Atmospheric ozone is a crucial absorber of solar radiation and an important greenhouse gas. However, most climate models participating in the Coupled Model Intercomparison Project (CMIP) still lack an interactive representation of ozone due to the high computational costs of atmospheric chemistry schemes. Here, we introduce a machine learning parameterization (mloz) to interactively model daily ozone variability and trends across the troposphere and stratosphere in standard climate sensitivity simulations, including two-way interactions of ozone with the Quasi-Biennial Oscillation. We demonstrate its high fidelity on decadal timescales and its flexible use online across two different climate models -- the UK Earth System Model (UKESM) and the German ICOsahedral Nonhydrostatic (ICON) model. With atmospheric temperature profile information as the only input, mloz produces stable ozone predictions around 31 times faster than the chemistry scheme in UKESM, contributing less than 4 percent of the respective total climate model runtimes. In particular, we also demonstrate its transferability to different climate models without chemistry schemes by transferring the parameterization from UKESM to ICON. This highlights the potential for widespread adoption in CMIP-level climate models that lack interactive chemistry for future climate change assessments, particularly when focusing on climate sensitivity simulations, where ozone trends and variability are known to significantly modulate atmospheric feedback processes.

As large language models (LLMs) are increasingly applied to real-world scenarios, it becomes crucial to understand their ability to follow multiple instructions simultaneously. To systematically evaluate these capabilities, we introduce two specialized benchmarks for fundamental domains where multiple instructions following is important: Many Instruction-Following Eval (ManyIFEval) for text generation with up to ten instructions, and Style-aware Mostly Basic Programming Problems (StyleMBPP) for code generation with up to six instructions. Our experiments with the created benchmarks across ten LLMs reveal that performance consistently degrades as the number of instructions increases. Furthermore, given the fact that evaluating all the possible combinations of multiple instructions is computationally impractical in actual use cases, we developed three types of regression models that can estimate performance on both unseen instruction combinations and different numbers of instructions which are not used during training. We demonstrate that a logistic regression model using instruction count as an explanatory variable can predict performance of following multiple instructions with approximately 10% error, even for unseen instruction combinations. We show that relatively modest sample sizes (500 for ManyIFEval and 300 for StyleMBPP) are sufficient for performance estimation, enabling efficient evaluation of LLMs under various instruction combinations.

This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options.

Tensor decompositions have emerged as powerful analytical tools across diverse fields including signal/image processing [1, 2, 3, 4, 5, 6], chemometrics [7], geophysics [8, 9], and neuroscience [10, 11, 12, 13]. Their effectiveness stems from their ability to approximate high-dimensional tensors with low-rank decompositions, offering efficient dimensionality reduction while preserving essential structural information. For example, tensor decomposition techniques [14, 15, 16] are applied in hyperspectral image (HSI) analysis to extract low-rank structures for dimensionality reduction [9], and used in electroencephalogram (EEG) analysis to capture latent patterns across multiple dimensions [10]. Over the past decade, tensor regression (TR) models have received attention, with numerous approaches proposed in the literature, including Tucker tensor regression [17], low-rank orthogonally decomposable tensor regression [18], Bayesian Kruskal tensor regression (KTR) [19], Bayesian low rank tensor ring completion [20], graph-regularized tensor regression [21], and tensor regression network [22].

A common way to estimate an unknown convex regression function $f_0: Ω\subset \mathbb{R}^d \rightarrow \mathbb{R}$ from a set of $n$ noisy observations is to fit a convex function that minimizes the sum of squared errors. However, this estimator is known for its tendency to overfit near the boundary of $Ω$, posing significant challenges in real-world applications. In this paper, we introduce a new estimator of $f_0$ that avoids this overfitting by minimizing a penalty on the subgradient while enforcing an upper bound $s_n$ on the sum of squared errors. The key advantage of this method is that $s_n$ can be directly estimated from the data. We establish the uniform almost sure consistency of the proposed estimator and its subgradient over $Ω$ as $n \rightarrow \infty$ and derive convergence rates. The effectiveness of our estimator is illustrated through its application to estimating waiting times in a single-server queue.

Time series analysis has emerged as an important tool for improving patient diagnosis and management in healthcare applications. However, these applications commonly face two critical challenges: time misalignment and data sparsity. Traditional approaches address these issues through a two-step process of imputation followed by prediction. We propose MAGIC (Multi-tAsk Gaussian Process for Imputation and Classification), a novel unified framework that simultaneously performs class-informed missing value imputation and label prediction within a hierarchical multi-task Gaussian process coupled with functional logistic regression. To handle intractable likelihood components, MAGIC employs Taylor expansion approximations with bounded error analysis, and parameter estimation is performed using EM algorithm with block coordinate optimization supported by convergence analysis. We validate MAGIC through two healthcare applications: prediction of post-traumatic headache improvement following mild traumatic brain injury and prediction of in-hospital mortality within 48 hours after ICU admission. In both applications, MAGIC achieves superior predictive accuracy compared to existing methods. The ability to generate real-time and accurate predictions with limited samples facilitates early clinical assessment and treatment planning, enabling healthcare providers to make more informed treatment decisions.

Surgical decision-making is complex and requires understanding causal relationships between patient characteristics, interventions, and outcomes. In high-stakes settings like spinal fusion or scoliosis correction, accurate estimation of individualized treatment effects (ITEs) remains limited due to the reliance on traditional statistical methods that struggle with complex, heterogeneous data. In this study, we develop a multi-task meta-learning framework, X-MultiTask, for ITE estimation that models each surgical decision (e.g., anterior vs. posterior approach, surgery vs. no surgery) as a distinct task while learning shared representations across tasks. To strengthen causal validity, we incorporate the inverse probability weighting (IPW) into the training objective. We evaluate our approach on two datasets: (1) a public spinal fusion dataset (1,017 patients) to assess the effect of anterior vs. posterior approaches on complication severity; and (2) a private AIS dataset (368 patients) to analyze the impact of posterior spinal fusion (PSF) vs. non-surgical management on patient-reported outcomes (PROs). Our model achieves the highest average AUC (0.84) in the anterior group and maintains competitive performance in the posterior group (0.77). It outperforms baselines in treatment effect estimation with the lowest overall $ε_{\text{NN-PEHE}}$ (0.2778) and $ε_{\text{ATE}}$ (0.0763). Similarly, when predicting PROs in AIS, X-MultiTask consistently shows superior performance across all domains, with $ε_{\text{NN-PEHE}}$ = 0.2551 and $ε_{\text{ATE}}$ = 0.0902. By providing robust, patient-specific causal estimates, X-MultiTask offers a powerful tool to advance personalized surgical care and improve patient outcomes. The code is available at https://github.com/Wizaaard/X-MultiTask.

We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset and delete entries in up to an $η$-fraction of samples per coordinate; a strong form of the Missing Not At Random model. In the corrupted data setting, the adversary instead replaces values arbitrarily, and the corruption locations are unknown to the learner. Despite substantial work on missing data, linear regression under such adversarial missingness remains poorly understood, even information-theoretically. Unlike the clean setting, where estimation error vanishes with more samples, here the optimal error remains a positive function of the problem parameters. Our main contribution is to characterize this error up to constant factors across essentially the entire parameter range. Specifically, we establish novel information-theoretic lower bounds on the achievable error that match the error of (computationally efficient) algorithms. A key implication is that, perhaps surprisingly, the optimal error in the missing data setting matches that in the corruption setting-so knowing the corruption locations offers no general advantage.

Evaluation of hydrocephalus in children is challenging, and the related research is limited by a lack of publicly available, expert-annotated datasets, particularly those with segmentation of the choroid plexus. To address this, we present HyKid, an open-source dataset from 48 pediatric patients with hydrocephalus. 3D MRIs were provided with 1mm isotropic resolution, which was reconstructed from routine low-resolution images using a slice-to-volume algorithm. Manually corrected segmentations of brain tissues, including white matter, grey matter, lateral ventricle, external CSF, and the choroid plexus, were provided by an experienced neurologist. Additionally, structured data was extracted from clinical radiology reports using a Retrieval-Augmented Generation framework. The strong correlation between choroid plexus volume and total CSF volume provided a potential biomarker for hydrocephalus evaluation, achieving excellent performance in a predictive model (AUC = 0.87). The proposed HyKid dataset provided a high-quality benchmark for neuroimaging algorithms development, and it revealed the choroid plexus-related features in hydrocephalus assessments. Our datasets are publicly available at https://www.synapse.org/Synapse:syn68544889.

Task vectors capture how a model changes during fine-tuning by recording the difference between pre-trained and task-specific weights. The composition of task vectors, a key operator in task arithmetic, enables models to integrate knowledge from multiple tasks without incurring additional inference costs. In this paper, we propose variational task vector composition, where composition coefficients are taken as latent variables and estimated in a Bayesian inference framework. Unlike previous methods that operate at the task level, our framework focuses on sample-specific composition. Motivated by the observation of structural redundancy in task vectors, we introduce a Spike-and-Slab prior that promotes sparsity and preserves only the most informative components. To further address the high variance and sampling inefficiency in sparse, high-dimensional spaces, we develop a gated sampling mechanism that constructs a controllable posterior by filtering the composition coefficients based on both uncertainty and importance. This yields a more stable and interpretable variational framework by deterministically selecting reliable task components, reducing sampling variance while improving transparency and generalization. Experimental results demonstrate that our method consistently outperforms existing approaches across all datasets by selectively leveraging the most reliable and informative components in task vectors. These findings highlight the practical value of our approach, establishing a new standard for efficient and effective task vector composition.