Out-of-distribution (OOD) detection is essential for determining when a supervised model encounters inputs that differ meaningfully from its training distribution. While widely studied in classification, OOD detection for regression and survival analysis remains limited due to the absence of discrete labels and the challenge of quantifying predictive uncertainty. We introduce a framework for OOD detection that is simultaneously model aware and subspace aware, and that embeds variable prioritization directly into the detection step. The method uses the fitted predictor to construct localized neighborhoods around each test case that emphasize the features driving the model's learned relationship and downweight directions that are less relevant to prediction. It produces OOD scores without relying on global distance metrics or estimating the full feature density. The framework is applicable across outcome types, and in our implementation we use random forests, where the rule structure yields transparent neighborhoods and effective scoring. Experiments on synthetic and real data benchmarks designed to isolate functional shifts show consistent improvements over existing methods. We further demonstrate the approach in an esophageal cancer survival study, where distribution shifts related to lymphadenectomy identify patterns relevant to surgical guidelines.

Identifying and comparing topological features, particularly cycles, across different topological objects remains a fundamental challenge in persistent homology and topological data analysis. This work introduces a novel framework for constructing cycle communities through two complementary approaches. First, a dendrogram-based methodology leverages merge-tree algorithms to construct hierarchical representations of homology classes from persistence intervals. The Wasserstein distance on merge trees is introduced as a metric for comparing dendrograms, establishing connections to hierarchical clustering frameworks. Through simulation studies, the discriminative power of dendrogram representations for identifying cycle communities is demonstrated. Second, an extension of Stratified Gradient Sampling simultaneously learns multiple filter functions that yield cycle barycenter functions capable of faithfully reconstructing distinct sets of cycles. The set of cycles each filter function can reconstruct constitutes cycle communities that are non-overlapping and partition the space of all cycles. Together, these approaches transform the problem of cycle matching into both a hierarchical clustering and topological optimization framework, providing principled methods to identify similar topological structures both within and across groups of topological objects.

Least absolute shrinkage and selection operator (Lasso), a popular method for high-dimensional regression, is now used widely for estimating high-dimensional time series models such as the vector autoregression (VAR). Selecting its tuning parameter efficiently and accurately remains a challenge, despite the abundance of available methods for doing so. We propose $\mathsf{autotune}$, a strategy for Lasso to automatically tune itself by optimizing a penalized Gaussian log-likelihood alternately over regression coefficients and noise standard deviation. Using extensive simulation experiments on regression and VAR models, we show that $\mathsf{autotune}$ is faster, and provides better generalization and model selection than established alternatives in low signal-to-noise regimes. In the process, $\mathsf{autotune}$ provides a new estimator of noise standard deviation that can be used for high-dimensional inference, and a new visual diagnostic procedure for checking the sparsity assumption on regression coefficients. Finally, we demonstrate the utility of $\mathsf{autotune}$ on a real-world financial data set. An R package based on C++ is also made publicly available on Github.

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.

Binary classification is one of the oldest, most prevalent, and studied problems in machine learning. However, the metrics used to evaluate model performance have received comparatively little attention. The area under the receiver operating characteristic curve (AUROC) has long been a standard choice for model comparison. Despite its advantages, AUROC is not always ideal, particularly for problems that are invariant to local exchange of classes (LxC), a new form of metric invariance introduced in this work. To address this limitation, we propose LxCIM (LxC-invariant metric), which is not only rank-based and invariant under local exchange of classes, but also intuitive, logically consistent, and always computable, while enabling more detailed analysis through the cumulative accuracy-decision rate curve. Moreover, LxCIM exhibits clear theoretical connections to AUROC, accuracy, and the area under the accuracy-decision rate curve (AUDRC). These relationships allow for multiple complementary interpretations: as a symmetric form of AUROC, a rank-based analogue of accuracy, or a more representative and more interpretable variant of AUDRC. Finally, we demonstrate the direct applicability of LxCIM to the bivariate causal discovery problem (which exhibits invariance to local exchange of classes) and show how it addresses the acknowledged limitations of existing metrics used in this field. All code and implementation details are publicly available at github.com/tiagobrogueira/Causal-Discovery-In-Exchangeable-Data.

Autoregressive (AR) models, common in sequence generation, are limited in many biological tasks such as de novo peptide sequencing and protein modeling by their unidirectional nature, failing to capture crucial global bidirectional token dependencies. Non-Autoregressive (NAR) models offer holistic, bidirectional representations but face challenges with generative coherence and scalability. To transcend this, we propose a hybrid framework enhancing AR generation by dynamically integrating rich contextual information from non-autoregressive mechanisms. Our approach couples a shared input encoder with two decoders: a non-autoregressive one learning latent bidirectional biological features, and an AR decoder synthesizing the biological sequence by leveraging these bidirectional features. A novel cross-decoder attention module enables the AR decoder to iteratively query and integrate these bidirectional features, enriching its predictions. This synergy is cultivated via a tailored training strategy with importance annealing for balanced objectives and cross-decoder gradient blocking for stable, focused learning. Evaluations on a demanding nine-species benchmark of de novo peptide sequencing show that our model substantially surpasses AR and NAR baselines. It uniquely harmonizes AR stability with NAR contextual awareness, delivering robust, superior performance on diverse downstream data. This research advances biological sequence modeling techniques and contributes a novel architectural paradigm for augmenting AR models with enhanced bidirectional understanding for complex sequence generation. Code is available at https://github.com/BEAM-Labs/denovo.

Large Language Models (LLMs) are prone to generating fluent but incorrect content, known as confabulation, which poses increasing risks in multi-turn or agentic applications where outputs may be reused as context. In this work, we investigate how in-context information influences model behavior and whether LLMs can identify their unreliable responses. We propose a reliability estimation that leverages token-level uncertainty to guide the aggregation of internal model representations. Specifically, we compute aleatoric and epistemic uncertainty from output logits to identify salient tokens and aggregate their hidden states into compact representations for response-level reliability prediction. Through controlled experiments on open QA benchmarks, we find that correct in-context information improves both answer accuracy and model confidence, while misleading context often induces confidently incorrect responses, revealing a misalignment between uncertainty and correctness. Our probing-based method captures these shifts in model behavior and improves the detection of unreliable outputs across multiple open-source LLMs. These results underscore the limitations of direct uncertainty signals and highlight the potential of uncertainty-guided probing for reliability-aware generation.

ABSTRACT We develop a Markov decision process (MDP) framework to autonomously make guidance decisions for satellite collision avoidance maneuver (CAM) and a reinforcement learning policy gradient (RL-PG) algorithm to enable direct optimization of guidance policy using historic CAM data. In addition to maintaining acceptable collision risks, this approach seeks to minimize the average propellant consumption of CAMs by making early maneuver decisions. We model CAM as a continuous state, discrete action and finite horizon MDP, where the critical decision is determining when to initiate the maneuver. By deciding to maneuver earlier than conventional methods, the Markov policy effectively favors CAMs that achieve comparable rates of collision risk reduction while consuming less propellant. Using historical data of tracked conjunction events, we verify this framework and conduct an extensive parameter-sensitivity study. When evaluated on synthetic conjunction events, the trained policy consumes significantly less propellant overall and per maneuver in comparison to a conventional cut-off policy that initiates maneuvers 24 hours before the time of closest approach (TCA). On historical conjunction events, the trained policy consumes more propellant overall but consumes less propellant per maneuver. For both historical and synthetic conjunction events, the trained policy is slightly more conservative in identifying conjunctions events that warrant CAMs in comparison to cutoff policies.

Understanding the spatial and temporal dynamics of automated vehicle (AV) crash severity is critical for advancing urban mobility safety and infrastructure planning. In this work, we introduce ST-GraphNet, a spatio-temporal graph neural network framework designed to model and predict AV crash severity by using both fine-grained and region-aggregated spatial graphs. Using a balanced dataset of 2,352 real-world AV-related crash reports from Texas (2024), including geospatial coordinates, crash timestamps, SAE automation levels, and narrative descriptions, we construct two complementary graph representations: (1) a fine-grained graph with individual crash events as nodes, where edges are defined via spatio-temporal proximity; and (2) a coarse-grained graph where crashes are aggregated into Hexagonal Hierarchical Spatial Indexing (H3)-based spatial cells, connected through hexagonal adjacency. Each node in the graph is enriched with multimodal data, including semantic, spatial, and temporal attributes, including textual embeddings from crash narratives using a pretrained Sentence-BERT model. We evaluate various graph neural network (GNN) architectures, such as Graph Convolutional Networks (GCN), Graph Attention Networks (GAT), and Dynamic Spatio-Temporal GCN (DSTGCN), to classify crash severity and predict high-risk regions. Our proposed ST-GraphNet, which utilizes a DSTGCN backbone on the coarse-grained H3 graph, achieves a test accuracy of 97.74\%, substantially outperforming the best fine-grained model (64.7\% test accuracy). These findings highlight the effectiveness of spatial aggregation, dynamic message passing, and multi-modal feature integration in capturing the complex spatio-temporal patterns underlying AV crash severity.

Panoramic imaging enables capturing 360° images with an ultra-wide Field-of-View (FoV) for dense omnidirectional perception, which is critical to applications, such as autonomous driving and augmented reality, etc. However, current panoramic semantic segmentation methods fail to identify outliers, and pinhole Out-of-distribution Segmentation (OoS) models perform unsatisfactorily in the panoramic domain due to pixel distortions and background clutter. To address these issues, we introduce a new task, Panoramic Out-of-distribution Segmentation (PanOoS), with the aim of achieving comprehensive and safe scene understanding. Furthermore, we propose the first solution, POS, which adapts to the characteristics of panoramic images through text-guided prompt distribution learning. Specifically, POS integrates a disentanglement strategy designed to materialize the cross-domain generalization capability of CLIP. The proposed Prompt-based Restoration Attention (PRA) optimizes semantic decoding by prompt guidance and self-adaptive correction, while Bilevel Prompt Distribution Learning (BPDL) refines the manifold of per-pixel mask embeddings via semantic prototype supervision. Besides, to compensate for the scarcity of PanOoS datasets, we establish two benchmarks: DenseOoS, which features diverse outliers in complex environments, and QuadOoS, captured by a quadruped robot with a panoramic annular lens system. Extensive experiments demonstrate superior performance of POS, with AuPRC improving by 34.25% and FPR95 decreasing by 21.42% on DenseOoS, outperforming state-of-the-art pinhole-OoS methods. Moreover, POS achieves leading closed-set segmentation capabilities and advances the development of panoramic understanding. Code and datasets will be available at https://github.com/MengfeiD/PanOoS.