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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.

Prediction-powered inference (PPI) combines a small gold-standard labeled sample with a large unlabeled sample scored by a black-box predictor, correcting the predictor's bias through a rectifier measured on labeled data. We recast PPI as posterior transport. The missing labels on the unlabeled set are treated as latent quantities and imputed by a learned conditional generative map, and the posterior over the estimand is the pushforward of a base measure through that map and the estimating equation. This is the Generative Bayesian Computation (GBC) construction applied to a missing-label problem. The additive rectifier of classical PPI, the power-tuning parameter of PPI++, Rubin's multiple imputation, and the augmentation term of doubly-robust estimation all appear as reductions of a single transport map: classical PPI is the feature-free mean-shift map, PPI++ is a shrinkage of the map toward the surrogate, multiple imputation is the map itself with a proper between-map variance, and the augmented inverse propensity weighted estimator is the Bayesian analogue with a labeling indicator whose propensity is known by design. Unlike linear corrections, the learned map captures nonlinear and heteroskedastic surrogate-totruth structure directly, so the stratified and filtered variants of PPI become choices of map class rather than separate methods. We give the transport formulation, prove the reductions, connect the construction to the semiparametric efficiency bound of the model that conditions on the surrogate, and provide an algorithm. We are explicit about the three places where the method can fail: honest extrapolation beyond labeled support, correct propagation of map uncertainty for calibration, and the price of a rich map relative to the PPI++ efficiency guarantee. When the map class contains the affine map, GBC-PPI inherits the guarantee that it is asymptotically no worse than the labeled-only estimator.

Prediction-powered inference is a recent methodology for the safe use of black-box ML models to impute missing data, strengthening inference of statistical parameters. However, many applications require strong properties besides valid inference, such as privacy, robustness or validity under continuous distribution shifts; deriving prediction-powered methods with such guarantees is generally an arduous process, and has to be done case by case. In this paper, we resolve this issue by connecting prediction-powered inference with conformal prediction: by performing imputation through a calibrated conformal set-predictor, we attain validity while achieving additional guarantees in a natural manner. We instantiate our procedure for the inference of means, Z- and M-estimation, as well as e-values and e-value-based procedures. Furthermore, in the case of e-values, ours is the first general prediction-powered procedure that operates off-line. We demonstrate these advantages by applying our method on private and time-series data. Both tasks are nontrivial within the standard prediction-powered framework but become natural under our method.

Prediction-powered inference (PPI) performs valid inference when a small gold-standard labeled sample is supplemented by a large pool of machine-learning predictions. Naive substitution of predictions for outcomes changes the estimand and invalidates uncertainty quantification; the shared remedy is rectification, in which the abundant predictions supply a lowvariance plug-in while the scarce labels estimate and correct the resulting distortion. We review PPI as a family of rectified M-estimators organised by the single object every method manipulates: the rectifier, the labeled-data estimate of the surrogate's inferential bias. Four operations on the rectifier organise the field. One may tune it by an optimal, generally matrix-valued gain (PPI++, cross-PPI, and the Bayes-linear form that unifies them); reweight it for informative or active label acquisition (inverse-probability weighting, active and stratified sampling); shrink it with a prior (frequentist-assisted-by-Bayes and Bayesian PPI, through global-local scale mixtures); or replace it by a recalibration model (Efron's bootstrap). We give a self-contained derivation of the tuned estimator's efficient influence function, from which the optimal gain, its equivalence to a Kalman gain, and the semiparametric efficiency bound follow; we prove that the failure of PPI to improve estimation of E{Y } is exactly the corner of optimal tuning; and we show that horseshoe shrinkage of the rectifier is a scale-mixture Kalman update rather than a special case of the linear form. A combined design-weighted, global-local estimator is proposed that is consistent under informative labeling and strictly tighter than inverse-probability-weighted PPI when the surrogate is well calibrated. A five-part simulation study delineates the regime in which each operator dominates, and a decision guide closes the paper.

Semi-supervised (SS) inference has received much attention in recent years. Apart from a moderate-sized labeled data, L, the SS setting is characterized by an additional, much larger sized, unlabeled data, U. The setting of |U| >> |L|, makes SS inference unique and different from the standard missing data problems, owing to natural violation of the so-called "positivity" or "overlap" assumption. However, most of the SS literature implicitly assumes L and U to be equally distributed, i.e., no selection bias in the labeling. Inferential challenges in missing at random (MAR) type labeling allowing for selection bias, are inevitably exacerbated by the decaying nature of the propensity score (PS). We address this gap for a prototype problem, the estimation of the response's mean. We propose a double robust SS (DRSS) mean estimator and give a complete characterization of its asymptotic properties. The proposed estimator is consistent as long as either the outcome or the PS model is correctly specified. When both models are correctly specified, we provide inference results with a non-standard consistency rate that depends on the smaller size |L|. The results are also extended to causal inference with imbalanced treatment groups. Further, we provide several novel choices of models and estimators of the decaying PS, including a novel offset logistic model and a stratified labeling model. We present their properties under both high and low dimensional settings. These may be of independent interest. Lastly, we present extensive simulations and also a real data application.

Prediction-powered inference (PPI) studies statistical inference when a small set of gold-standard labels is combined with a much larger pool of machine-generated predictions. The central difficulty is that predictions can substantially reduce variance, yet naive substitution of predictions for outcomes generally changes the estimand and invalidates uncertainty quantification. The basic remedy in the literature is rectification: predictions are used to construct a low-variance plug-in term, while labeled observations are used to estimate and correct the inferential distortion induced by prediction substitution. We review PPI as a family of rectified plug-in procedures for hybrid measurement regimes. The survey develops a common statistical template based on mean estimation, estimating equations, and loss-based formulations, and then uses that template to compare modern variants according to the component they modify: the rectification engine, the label-acquisition design, predictor dependence, or the validity target. We also position PPI relative to model-assisted survey sampling, post-prediction correction, surrogate-outcome methods, classical measurement-error models, and semiparametric augmentation. Throughout, we distinguish questions of validity from questions of efficiency, robustness, and computation, and we emphasize that valid use of prediction assistance does not require a correct predictive model but does depend on how rectification, dependence, and sampling design are handled. The survey closes with recurrent failure modes, practical reporting recommendations, and open problems in finite-sample theory, heterogeneous proxy quality, and protocol-aware deployment.

Recent advances in artificial intelligence have enabled the generation of large-scale, low-cost predictions with increasingly high fidelity. As a result, the primary challenge in statistical inference has shifted from data scarcity to data reliability. Prediction-powered inference methods seek to exploit such predictions to improve efficiency when labeled data are limited. However, existing approaches implicitly adopt a use-all philosophy, under which incorporating more predictions is presumed to improve inference. When prediction quality is heterogeneous, this assumption can fail, and indiscriminate use of unlabeled data may dilute informative signals and degrade inferential accuracy. In this paper, we propose Filtered Prediction-Powered Inference (FPPI), a framework that selectively incorporates predictions by identifying a data-adaptive filtered region in which predictions are informative for inference. We show that this region can be consistently estimated under a margin condition, achieving fast rates of convergence. By restricting the prediction-powered correction to the estimated filtered region, FPPI adaptively mitigates the impact of biased or noisy predictions. We establish that FPPI attains strictly improved asymptotic efficiency compared with existing prediction-powered inference methods. Numerical studies and a real-data application to large language model evaluation demonstrate that FPPI substantially reduces reliance on expensive labels by selectively leveraging reliable predictions, yielding accurate inference even in the presence of heterogeneous prediction quality.

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 [A. N. Angelopoulos, S. Bates, C. Fannjiang, M. I. Jordan, T. Zrnic, Science 382 , 669–674 (2023)], which assumes that a good pretrained 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 CIs typically have significantly lower variability.

Second-person neuroscience holds social cognition as embodied meaning co-regulation through reciprocal interaction, modeled here as coupled active inference with affect emerging as inference over identity-relevant surprise. Each agent maintains a self-model that tracks violations in its predictive coherence while recursively modeling the other. Valence is computed from self-model prediction error, weighted by self-relevance, and modulated by prior affective states and by what we term temporal aiming, which captures affective appraisal over time. This accommodates shifts in the self-other boundary, allowing affect to emerge at individual and dyadic levels. We propose a novel method termed geometric hyperscanning, based on the Forman-Ricci curvature, to empirically operationalize these processes: it tracks topological reconfigurations in inter-brain networks, with its entro-py serving as a proxy for affective phase transitions such as rupture, co-regulation, and re-attunement.

Prediction-powered inference (PPI) and its subsequent development called PPI++ provide a novel approach to standard statistical estimation leveraging machine learning systems to enhance unlabeled data with predictions. We use this paradigm in clinical trials. The predictions are provided by disease progression models, providing prognostic scores for all the participants as a function of baseline covariates. The proposed method would empower clinical trials by providing untreated digital twins of the treated patients while remaining statistically valid. The potential implications of this new estimator of the treatment effect in a two-arm randomized clinical trial (RCT) are manifold. First, it leads to an overall reduction of the sample size required to reach the same power as a standard RCT. Secondly, it advocates for an imbalance of controls and treated patients, requiring fewer controls to achieve the same power. Finally, this technique directly transfers any disease prediction model trained on large cohorts to practical and scientifically valid use. In this paper, we demonstrate the theoretical properties of this estimator and illustrate them through simulations. We show that it is asymptotically unbiased for the Average Treatment Effect and derive an explicit formula for its variance. An application to an Alzheimer's disease clinical trial showcases the potential to reduce the sample size.