The centrality of data collection to the development of statistical machine learning is evident [12], with numerous challenge datasets driving advances [27, 25, 1, 22, 11, 37, 38]. Essential to these is the collection of labeled data. While in the past, experts could provide reliable labels for reasonably sized datasets, the cost and size of modern datasets often precludes this expert annotation, motivating a growing literature on crowdsourcing and other sophisticated dataset generation strategies that aggregate expert and non-expert feedback or collect internet-based loosely supervised and multimodal data [10, 20, 48, 37, 34, 38, 13]. By aggregating multiple labels, one typically hopes to obtain clean, true, "gold-standard" data. Yet most statistical machine learning development--theoretical or methodological--does not investigate this full data generating process, assuming only that data comes in the form of (X, Y) pairs of covariates X and targets (labels) Y [45, 5, 2, 17]. Here, we argue for a more holistic perspective: broadly, that analysis and algorithmic development should focus on the more complete machine learning pipeline, from dataset construction to model output; and more narrowly, questioning such aggregation strategies and the extent to which such cleaned data is essential or even useful. To that end, we develop a stylized theoretical model to capture uncertainties in the labeling process, allowing us to understand the contrasts, limitations and possible improvements of using aggregated or non-aggregated data in a statistical learning pipeline.

Releasing statistics using sensitive data can hurt the privacy of individuals contributing to the data (Narayanan and Shmatikov, 2008; Dick et al., 2023). Differential privacy (Dwork et al., 2006) is now a widely accepted solution for performing statistical analysis while protecting sensitive data. In the years since its release, researchers have made considerable progress in the development of differentially private estimators for a range of statistical problems such as mean estimation, median estimation, logistic regression (Asi and Duchi, 2020; Chaudhuri et al., 2011). However, deriving a conclusion from a single point estimate--whether an empirical mean or a classifier prediction-- without any consideration of uncertainty can lead to faulty, inaccurate decision-making (Gelman and Loken, 2013). To have any hope of making private statistical tools broadly applicable, we must build the requisite inferential tools. Constructing confidence intervals around a give point estimate is the most basic inferential task. We therefore develop tools to do so for a broad class of statistics of interest with differential privacy.

We study the problem of collaboratively learning least squares estimates for $m$ agents. Each agent observes a different subset of the features$\unicode{x2013}$e.g., containing data collected from sensors of varying resolution. Our goal is to determine how to coordinate the agents in order to produce the best estimator for each agent. We propose a distributed, semi-supervised algorithm Collab, consisting of three steps: local training, aggregation, and distribution. Our procedure does not require communicating the labeled data, making it communication efficient and useful in settings where the labeled data is inaccessible. Despite this handicap, our procedure is nearly asymptotically local minimax optimal$\unicode{x2013}$even among estimators allowed to communicate the labeled data such as imputation methods. We test our method on real and synthetic data.

In this work, we study practical heuristics to improve the performance of prefix-tree based algorithms for differentially private heavy hitter detection. Our model assumes each user has multiple data points and the goal is to learn as many of the most frequent data points as possible across all users' data with aggregate and local differential privacy. We propose an adaptive hyperparameter tuning algorithm that improves the performance of the algorithm while satisfying computational, communication and privacy constraints. We explore the impact of different data-selection schemes as well as the impact of introducing deny lists during multiple runs of the algorithm. We test these improvements using extensive experimentation on the Reddit dataset~\cite{caldas2018leaf} on the task of learning the most frequent words.

We design an $(\varepsilon, \delta)$-differentially private algorithm to estimate the mean of a $d$-variate distribution, with unknown covariance $\Sigma$, that is adaptive to $\Sigma$. To within polylogarithmic factors, the estimator achieves optimal rates of convergence with respect to the induced Mahalanobis norm $||\cdot||_\Sigma$, takes time $\tilde{O}(n d^2)$ to compute, has near linear sample complexity for sub-Gaussian distributions, allows $\Sigma$ to be degenerate or low rank, and adaptively extends beyond sub-Gaussianity. Prior to this work, other methods required exponential computation time or the superlinear scaling $n = \Omega(d^{3/2})$ to achieve non-trivial error with respect to the norm $||\cdot||_\Sigma$.

We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple overparameterized linear regression $y = X \theta + w$ with random design $X \in \mathbb{R}^{n \times d}$ under the proportional asymptotics $d/n \to \gamma \in (1, \infty)$. We precisely characterize how prediction (test) error necessarily scales with training error in this setting. An implication of this characterization is that as the label noise variance $\sigma^2 \to 0$, any estimator that incurs at least $\mathsf{c}\sigma^4$ training error for some constant $\mathsf{c}$ is necessarily suboptimal and will suffer growth in excess prediction error at least linear in the training error. Thus, optimal performance requires fitting training data to substantially higher accuracy than the inherent noise floor of the problem.

The cost and scarcity of fully supervised labels in statistical machine learning encourage using partially labeled data for model validation as a cheaper and more accessible alternative. Effectively collecting and leveraging weakly supervised data for large-space structured prediction tasks thus becomes an important part of an end-to-end learning system. We propose a new computationally-friendly methodology to construct predictive sets using only partially labeled data on top of black-box predictive models. To do so, we introduce "probe" functions as a way to describe weakly supervised instances and define a false discovery proportion-type loss, both of which seamlessly adapt to partial supervision and structured prediction -- ranking, matching, segmentation, multilabel or multiclass classification. Our experiments highlight the validity of our predictive set construction as well as the attractiveness of a more flexible user-dependent loss framework.

Consider the typical supervised learning pipeline that we teach students learning statistical machine learning: we collect data in (X, Y) pairs, where Y is a label or target to be predicted; we pick a model and loss measuring the fidelity of the model to observed data; we choose the model minimizing the loss and validate it on held-out data. This picture obscures what is becoming one of the major challenges in this endeavor: that of actually collecting highquality labeled data [44, 13, 38]. Hand labeling large-scale training sets is often impractically expensive. Consider, as simple motivation, a ranking problem: a prediction is an ordered list of a set of items, yet available feedback is likely to be incomplete and partial, such as a top element (for example, in web search a user clicks on a single preferred link, or in a grocery, an individual buys one kind of milk but provides no feedback on the other brands present). Developing methods to leverage such partial and weak feedback is therefore becoming a major focus, and researchers have developed methods to transform weak and noisy labels into a dataset with strong, "gold-standard" labels [38, 56]. In this paper, we adopt this weakly labeled setting, but instead of considering model fitting and the construction of strong labels, we focus on validation, model confidence, and predictive inference, moving beyond point predictions and single labels. Our goal is to develop methods to rigorously quantify the confidence a practitioner should have in a model given only weak labels.

We study the performance of federated learning algorithms and their variants in an asymptotic framework. Our starting point is the formulation of federated learning as a multi-criterion objective, where the goal is to minimize each client's loss using information from all of the clients. We propose a linear regression model, where, for a given client, we theoretically compare the performance of various algorithms in the high-dimensional asymptotic limit. This asymptotic multi-criterion approach naturally models the high-dimensional, many-device nature of federated learning and suggests that personalization is central to federated learning. Our theory suggests that Fine-tuned Federated Averaging (FTFA), i.e., Federated Averaging followed by local training, and the ridge regularized variant Ridge-tuned Federated Averaging (RTFA) are competitive with more sophisticated meta-learning and proximal-regularized approaches. In addition to being conceptually simpler, FTFA and RTFA are computationally more efficient than its competitors. We corroborate our theoretical claims with extensive experiments on federated versions of the EMNIST, CIFAR-100, Shakespeare, and Stack Overflow datasets.

We develop algorithms for private stochastic convex optimization that adapt to the hardness of the specific function we wish to optimize. While previous work provide worst-case bounds for arbitrary convex functions, it is often the case that the function at hand belongs to a smaller class that enjoys faster rates. Concretely, we show that for functions exhibiting $\kappa$-growth around the optimum, i.e., $f(x) \ge f(x^*) + \lambda \kappa^{-1} \|x-x^*\|_2^\kappa$ for $\kappa > 1$, our algorithms improve upon the standard ${\sqrt{d}}/{n\varepsilon}$ privacy rate to the faster $({\sqrt{d}}/{n\varepsilon})^{\tfrac{\kappa}{\kappa - 1}}$. Crucially, they achieve these rates without knowledge of the growth constant $\kappa$ of the function. Our algorithms build upon the inverse sensitivity mechanism, which adapts to instance difficulty (Asi & Duchi, 2020), and recent localization techniques in private optimization (Feldman et al., 2020). We complement our algorithms with matching lower bounds for these function classes and demonstrate that our adaptive algorithm is \emph{simultaneously} (minimax) optimal over all $\kappa \ge 1+c$ whenever $c = \Theta(1)$.