrate that the provably tight certificates can offer much stronger guarantees, but that in practical scenarios the orbit-based method is a good approximation.