When an individual reports a negative interaction with some system, how can their personal experience be contextualized within broader patterns of system behavior? We study the incident database problem, where individual reports of adverse events arrive sequentially, and are aggregated over time. In this work, our goal is to identify whether there are subgroups--defined by any combination of relevant features--that are disproportionately likely to experience harmful interactions with the system. We formalize this problem as a sequential hypothesis test, and identify conditions on reporting behavior that are sufficient for making inferences about disparities in true rates of harm across subgroups. We show that algorithms for sequential hypothesis tests can be applied to this problem with a standard multiple testing correction. We then demonstrate our method on real-world datasets, including mortgage decisions and vaccine side effects; on each, our method (re-)identifies subgroups known to experience disproportionate harm using only a fraction of the data that was initially used to discover them.

In this work, we consider how preference models in interactive recommendation systems determine the availability of content and users' opportunities for discovery. We propose an evaluation procedure based on stochastic reachability to quantify the maximum probability of recommending a target piece of content to an user for a set of allowable strategic modifications. This framework allows us to compute an upper bound on the likelihood of recommendation with minimal assumptions about user behavior. Stochastic reachability can be used to detect biases in the availability of content and diagnose limitations in the opportunities for discovery granted to users. We show that this metric can be computed efficiently as a convex program for a variety of practical settings, and further argue that reachability is not inherently at odds with accuracy. We demonstrate evaluations of recommendation algorithms trained on large datasets of explicit and implicit ratings. Our results illustrate how preference models, selection rules, and user interventions impact reachability and how these effects can be distributed unevenly.

Datasets play a critical role in shaping the perception of performance and progress in machine learning (ML)--the way we collect, process, and analyze data affects the way we benchmark success and form new research agendas (Paullada et al., 2020; Dotan & Milli, 2020). A growing appreciation of this determinative role of datasets has sparked a concomitant concern that standard datasets used for training and evaluating ML models lack diversity along significant dimensions, for example, geography, gender, and skin type (Shankar et al., 2017; Buolamwini & Gebru, 2018). Lack of diversity in evaluation data can obfuscate disparate performance when evaluating based on aggregate accuracy (Buolamwini & Gebru, 2018). Lack of diversity in training data can limit the extent to which learned models can adequately apply to all portions of a population, a concern highlighted in recent work in the medical domain (Habib et al., 2019; Hofmanninger et al., 2020). Our work aims to develop a general unifying perspective on the way that dataset composition affects outcomes of machine learning systems.

This graduate textbook on machine learning tells a story of how patterns in data support predictions and consequential actions. Starting with the foundations of decision making, we cover representation, optimization, and generalization as the constituents of supervised learning. A chapter on datasets as benchmarks examines their histories and scientific bases. Self-contained introductions to causality, the practice of causal inference, sequential decision making, and reinforcement learning equip the reader with concepts and tools to reason about actions and their consequences. Throughout, the text discusses historical context and societal impact. We invite readers from all backgrounds; some experience with probability, calculus, and linear algebra suffices.

This paper provides elementary analyses of the regret and generalization of minimum-norm interpolating classifiers (MNIC). The MNIC is the function of smallest Reproducing Kernel Hilbert Space norm that perfectly interpolates a label pattern on a finite data set. We derive a mistake bound for MNIC and a regularized variant that holds for all data sets. This bound follows from elementary properties of matrix inverses. Under the assumption that the data is independently and identically distributed, the mistake bound implies that MNIC generalizes at a rate proportional to the norm of the interpolating solution and inversely proportional to the number of data points. This rate matches similar rates derived for margin classifiers and perceptrons. We derive several plausible generative models where the norm of the interpolating classifier is bounded or grows at a rate sublinear in $n$. We also show that as long as the population class conditional distributions are sufficiently separable in total variation, then MNIC generalizes with a fast rate.

Modern nonlinear control theory seeks to develop feedback controllers that endow systems with properties such as safety and stability. The guarantees ensured by these controllers often rely on accurate estimates of the system state for determining control actions. In practice, measurement model uncertainty can lead to error in state estimates that degrades these guarantees. In this paper, we seek to unify techniques from control theory and machine learning to synthesize controllers that achieve safety in the presence of measurement model uncertainty. We define the notion of a Measurement-Robust Control Barrier Function (MR-CBF) as a tool for determining safe control inputs when facing measurement model uncertainty. Furthermore, MR-CBFs are used to inform sampling methodologies for learning-based perception systems and quantify tolerable error in the resulting learned models. We demonstrate the efficacy of MR-CBFs in achieving safety with measurement model uncertainty on a simulated Segway system.

We study how robust current ImageNet models are to distribution shifts arising from natural variations in datasets. Most research on robustness focuses on synthetic image perturbations (noise, simulated weather artifacts, adversarial examples, etc.), which leaves open how robustness on synthetic distribution shift relates to distribution shift arising in real data. Informed by an evaluation of 204 ImageNet models in 213 different test conditions, we find that there is often little to no transfer of robustness from current synthetic to natural distribution shift. Moreover, most current techniques provide no robustness to the natural distribution shifts in our testbed. The main exception is training on larger and more diverse datasets, which in multiple cases increases robustness, but is still far from closing the performance gaps. Our results indicate that distribution shifts arising in real data are currently an open research problem. We provide our testbed and data as a resource for future work at https://modestyachts.github.io/imagenet-testbed/ .

Machine learning provides a promising avenue for incorporating rich sensing modalities into autonomous systems. However, our coarse understanding of how ML systems fail limits the adoption of data-driven techniques in real-world applications. In particular, applications involving feedback require that errors do not accumulate and lead to instability. In this work, we propose and analyze a baseline method for incorporating a learning-enabled component into closed-loop control, providing bounds on the sample complexity of a reference tracking problem. Much recent work on developing guarantees for learning and control has focused on the case that dynamics are unknown [Dean et al., 2017, Simchowitz and Foster, 2020, Mania et al., 2020].

While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and actions or for systems that can be identified from data generated by i.i.d. random inputs. Nonetheless, many interesting dynamical systems have continuous states and actions and can only be identified through a judicious choice of inputs. Motivated by practical settings, we study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. To estimate such systems in finite time identification methods must explore all directions in feature space. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.

Excessive reuse of test data has become commonplace in today's machine learning workflows. Popular benchmarks, competitions, industrial scale tuning, among other applications, all involve test data reuse beyond guidance by statistical confidence bounds. Nonetheless, recent replication studies give evidence that popular benchmarks continue to support progress despite years of extensive reuse. We proffer a new explanation for the apparent longevity of test data: Many proposed models are similar in their predictions and we prove that this similarity mitigates overfitting. Specifically, we show empirically that models proposed for the ImageNet ILSVRC benchmark agree in their predictions well beyond what we can conclude from their accuracy levels alone.