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/.

Decision-makers rely on weather forecasts to plant crops, manage wildfires, allocate water and energy, and prepare for weather extremes. Today, such forecasts enjoy unprecedented accuracy out to two weeks thanks to steady advances in physics-based dynamical models and data-driven artificial intelligence (AI) models. However, model skill drops precipitously at subseasonal timescales (2 - 6 weeks ahead), due to compounding errors and persistent biases. To counter this degradation, we introduce probabilistic bias correction (PBC), a machine learning framework that substantially reduces systematic error by learning to correct historical probabilistic forecasts. When applied to the leading dynamical and AI models from the European Centre for Medium-Range Weather Forecasts (ECMWF), PBC doubles the subseasonal skill of the AI Forecasting System and improves the skill of the operationally-debiased dynamical model for 91% of pressure, 92% of temperature, and 98% of precipitation targets. We designed PBC for operational deployment, and, in ECMWF's 2025 real-time forecasting competition, its global forecasts placed first for all weather variables and lead times, outperforming the dynamical models from six operational forecasting centers, an international dynamical multi-model ensemble, ECMWF's AI Forecasting System, and the forecasting systems of 34 teams worldwide. These probabilistic skill gains translate into more accurate prediction of extreme events and have the potential to improve agricultural planning, energy management, and disaster preparedness in vulnerable communities.

We study adaptive pooling under predictive heterogeneity in high-dimensional multivariate time series forecasting, where global models improve statistical efficiency but may fail to capture heterogeneous predictive structure, while naive specialization can induce negative transfer. We formulate adaptive pooling as a statistical decision problem and propose a validation-driven framework that determines when and how specialization should be applied. Rather than grouping series based on representation similarity, we define partitions through out-of-sample predictive performance, thereby aligning data organization with predictive risk, defined as expected out-of-sample loss and approximated via validation error. Cluster assignments are iteratively updated using validation losses for both point (Huber) and probabilistic (pinball) forecasting, improving robustness to heavy-tailed errors and local anomalies. To ensure reliability, we introduce a leakage-free fallback mechanism that reverts to a global model whenever specialization fails to improve validation performance, providing a safeguard against performance degradation under a strict training-validation-test protocol. Experiments on large-scale traffic datasets demonstrate consistent improvements over strong baselines while avoiding degradation when heterogeneity is weak. Overall, the proposed framework provides a principled and practically reliable approach to adaptive pooling in high-dimensional forecasting problems.

Accurately identifying patients with specific medical conditions is a key challenge when using clinical data from electronic health records. Our objective was to comprehensively assess when weakly-supervised prediction methods, which use silver-standard labels (proxy measures of the true outcome) rather than gold-standard true labels, perform well in rare-outcome settings like vaccine safety studies. We compared three methods (PheNorm, MAP, and sureLDA) that combine structured features and features derived from clinical text using natural language processing, through an extensive simulation study with data-generating mechanisms ranging from simple to complex, varying outcome rates, and varying degrees of informative silver labels. We also considered using predicted probabilities to design a chart review validation study. No single method dominated the other across all prediction performance metrics. Probability-guided sampling selected a cohort enriched for patients with more mentions of important concepts in chart notes. SureLDA, the most complex of the three algorithms we considered, often performed well in simulations. Performance depended greatly on selected tuning parameters. Care should be taken when using weakly-supervised prediction methods in rare-outcome settings, particularly if the probabilities will be used in downstream analysis, but these methods can work well when silver labels are strong predictors of true outcomes.

Contextual learning seeks to learn a decision policy that maps an individual's characteristics to an action through data collection. In operations management, such data may come from various sources, and a central question is when data collection can stop while still guaranteeing that the learned policy is sufficiently accurate. We study this question under two precision criteria: a context-wise criterion and an aggregate policy-value criterion. We develop unified stopping rules for contextual learning with unknown sampling variances in both unstructured and structured linear settings. Our approach is based on generalized likelihood ratio (GLR) statistics for pairwise action comparisons. To calibrate the corresponding sequential boundaries, we derive new time-uniform deviation inequalities that directly control the self-normalized GLR evidence and thus avoid the conservativeness caused by decoupling mean and variance uncertainty. Under the Gaussian sampling model, we establish finite-sample precision guarantees for both criteria. Numerical experiments on synthetic instances and two case studies demonstrate that the proposed stopping rules achieve the target precision with substantially fewer samples than benchmark methods. The proposed framework provides a practical way to determine when enough information has been collected in personalized decision problems. It applies across multiple data-collection environments, including historical datasets, simulation models, and real systems, enabling practitioners to reduce unnecessary sampling while maintaining a desired level of decision quality.

Cross-validation (CV) is commonly used to estimate predictive risk when independent test data are unavailable. Its validity depends on the assumption that validation tasks are sampled from the same distribution as prediction tasks encountered during deployment. In spatial prediction and other settings with structured data, this assumption is frequently violated, leading to biased estimates of deployment risk. We propose Target-Weighted CV (TWCV), an estimator of deployment risk that accounts for discrepancies between validation and deployment task distributions, thus accounting for (1) covariate shift and (2) task-difficulty shift. We characterize prediction tasks by descriptors such as covariates and spatial configuration. TWCV assigns weights to validation losses such that the weighted empirical distribution of validation tasks matches the corresponding distribution over a target domain. The weights are obtained via calibration weighting, yielding an importance-weighted estimator that targets deployment risk. Since TWCV requires adequate coverage of the deployment distribution's support, we combine it with spatially buffered resampling that diversifies the task difficulty distribution. In a simulation study, conventional as well as spatial estimators exhibit substantial bias depending on sampling, whereas buffered TWCV remains approximately unbiased across scenarios. A case study in environmental pollution mapping further confirms that discrepancies between validation and deployment task distributions can affect performance assessment, and that buffered TWCV better reflects the prediction task over the target domain. These results establish task distribution mismatch as a primary source of CV bias in spatial prediction and show that calibration weighting combined with a suitable validation task generator provides a viable approach to estimating predictive risk under dataset shift.

Aircraft design relies heavily on solving challenging and computationally expensive Multidisciplinary Design Optimization problems. In this context, there has been growing interest in multi-fidelity models for Bayesian optimization to improve the MDO process by balancing computational cost and accuracy through the combination of high- and low-fidelity simulation models, enabling efficient exploration of the design process at a minimal computational effort. In the existing literature, fidelity selection focuses only on the objective function to decide how to integrate multiple fidelity levels, balancing precision and computational cost using variance reduction criteria. In this work, we propose novel multi-fidelity selection strategies. Specifically, we demonstrate how incorporating information from both the objective and the constraints can further reduce computational costs without compromising the optimality of the solution. We validate the proposed multi-fidelity optimization strategy by applying it to four analytical test cases, showcasing its effectiveness. The proposed method is used to efficiently solve a challenging aircraft wing aero-structural design problem. The proposed setting uses a linear vortex lattice method and a finite element method for the aerodynamic and structural analysis respectively. We show that employing our proposed multi-fidelity approach leads to $86\%$ to $200\%$ more constraint compliant solutions given a limited budget compared to the state-of-the-art approach.

In this work, we investigate how to develop sharp concentration inequalities for sub-Weibull random variables, including sub-Gaussian and sub-exponential distributions. Although the random variables may not be sub-Guassian, the tail probability around the origin behaves as if they were sub-Gaussian, and the tail probability decays align with the Orlicz $Ψ_α$-tail elsewhere. Specifically, for independent and identically distributed (i.i.d.) $\{X_i\}_{i=1}^n$ with finite Orlicz norm $\|X\|_{Ψ_α}$, our theory unveils that there is an interesting phase transition at $α= 2$ in that $\PPł(ł|\sum_{i=1}^n X_i \r| \geq t\r)$ with $t > 0$ is upper bounded by $2\expł(-C\maxł\{\frac{t^2}{n\|X\|_{Ψ_α}^2},\frac{t^α}{ n^{α-1} \|X\|_{Ψ_α}^α}\r\}\r)$ for $α\geq 2$, and by $2\expł(-C\minł\{\frac{t^2}{n\|X\|_{Ψ_α}^2},\frac{t^α}{ n^{α-1} \|X\|_{Ψ_α}^α}\r\}\r)$ for $1\leq α\leq 2$ with some positive constant $C$. In many scenarios, it is often necessary to distinguish the standard deviation from the Orlicz norm when the latter can exceed the former greatly. To accommodate this, we build a new theoretical analysis framework, and our sharp, flexible concentration inequalities involve the variance and a mixing of Orlicz $Ψ_α$-tails through the min and max functions. Our theory yields new, improved concentration inequalities even for the cases of sub-Gaussian and sub-exponential distributions with $α= 2$ and $1$, respectively. We further demonstrate our theory on martingales, random vectors, random matrices, and covariance matrix estimation. These sharp concentration inequalities can empower more precise non-asymptotic analyses across different statistical and machine learning applications.

Tensor-on-tensor (TOT) regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a corresponding set of predictor tensors. However, standard TOT regression is sensitive to outliers, which may be present in both the response and the predictor. It can be affected by casewise outliers, which are observations that deviate from the bulk of the data, as well as by cellwise outliers, which are individual anomalous cells within the tensors. The latter are particularly common due to the typically large number of cells in tensor data. This paper introduces a novel robust TOT regression method, named ROTOT, that can handle both types of outliers simultaneously, and can cope with missing values as well. This method uses a single loss function to reduce the influence of both casewise and cellwise outliers in the response. The outliers in the predictor are handled using a robust Multilinear Principal Component Analysis method. Graphical diagnostic tools are also proposed to identify the different types of outliers detected. The performance of ROTOT is evaluated through extensive simulations and further illustrated using the Labeled Faces in the Wild dataset, where ROTOT is applied to predict facial attributes.

The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude characteristics observed in individual source signals. On the other hand, many existing non-Gaussian amplitude distributions derived from hyperspherical models achieve good empirical fit due to their power-law structures, while they do not explicitly account for the complex-plane geometry inherent in complex-valued observations. In this paper, we propose a new probabilistic model for complex-valued random variables, which can be interpreted as a power-weighted noncentral complex Gaussian distribution. Unlike conventional hyperspherical amplitude models, the proposed model is formulated directly on the complex plane and preserves the geometric structure of complex-valued observations while retaining a higher-dimensional interpretation. The model introduces a nonlinear phase diffusion through a single shape parameter, enabling continuous control of the distributional geometry from arc-shaped diffusion along the phase direction to concentration of probability mass toward the origin. We formulate the proposed distribution and analyze the statistical properties of the induced amplitude distribution. The derived amplitude and power distributions provide a unified framework encompassing several widely used distributions in signal modeling, including the Rice, Nakagami, and gamma distributions. Experimental results on speech power spectra demonstrate that the proposed model consistently outperforms conventional distributions in terms of log-likelihood.