We study semisupervised mean estimation with a small labeled sample, a large unlabeled sample, and a black-box prediction model whose output may be miscalibrated. A standard approach in this setting is augmented inverse-probability weighting (AIPW) [Robins et al., 1994], which protects against prediction-model misspecification but can be inefficient when the prediction score is poorly aligned with the outcome scale. We introduce Calibrated Prediction-Powered Inference, which post-hoc calibrates the prediction score on the labeled sample before using it for semisupervised estimation. This simple step requires no retraining and can improve the original score both as a predictor of the outcome and as a regression adjustment for semisupervised inference. We study both linear and isotonic calibration. For isotonic calibration, we establish first-order optimality guarantees: isotonic post-processing can improve predictive accuracy and estimator efficiency relative to the original score and simpler post-processing rules, while no further post-processing of the fitted isotonic score yields additional first-order gains. For linear calibration, we show first-order equivalence to PPI++. We also clarify the relationship among existing estimators, showing that the original PPI estimator is a special case of AIPW and can be inefficient when the prediction model is accurate, while PPI++ is AIPW with empirical efficiency maximization [Rubin et al., 2008]. In simulations and real-data experiments, our calibrated estimators often outperform PPI and are competitive with, or outperform, AIPW and PPI++. We provide an accompanying Python package, ppi_aipw, at https://larsvanderlaan.github.io/ppi-aipw/.

Michael Dell and Susan Dell became the first donors to give more than $1 billion to the University of Texas at Austin, funding a massive AI-native hospital and research campus.

Predictions from machine learning algorithms can vary across random seeds, inducing instability in downstream debiased machine learning estimators. We formalize random seed stability via a concentration condition and prove that subbagging guarantees stability for any bounded-outcome regression algorithm. We introduce a new cross-fitting procedure, adaptive cross-bagging, which simultaneously eliminates seed dependence from both nuisance estimation and sample splitting in debiased machine learning. Numerical experiments confirm that the method achieves the targeted level of stability whereas alternatives do not. Our method incurs a small computational penalty relative to standard practice whereas alternative methods incur large penalties.

Conformal risk control (CRC) provides distribution-free guarantees for controlling the expected loss at a user-specified level. Existing theory typically assumes that the loss decreases monotonically with a tuning parameter that governs the size of the prediction set. However, this assumption is often violated in practice, where losses may behave non-monotonically due to competing objectives such as coverage and efficiency. In this paper, we study CRC under non-monotone loss functions when the tuning parameter is selected from a finite grid, a setting commonly arising in thresholding and discretized decision rules. Revisiting a known counterexample, we show that the validity of CRC without monotonicity depends critically on the relationship between the calibration sample size and the grid resolution. In particular, reliable risk control can still be achieved when the calibration sample is sufficiently large relative to the grid size. We establish a finite-sample guarantee for bounded losses over a grid of size $m$, showing that the excess risk above the target level $α$ scales on the order of $\sqrt{\log(m)/n}$, where $n$ is the calibration sample size. A matching lower bound demonstrates that this rate is minimax optimal. We also derive refined guarantees under additional structural conditions, including Lipschitz continuity and monotonicity, and extend the analysis to settings with distribution shift via importance weighting. Numerical experiments on synthetic multilabel classification and real object detection data illustrate the practical implications of non-monotonicity. Methods that explicitly account for finite-sample uncertainty achieve more stable risk control than approaches based on monotonicity transformations, while maintaining competitive prediction set sizes.

Synthetic augmentation is increasingly used to mitigate data scarcity in financial machine learning, yet its statistical role remains poorly understood. We formalize synthetic augmentation as a modification of the effective training distribution and show that it induces a structural bias--variance trade-off: while additional samples may reduce estimation error, they may also shift the population objective whenever the synthetic distribution deviates from regions relevant under evaluation. To isolate informational gains from mechanical sample-size effects, we introduce a size-matched null augmentation and a finite-sample, non-parametric block permutation test that remains valid under weak temporal dependence. We evaluate this framework in both controlled Markov-switching environments and real financial datasets, including high-frequency option trade data and a daily equity panel. Across generators spanning bootstrap, copula-based models, variational autoencoders, diffusion models, and TimeGAN, we vary augmentation ratio, model capacity, task type, regime rarity, and signal-to-noise. We show that synthetic augmentation is beneficial only in variance-dominant regimes, such as persistent volatility forecasting-while it deteriorates performance in bias-dominant settings, including near-efficient directional prediction. Rare-regime targeting can improve domain-specific metrics but may conflict with unconditional permutation inference. Our results provide a structural perspective on when synthetic data improves financial learning performance and when it induces persistent distributional distortion.

Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such acceleration remain unclear. In this work, we establish the first score query lower bounds for diffusion sampling. We prove that for $d$-dimensional distributions, given access to score estimates with polynomial accuracy $\varepsilon=d^{-O(1)}$ (in any $L^p$ sense), any sampling algorithm requires $\widetildeΩ(\sqrt{d})$ adaptive score queries. In particular, our proof shows that any sampler must search over $\widetildeΩ(\sqrt{d})$ distinct noise levels, providing a formal explanation for why multiscale noise schedules are necessary in practice.

We initiate the study of language generation in the limit, a model recently introduced by Kleinberg and Mullainathan [KM24], under the constraint of differential privacy. We consider the continual release model, where a generator must eventually output a stream of valid strings while protecting the privacy of the entire input sequence. Our first main result is that for countable collections of languages, privacy comes at no qualitative cost: we provide an $\varepsilon$-differentially-private algorithm that generates in the limit from any countable collection. This stands in contrast to many learning settings where privacy renders learnability impossible. However, privacy does impose a quantitative cost: there are finite collections of size $k$ for which uniform private generation requires $Ω(k/\varepsilon)$ samples, whereas just one sample suffices non-privately. We then turn to the harder problem of language identification in the limit. Here, we show that privacy creates fundamental barriers. We prove that no $\varepsilon$-DP algorithm can identify a collection containing two languages with an infinite intersection and a finite set difference, a condition far stronger than the classical non-private characterization of identification. Next, we turn to the stochastic setting where the sample strings are sampled i.i.d. from a distribution (instead of being generated by an adversary). Here, we show that private identification is possible if and only if the collection is identifiable in the adversarial model. Together, our results establish new dimensions along which generation and identification differ and, for identification, a separation between adversarial and stochastic settings induced by privacy constraints.

Dr. David Blackwell was a mathematician and statistician of the first rank, whose contributions to statistical theory, game theory, and decision theory predated many of the algorithmic breakthroughs that define modern artificial intelligence. This survey examines three of his most consequential theoretical results the Rao Blackwell theorem, the Blackwell Approachability theorem, and the Blackwell Informativeness theorem (comparison of experiments) and traces their direct influence on contemporary AI and machine learning. We show that these results, developed primarily in the 1940s and 1950s, remain technically live across modern subfields including Markov Chain Monte Carlo inference, autonomous mobile robot navigation (SLAM), generative model training, no-regret online learning, reinforcement learning from human feedback (RLHF), large language model alignment, and information design. NVIDIAs 2024 decision to name their flagship GPU architecture (Blackwell) provides vivid testament to his enduring relevance. We also document an emerging frontier: explicit Rao Blackwellized variance reduction in LLM RLHF pipelines, recently proposed but not yet standard practice. Together, Blackwell theorems form a unified framework addressing information compression, sequential decision making under uncertainty, and the comparison of information sources precisely the problems at the core of modern AI.

Obtaining high-quality labels is costly, whereas unlabeled covariates are often abundant, motivating semi-supervised inference methods with reliable uncertainty quantification. Prediction-powered inference (PPI) leverages a machine-learning predictor trained on a small labeled sample to improve efficiency, but it can lose efficiency under model misspecification and suffer from coverage distortions due to label reuse. We introduce Machine-Learning-Assisted Generalized Entropy Calibration (MEC), a cross-fitted, calibration-weighted variant of PPI. MEC improves efficiency by reweighting labeled samples to better align with the target population, using a principled calibration framework based on Bregman projections. This yields robustness to affine transformations of the predictor and relaxes requirements for validity by replacing conditions on raw prediction error with weaker projection-error conditions. As a result, MEC attains the semiparametric efficiency bound under weaker assumptions than existing PPI variants. Across simulations and a real-data application, MEC achieves near-nominal coverage and tighter confidence intervals than CF-PPI and vanilla PPI.

Overlap, also known as positivity, is a key condition for causal treatment effect estimation. Many popular estimators suffer from high variance and become brittle when features differ strongly across treatment groups. This is especially challenging in high dimensions: the curse of dimensionality can make overlap implausible. To address this, we propose a class of feature representations called deconfounding scores, which preserve both identification and the target of estimation; the classical propensity and prognostic scores are two special cases. We characterize the problem of finding a representation with better overlap as minimizing an overlap divergence under a deconfounding score constraint. We then derive closed-form expressions for a class of deconfounding scores under a broad family of generalized linear models with Gaussian features and show that prognostic scores are overlap-optimal within this class. We conduct extensive experiments to assess this behavior empirically.