Machine learning models are increasingly used to produce predictions that serve as input data in subsequent statistical analyses. For example, computer vision predictions of economic and environmental indicators based on satellite imagery are used in downstream regressions; similarly, language models are widely used to approximate human ratings and opinions in social science research. However, failure to properly account for errors in the machine learning predictions renders standard statistical procedures invalid. Prior work uses what we call the Predict-Then-Debias estimator to give valid confidence intervals when machine learning algorithms impute missing variables, assuming a small complete sample from the population of interest. We expand the scope by introducing bootstrap confidence intervals that apply when the complete data is a nonuniform (i.e., weighted, stratified, or clustered) sample and to settings where an arbitrary subset of features is imputed. Importantly, the method can be applied to many settings without requiring additional calculations. We prove that these confidence intervals are valid under no assumptions on the quality of the machine learning model and are no wider than the intervals obtained by methods that do not use machine learning predictions.

We establish a formal connection between the decades-old surrogate outcome model in biostatistics and economics and the emerging field of prediction-powered inference (PPI). The connection treats predictions from pre-trained models, prevalent in the age of AI, as cost-effective surrogates for expensive outcomes. Building on the surrogate outcomes literature, we develop recalibrated prediction-powered inference, a more efficient approach to statistical inference than existing PPI proposals. Our method departs from the existing proposals by using flexible machine learning techniques to learn the optimal ``imputed loss'' through a step we call recalibration. Importantly, the method always improves upon the estimator that relies solely on the data with available true outcomes, even when the optimal imputed loss is estimated imperfectly, and it achieves the smallest asymptotic variance among PPI estimators if the estimate is consistent. Computationally, our optimization objective is convex whenever the loss function that defines the target parameter is convex. We further analyze the benefits of recalibration, both theoretically and numerically, in several common scenarios where machine learning predictions systematically deviate from the outcome of interest. We demonstrate significant gains in effective sample size over existing PPI proposals via three applications leveraging state-of-the-art machine learning/AI models.

Across science and policy, decision-makers often need to draw conclusions about the best candidate among competing alternatives. For instance, researchers may seek to infer the effectiveness of the most successful treatment or determine which demographic group benefits most from a specific treatment. Similarly, in machine learning, practitioners are often interested in the population performance of the model that performs best empirically. However, cherry-picking the best candidate leads to the winner's curse: the observed performance for the winner is biased upwards, rendering conclusions based on standard measures of uncertainty invalid. We introduce the zoom correction, a novel approach for valid inference on the winner. Our method is flexible: it can be employed in both parametric and nonparametric settings, can handle arbitrary dependencies between candidates, and automatically adapts to the level of selection bias. The method easily extends to important related problems, such as inference on the top k winners, inference on the value and identity of the population winner, and inference on "near-winners."

Black-box predictive models are increasingly used to generate efficient substitutes for gold-standard labels when the latter are difficult to come by. For example, predictions of protein structures are used as efficient substitutes for slow and expensive experimental measurements [3, 4, 8], and large language models are used to cheaply generate substitutes for scarce human annotations [5, 7, 14]. Prediction-powered inference (PPI) [1] is a recent framework for statistical inference that combines a large amount of machine-learning predictions with a small amount of real data to ensure simultaneously valid and statistically powerful conclusions. While PPI [1] (and its improvement PPI++ [2]) offers a principled solution to incorporating black-box predictions into the scientific workflow, its scope of application is still limited. The current analyses focus on certain convex M-estimators such as means, quantiles, and GLMs to ensure tractable implementation.

Inspired by the concept of active learning, we propose active inference$\unicode{x2013}$a methodology for statistical inference with machine-learning-assisted data collection. Assuming a budget on the number of labels that can be collected, the methodology uses a machine learning model to identify which data points would be most beneficial to label, thus effectively utilizing the budget. It operates on a simple yet powerful intuition: prioritize the collection of labels for data points where the model exhibits uncertainty, and rely on the model's predictions where it is confident. Active inference constructs provably valid confidence intervals and hypothesis tests while leveraging any black-box machine learning model and handling any data distribution. The key point is that it achieves the same level of accuracy with far fewer samples than existing baselines relying on non-adaptively-collected data. This means that for the same number of collected samples, active inference enables smaller confidence intervals and more powerful p-values. We evaluate active inference on datasets from public opinion research, census analysis, and proteomics.

Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing provably valid confidence intervals for quantities such as means, quantiles, and linear and logistic regression coefficients, without making any assumptions on the machine-learning algorithm that supplies the predictions. Furthermore, more accurate predictions translate to smaller confidence intervals. Prediction-powered inference could enable researchers to draw valid and more data-efficient conclusions using machine learning. The benefits of prediction-powered inference are demonstrated with datasets from proteomics, astronomy, genomics, remote sensing, census analysis, and ecology.

We present PPI++: a computationally lightweight methodology for estimation and inference based on a small labeled dataset and a typically much larger dataset of machine-learning predictions. The methods automatically adapt to the quality of available predictions, yielding easy-to-compute confidence sets -- for parameters of any dimensionality -- that always improve on classical intervals using only the labeled data. PPI++ builds on prediction-powered inference (PPI), which targets the same problem setting, improving its computational and statistical efficiency. Real and synthetic experiments demonstrate the benefits of the proposed adaptations.

When predictions are performative, the choice of which predictor to deploy influences the distribution of future observations. The overarching goal in learning under performativity is to find a predictor that has low \emph{performative risk}, that is, good performance on its induced distribution. One family of solutions for optimizing the performative risk, including bandits and other derivative-free methods, is agnostic to any structure in the performative feedback, leading to exceedingly slow convergence rates. A complementary family of solutions makes use of explicit \emph{models} for the feedback, such as best-response models in strategic classification, enabling significantly faster rates. However, these rates critically rely on the feedback model being well-specified. In this work we initiate a study of the use of possibly \emph{misspecified} models in performative prediction. We study a general protocol for making use of models, called \emph{plug-in performative optimization}, and prove bounds on its excess risk. We show that plug-in performative optimization can be far more efficient than model-agnostic strategies, as long as the misspecification is not too extreme. Altogether, our results support the hypothesis that models--even if misspecified--can indeed help with learning in performative settings.

While reliable data-driven decision-making hinges on high-quality labeled data, the acquisition of quality labels often involves laborious human annotations or slow and expensive scientific measurements. Machine learning is becoming an appealing alternative as sophisticated predictive techniques are being used to quickly and cheaply produce large amounts of predicted labels; e.g., predicted protein structures are used to supplement experimentally derived structures, predictions of socioeconomic indicators from satellite imagery are used to supplement accurate survey data, and so on. Since predictions are imperfect and potentially biased, this practice brings into question the validity of downstream inferences. We introduce cross-prediction: a method for valid inference powered by machine learning. With a small labeled dataset and a large unlabeled dataset, cross-prediction imputes the missing labels via machine learning and applies a form of debiasing to remedy the prediction inaccuracies. The resulting inferences achieve the desired error probability and are more powerful than those that only leverage the labeled data. Closely related is the recent proposal of prediction-powered inference, which assumes that a good pre-trained model is already available. We show that cross-prediction is consistently more powerful than an adaptation of prediction-powered inference in which a fraction of the labeled data is split off and used to train the model. Finally, we observe that cross-prediction gives more stable conclusions than its competitors; its confidence intervals typically have significantly lower variability.

We initiate a principled study of algorithmic collective action on digital platforms that deploy machine learning algorithms. We propose a simple theoretical model of a collective interacting with a firm's learning algorithm. The collective pools the data of participating individuals and executes an algorithmic strategy by instructing participants how to modify their own data to achieve a collective goal. We investigate the consequences of this model in three fundamental learning-theoretic settings: the case of a nonparametric optimal learning algorithm, a parametric risk minimizer, and gradient-based optimization. In each setting, we come up with coordinated algorithmic strategies and characterize natural success criteria as a function of the collective's size. Complementing our theory, we conduct systematic experiments on a skill classification task involving tens of thousands of resumes from a gig platform for freelancers. Through more than two thousand model training runs of a BERT-like language model, we see a striking correspondence emerge between our empirical observations and the predictions made by our theory. Taken together, our theory and experiments broadly support the conclusion that algorithmic collectives of exceedingly small fractional size can exert significant control over a platform's learning algorithm.