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 mean estimation of a random vector $X$ in a distributed parameter-server-worker setup. Worker $i$ observes samples of $a_i^\top X$, where $a_i^\top$ is the $i$th row of a known sensing matrix $A$. The key challenges are adversarial measurements and asynchrony: a fixed subset of workers may transmit corrupted measurements, and workers are activated asynchronously--only one is active at any time. In our previous work, we proposed a two-timescale $\ell_1$-minimization algorithm and established asymptotic recovery under a null-space-property-like condition on $A$. In this work, we establish tight non-asymptotic convergence rates under the same null-space-property-like condition. We also identify relaxed conditions on $A$ under which exact recovery may fail but recovery of a projected component of $\mathbb{E}[X]$ remains possible. Overall, our results provide a unified finite-time characterization of robustness, identifiability, and statistical efficiency in distributed linear estimation with adversarial workers, with implications for network tomography and related distributed sensing problems.

Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical bottleneck for emerging scientific data, such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular, sparse manifolds. Consequently, researchers currently face a forced choice: either sacrifice single-cell resolution via voxelization to utilize image-based tools, or ignore the critical functional signal to utilize geometric tools. To resolve this dilemma, we propose Domain Elastic Transform (DET), a grid-free probabilistic framework that unifies geometric and functional alignment. By treating data as functions on irregular domains, DET registers high-dimensional signals directly without binning. We formulate the problem within a rigorous Bayesian framework, modeling domain deformation as an elastic motion guided by a joint spatial-functional likelihood. The method is fully unsupervised and scalable, utilizing feature-sensitive downsampling to handle massive atlases. We demonstrate that DET achieves 92\% topological preservation on MERFISH data where state-of-the-art optimal transport methods struggle ($<$5\%), and successfully registers whole-embryo Stereo-seq atlases across developmental stages -- a task involving massive scale and complex nonrigid growth. The implementation of DET is available on {https://github.com/ohirose/bcpd} (since Mar, 2025).

Extensive experiments and analyses have been conducted to characterize and demonstrate the effectiveness of the proposed DivOE.

We present an approach to denoising spatial transcriptomics images that is particularly effective for uncovering cell identities in the regime of ultra-low sequencing depths, and also allows for interpolation of gene expression. The method -- Spatial Transcriptomics via Adaptive Regularization and Kernels (STARK) -- augments kernel ridge regression with an incrementally adaptive graph Laplacian regularizer. In each iteration, we (1) perform kernel ridge regression with a fixed graph to update the image, and (2) update the graph based on the new image. The kernel ridge regression step involves reducing the infinite dimensional problem on a space of images to finite dimensions via a modified representer theorem. Starting with a purely spatial graph, and updating it as we improve our image makes the graph more robust to noise in low sequencing depth regimes. We show that the aforementioned approach optimizes a block-convex objective through an alternating minimization scheme wherein the sub-problems have closed form expressions that are easily computed. This perspective allows us to prove convergence of the iterates to a stationary point of this non-convex objective. Statistically, such stationary points converge to the ground truth with rate $\mathcal{O}(R^{-1/2})$ where $R$ is the number of reads. In numerical experiments on real spatial transcriptomics data, the denoising performance of STARK, evaluated in terms of label transfer accuracy, shows consistent improvement over the competing methods tested.

A reliable fault diagnosis system should not only accurately classify known health states but also effectively identify unknown faults. In multimode processes, samples belonging to the same health state often show multiple cluster distributions, making it difficult to construct compact and accurate decision boundaries for that state. To address this challenge, a novel open-set fault diagnosis model named fine-grained clustering and rejection network (FGCRN) is proposed. It combines multiscale depthwise convolution, bidirectional gated recurrent unit and temporal attention mechanism to capture discriminative features. A distance-based loss function is designed to enhance the intra-class compactness. Fine-grained feature representations are constructed through unsupervised learning to uncover the intrinsic structures of each health state. Extreme value theory is employed to model the distance between sample features and their corresponding fine-grained representations, enabling effective identification of unknown faults. Extensive experiments demonstrate the superior performance of the proposed method.

Optimization modeling and solving are fundamental to the application of Operations Research (OR) in real-world decision making, yet the process of translating natural language problem descriptions into formal models and solver code remains highly expertise intensive. While recent advances in large language models (LLMs) have opened new opportunities for automation, the generalization ability and data efficiency of existing LLM-based methods are still limited, asmost require vast amounts of annotated or synthetic data, resulting in high costs and scalability barriers. In this work, we present OR-R1, a data-efficient training framework for automated optimization modeling and solving. OR-R1 first employs supervised fine-tuning (SFT) to help the model acquire the essential reasoning patterns for problem formulation and code generation from limited labeled data. In addition, it improves the capability and consistency through Test-Time Group Relative Policy Optimization (TGRPO). This two-stage design enables OR-R1 to leverage both scarce labeled and abundant unlabeled data for effective learning. Experiments show that OR-R1 achieves state-of-the-art performance with an average solving accuracy of $67.7\%$, using only $1/10$ the synthetic data required by prior methods such as ORLM, exceeding ORLM's solving accuracy by up to $4.2\%$. Remarkably, OR-R1 outperforms ORLM by over $2.4\%$ with just $100$ synthetic samples. Furthermore, TGRPO contributes an additional $3.1\%-6.4\%$ improvement in accuracy, significantly narrowing the gap between single-attempt (Pass@1) and multi-attempt (Pass@8) performance from $13\%$ to $7\%$. Extensive evaluations across diverse real-world benchmarks demonstrate that OR-R1 provides a robust, scalable, and cost-effective solution for automated OR optimization problem modeling and solving, lowering the expertise and data barriers for industrial OR applications.

This paper presents a comprehensive theoretical investigation into the parameterized complexity of explanation problems in various machine learning (ML) models. Contrary to the prevalent black-box perception, our study focuses on models with transparent internal mechanisms. We address two principal types of explanation problems: abductive and contrastive, both in their local and global variants. Our analysis encompasses diverse ML models, including Decision Trees, Decision Sets, Decision Lists, Boolean Circuits, and ensembles thereof, each offering unique explanatory challenges. This research fills a significant gap in explainable AI (XAI) by providing a foundational understanding of the complexities of generating explanations for these models. This work provides insights vital for further research in the domain of XAI, contributing to the broader discourse on the necessity of transparency and accountability in AI systems.

In this work, we present a hierarchical framework designed to support robotic inspection under environment uncertainty. By leveraging a known environment model, existing methods plan and safely track inspection routes to visit points of interest. However, discrepancies between the model and actual site conditions, caused by either natural or human activities, can alter the surface morphology or introduce path obstructions. To address this challenge, the proposed framework divides the inspection task into: (a) generating the initial global view-plan for region of interests based on a historical map and (b) local view replanning to adapt to the current morphology of the inspection scene. The proposed hierarchy preserves global coverage objectives while enabling reactive adaptation to the local surface morphology. This enables the local autonomy to remain robust against environment uncertainty and complete the inspection tasks. We validate the approach through deployments in real-world subterranean mines using quadrupedal robot.

Dropout is common in clinical studies, with up to half of patients leaving early due to side effects or other reasons. When dropout is informative (i.e., dependent on survival time), it introduces censoring bias, because of which treatment effect estimates are also biased. In this paper, we propose an assumption-lean framework to assess the robustness of conditional average treatment effect (CATE) estimates in survival analysis when facing censoring bias. Unlike existing works that rely on strong assumptions, such as non-informative censoring, to obtain point estimation, we use partial identification to derive informative bounds on the CATE. Thereby, our framework helps to identify patient subgroups where treatment is effective despite informative censoring. We further develop a novel meta-learner that estimates the bounds using arbitrary machine learning models and with favorable theoretical properties, including double robustness and quasi-oracle efficiency. We demonstrate the practical value of our meta-learner through numerical experiments and in an application to a cancer drug trial. Together, our framework offers a practical tool for assessing the robustness of estimated treatment effects in the presence of censoring and thus promotes the reliable use of survival data for evidence generation in medicine and epidemiology.