When data are collected adaptively, such as in bandit algorithms, classical statistical approaches such as ordinary least squares and $M$-estimation will often fail to achieve asymptotic normality. Although recent lines of work have modified the classical approaches to ensure valid inference on adaptively collected data, most of these works assume that the model is correctly specified. We propose a method that provides valid inference for M-estimators that use adaptively collected bandit data with a (possibly) misspecified working model. A key ingredient in our approach is the use of flexible machine learning approaches to stabilize the variance induced by adaptive data collection. A major novelty is that our procedure enables the construction of valid confidence sets even in settings where treatment policies are unstable and non-converging, such as when there is no unique optimal arm and standard bandit algorithms are used. Empirical results on semi-synthetic datasets constructed from the Osteoarthritis Initiative demonstrate that the method maintains type I error control, while existing methods for inference in adaptive settings do not cover in the misspecified case.

In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate upon the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield the rate of normal approximation of order $\sqrt{\log{n}/n}$, provided that the sample size $n$ is large enough.

Modern multi-modal and multi-site data frequently suffer from blockwise missingness, where subsets of features are missing for groups of individuals, creating complex patterns that challenge standard inference methods. Existing approaches have critical limitations: complete-case analysis discards informative data and is potentially biased; doubly robust estimators for non-monotone missingness-where the missingness patterns are not nested subsets of one another-can be theoretically efficient but lack closed-form solutions and often fail to scale; and blackbox imputation can leverage partially observed data to improve efficiency but provides no inferential guarantees when misspecified. To address the limitations of these existing methods, we propose imputation-powered inference (IPI), a model-lean framework that combines the flexibility of blackbox imputation with bias correction using fully observed data, drawing on ideas from prediction-powered inference and semiparametric inference. IPI enables valid and efficient M-estimation under missing completely at random (MCAR) blockwise missingness and improves subpopulation inference under a weaker assumption we formalize as first-moment MCAR, for which we also provide practical diagnostics. Simulation studies and a clinical application demonstrate that IPI may substantially improve subpopulation efficiency relative to complete-case analysis, while maintaining statistical validity in settings where both doubly robust estimators and naive imputation fail to achieve nominal coverage.

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which admit discrete spectral decompositions, and (ii) diagonal kernels of the form $K(x,x')=k(x,x')T$, where $k$ is a scalar-valued kernel and $T$ is a positive operator on the output space. This broad setting induces expressive vector-valued reproducing kernel Hilbert spaces (RKHSs) that generalize the classical $K=kI$ paradigm, thereby enabling rich structural modeling with rigorous theoretical guarantees. To address target operators lying outside the RKHS, we introduce vector-valued interpolation spaces to precisely quantify misspecification error. Within this framework, we establish dimension-free polynomial convergence rates, demonstrating that nonlinear operator learning can overcome the curse of dimensionality. The use of general operator-valued kernels further allows us to derive rates for intrinsically nonlinear operator learning, going beyond the linear-type behavior inherent in diagonal constructions of $K=kI$. Importantly, this framework accommodates a wide range of operator learning tasks, ranging from integral operators such as Fredholm operators to architectures based on encoder-decoder representations. Moreover, we validate its effectiveness through numerical experiments on the two-dimensional Navier-Stokes equations.

Estimating heterogeneous treatment effects is critical in domains such as personalized medicine, resource allocation, and policy evaluation. A central challenge lies in identifying subpopulations that respond differently to interventions, thereby enabling more targeted and effective decision-making. While clustering methods are well-studied in unsupervised learning, their integration with causal inference remains limited. We propose a novel framework that clusters individuals based on estimated treatment effects using a learned kernel derived from causal forests, revealing latent subgroup structures. Our approach consists of two main steps. First, we estimate debiased Conditional Average Treatment Effects (CATEs) using orthogonalized learners via the Robinson decomposition, yielding a kernel matrix that encodes sample-level similarities in treatment responsiveness. Second, we apply kernelized clustering to this matrix to uncover distinct, treatment-sensitive subpopulations and compute cluster-level average CATEs. We present this kernelized clustering step as a form of regularization within the residual-on-residual regression framework. Through extensive experiments on semi-synthetic and real-world datasets, supported by ablation studies and exploratory analyses, we demonstrate the effectiveness of our method in capturing meaningful treatment effect heterogeneity.

Abstract--This work proposes an evidence-retrieval mechanism for uncertainty-aware decision-making that replaces a single global cutoff with an evidence-conditioned, instance-adaptive criterion. For each test instance, proximal exemplars are retrieved in an embedding space; their predictive distributions are fused via Dempster-Shafer theory. Because the supporting evidences are explicit, decisions are transparent and auditable. Experiments on CIF AR-10/100 with BiT and ViT backbones show higher or comparable uncertainty-aware performance with materially fewer confidently incorrect outcomes and a sustainable review load compared with applying threshold on prediction entropy. Notably, only a few evidences are sufficient to realize these gains; increasing the evidence set yields only modest changes. These results indicate that evidence-conditioned tagging provides a more reliable and interpretable alternative to fixed prediction entropy thresholds for operational uncertainty-aware decision-making. N the landscape of modern artificial intelligence (AI), the pursuit of predictive accuracy has driven neural networks (NNs) to achieve superhuman performance across a multitude of domains. However, in many real-world applications, particularly those with high stakes, a correct prediction is only part of the requirement. This is crucial because most conventional machine learning (ML) models issue single-point predictions. In particular, NNs typically output class probabilities through a softmax layer, which represent only a deterministic point estimate conditioned on the model's fixed parameters and training data. These probabilities reflect the model's relative preference among classes given its fixed state after training. High probability does not necessarily imply that the prediction is reliable. This is where uncertainty quantification (UQ) methods emerges as a critical paradigm.

Personalized ultra-fractionated stereotactic adaptive radiotherapy (PULSAR) is a novel treatment that delivers radiation in pulses of protracted intervals. Accurate prediction of gross tumor volume (GTV) changes through regression models has substantial prognostic value. This study aims to develop a multi-omics based support vector regression (SVR) model for predicting GTV change. A retrospective cohort of 39 patients with 69 brain metastases was analyzed, based on radiomics (MRI images) and dosiomics (dose maps) features. Delta features were computed to capture relative changes between two time points. A feature selection pipeline using least absolute shrinkage and selection operator (Lasso) algorithm with weight- or frequency-based ranking criterion was implemented. SVR models with various kernels were evaluated using the coefficient of determination (R2) and relative root mean square error (RRMSE). Five-fold cross-validation with 10 repeats was employed to mitigate the limitation of small data size. Multi-omics models that integrate radiomics, dosiomics, and their delta counterparts outperform individual-omics models. Delta-radiomic features play a critical role in enhancing prediction accuracy relative to features at single time points. The top-performing model achieves an R2 of 0.743 and an RRMSE of 0.022. The proposed multi-omics SVR model shows promising performance in predicting continuous change of GTV. It provides a more quantitative and personalized approach to assist patient selection and treatment adjustment in PULSAR.

Vital signs, such as heart rate and blood pressure, are critical indicators of patient health and are widely used in clinical monitoring and decision-making. While deep learning models have shown promise in forecasting these signals, their deployment in healthcare remains limited in part because clinicians must be able to trust and interpret model outputs. Without reliable uncertainty quantification -- particularly calibrated prediction intervals (PIs) -- it is unclear whether a forecasted abnormality constitutes a meaningful warning or merely reflects model noise, hindering clinical decision-making. To address this, we present two methods for deriving PIs from the Reconstruction Uncertainty Estimate (RUE), an uncertainty measure well-suited to vital-sign forecasting due to its sensitivity to data shifts and support for label-free calibration. Our parametric approach assumes that prediction errors and uncertainty estimates follow a Gaussian copula distribution, enabling closed-form PI computation. Our non-parametric approach, based on k-nearest neighbours (KNN), empirically estimates the conditional error distribution using similar validation instances. We evaluate these methods on two large public datasets with minute- and hour-level sampling, representing high- and low-frequency health signals. Experiments demonstrate that the Gaussian copula method consistently outperforms conformal prediction baselines on low-frequency data, while the KNN approach performs best on high-frequency data. These results underscore the clinical promise of RUE-derived PIs for delivering interpretable, uncertainty-aware vital sign forecasts.

Sophisticated instrumentation for AI systems might have indicators that signal misalignment from human values, not unlike a "check engine" light in cars. One such indicator of misalignment is deceptiveness in generated responses. Future AI instrumentation may have the ability to detect when an LLM generates deceptive responses while reasoning about seemingly plausible but incorrect answers to factual questions. In this work, we demonstrate that linear probes on LLMs internal activations can detect deception in their responses with extremely high accuracy. Our probes reach a maximum of greater than 90% accuracy in distinguishing between deceptive and non-deceptive arguments generated by llama and qwen models ranging from 1.5B to 14B parameters, including their DeepSeek-r1 finetuned variants. We observe that probes on smaller models (1.5B) achieve chance accuracy at detecting deception, while larger models (greater than 7B) reach 70-80%, with their reasoning counterparts exceeding 90%. The layer-wise probe accuracy follows a three-stage pattern across layers: near-random (50%) in early layers, peaking in middle layers, and slightly declining in later layers. Furthermore, using an iterative null space projection approach, we find multitudes of linear directions that encode deception, ranging from 20 in Qwen 3B to nearly 100 in DeepSeek 7B and Qwen 14B models.

Many incarcerated individuals face significant and complex challenges, including mental illness, substance dependence, and homelessness, yet jails and prisons are often poorly equipped to address these needs. With little support from the existing criminal justice system, these needs can remain untreated and worsen, often leading to further offenses and a cycle of incarceration with adverse outcomes both for the individual and for public safety, with particularly large impacts on communities of color that continue to widen the already extensive racial disparities in criminal justice outcomes. Responding to these failures, a growing number of criminal justice stakeholders are seeking to break this cycle through innovative approaches such as community-driven and alternative approaches to policing, mentoring, community building, restorative justice, pretrial diversion, holistic defense, and social service connections. Here we report on a collaboration between Johnson County, Kansas, and Carnegie Mellon University to perform targeted, proactive mental health outreach in an effort to reduce reincarceration rates. This paper describes the data used, our predictive modeling approach and results, as well as the design and analysis of a field trial conducted to confirm our model's predictive power, evaluate the impact of this targeted outreach, and understand at what level of reincarceration risk outreach might be most effective. Through this trial, we find that our model is highly predictive of new jail bookings, with more than half of individuals in the trial's highest-risk group returning to jail in the following year. Outreach was most effective among these highest-risk individuals, with impacts on mental health utilization, EMS dispatches, and criminal justice involvement.