Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target distribution, progressively adding noise. In this work, we establish the first (nearly) dimension-free sample complexity bounds for learning these score functions, achieving a double exponential improvement in dimension over prior results. A key aspect of our analysis is the use of a single function approximator to jointly estimate scores across noise levels, a critical feature of diffusion models in practice which enables generalization across timesteps. Our analysis introduces a novel martingale-based error decomposition and sharp variance bounds, enabling efficient learning from dependent data generated by Markov processes, which may be of independent interest. Building on these insights, we propose Bootstrapped Score Matching (BSM), a variance reduction technique that utilizes previously learned scores to improve accuracy at higher noise levels. These results provide crucial insights into the efficiency and effectiveness of diffusion models for generative modeling.

The frequency of extreme flood events is increasing throughout the world. Daily, high-resolution (30m) Flood Inundation Maps (FIM) observed from space play a key role in informing mitigation and preparedness efforts to counter these extreme events. However, the temporal frequency of publicly available high-resolution FIMs, e.g., from Landsat, is at the order of two weeks thus limiting the effective monitoring of flood inundation dynamics. Conversely, global, low-resolution (~300m) Water Fraction Maps (WFM) are publicly available from NOAA VIIRS daily. Motivated by the recent successes of deep learning methods for single image super-resolution, we explore the effectiveness and limitations of similar data-driven approaches to downscaling low-resolution WFMs to high-resolution FIMs. To overcome the scarcity of high-resolution FIMs, we train our models with high-quality synthetic data obtained through physics-based simulations. We evaluate our models on real-world data from flood events in the state of Iowa. The study indicates that data-driven approaches exhibit superior reconstruction accuracy over non-data-driven alternatives and that the use of synthetic data is a viable proxy for training purposes. Additionally, we show that our trained models can exhibit superior zero-shot performance when transferred to regions with hydroclimatological similarity to the U.S. Midwest.

The recent adoption of artificial intelligence (AI) in robotics has driven the development of algorithms that enable autonomous systems to adapt to complex social environments. In particular, safe and efficient social navigation is a key challenge, requiring AI not only to avoid collisions and deadlocks but also to interact intuitively and predictably with its surroundings. To date, methods based on probabilistic models and the generation of conformal safety regions have shown promising results in defining safety regions with a controlled margin of error, primarily relying on classification approaches and explicit rules to describe collision-free navigation conditions. This work explores how topological features contribute to explainable safety regions in social navigation. Instead of using behavioral parameters, we leverage topological data analysis to classify and characterize different simulation behaviors. First, we apply global rule-based classification to distinguish between safe (collision-free) and unsafe scenarios based on topological properties. Then, we define safety regions, $S_\varepsilon$, in the topological feature space, ensuring a maximum classification error of $\varepsilon$. These regions are built with adjustable SVM classifiers and order statistics, providing robust decision boundaries. Local rules extracted from these regions enhance interpretability, keeping the decision-making process transparent. Our approach initially separates simulations with and without collisions, outperforming methods that not incorporate topological features. It offers a deeper understanding of robot interactions within a navigable space. We further refine safety regions to ensure deadlock-free simulations and integrate both aspects to define a compliant simulation space that guarantees safe and efficient navigation.

Random forests are widely used in regression. However, the decision trees used as base learners are poor approximators of linear relationships. To address this limitation we propose RaFFLE (Random Forest Featuring Linear Extensions), a novel framework that integrates the recently developed PILOT trees (Piecewise Linear Organic Trees) as base learners within a random forest ensemble. PILOT trees combine the computational efficiency of traditional decision trees with the flexibility of linear model trees. To ensure sufficient diversity of the individual trees, we introduce an adjustable regularization parameter and use node-level feature sampling. These modifications improve the accuracy of the forest. We establish theoretical guarantees for the consistency of RaFFLE under weak conditions, and its faster convergence when the data are generated by a linear model. Empirical evaluations on 136 regression datasets demonstrate that RaFFLE outperforms the classical CART and random forest methods, the regularized linear methods Lasso and Ridge, and the state-of-the-art XGBoost algorithm, across both linear and nonlinear datasets. By balancing predictive accuracy and computational efficiency, RaFFLE proves to be a versatile tool for tackling a wide variety of regression problems.

Prompt engineering has emerged as a powerful technique for optimizing large language models (LLMs) for specific applications, enabling faster prototyping and improved performance, and giving rise to the interest of the community in protecting proprietary system prompts. In this work, we explore a novel perspective on prompt privacy through the lens of membership inference. We develop Prompt Detective, a statistical method to reliably determine whether a given system prompt was used by a third-party language model. Our approach relies on a statistical test comparing the distributions of two groups of model outputs corresponding to different system prompts. Through extensive experiments with a variety of language models, we demonstrate the effectiveness of Prompt Detective for prompt membership inference. Our work reveals that even minor changes in system prompts manifest in distinct response distributions, enabling us to verify prompt usage with statistical significance.

Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately, the usual Bayesian computations can be quite challenging and expensive. Here we start with a recently proposed empirical Bayes solution, with strong theoretical convergence properties, and develop a novel and computationally efficient variational approximation thereof. One such novelty is that we develop this approximation directly for the marginal distribution on the model space, rather than on the regression coefficients themselves. We demonstrate the method's strong performance in simulations, and prove that our variational approximation inherits the strong selection consistency property satisfied by the posterior distribution that it is approximating.

Stemming from physics and later applied to other fields such as ecology, the theory of critical transitions suggests that some regime shifts are preceded by statistical early warning signals. Reddit's r/place experiment, a large-scale social game, provides a unique opportunity to test these signals consistently across thousands of subsystems undergoing critical transitions. In r/place, millions of users collaboratively created compositions, or pixel-art drawings, in which transitions occur when one composition rapidly replaces another. We develop a machine-learning-based early warning system that combines the predictive power of multiple system-specific time series via gradient-boosted decision trees with memory-retaining features. Our method significantly outperforms standard early warning indicators. Trained on the 2022 r/place data, our algorithm detects half of the transitions occurring within 20 minutes at a false positive rate of just 3.7%. Its performance remains robust when tested on the 2023 r/place event, demonstrating generalizability across different contexts. Using SHapley Additive exPlanations (SHAP) for interpreting the predictions, we investigate the underlying drivers of warnings, which could be relevant to other complex systems, especially online social systems. We reveal an interplay of patterns preceding transitions, such as critical slowing down or speeding up, a lack of innovation or coordination, turbulent histories, and a lack of image complexity. These findings show the potential of machine learning indicators in socio-ecological systems for predicting regime shifts and understanding their dynamics.

Predicting drug-gene associations is crucial for drug development and disease treatment. While graph neural networks (GNN) have shown effectiveness in this task, they face challenges with data sparsity and efficient contrastive learning implementation. We introduce a graph diffusion network for drug-gene prediction (GDNDGP), a framework that addresses these limitations through two key innovations. First, it employs meta-path-based homogeneous graph learning to capture drug-drug and gene-gene relationships, ensuring similar entities share embedding spaces. Second, it incorporates a parallel diffusion network that generates hard negative samples during training, eliminating the need for exhaustive negative sample retrieval. Our model achieves superior performance on the DGIdb 4.0 dataset and demonstrates strong generalization capability on tripartite drug-gene-disease networks. Results show significant improvements over existing methods in drug-gene prediction tasks, particularly in handling complex heterogeneous relationships. The source code is publicly available at https://github.com/csjywu1/GDNDGP.

Importance: Emergency department (ED) returns for mental health conditions pose a major healthcare burden, with 24-27% of patients returning within 30 days. Traditional machine learning models for predicting these returns often lack interpretability for clinical use. Objective: To assess whether integrating large language models (LLMs) with machine learning improves predictive accuracy and clinical interpretability of ED mental health return risk models. Methods: This retrospective cohort study analyzed 42,464 ED visits for 27,904 unique mental health patients at an academic medical center in the Deep South from January 2018 to December 2022. Main Outcomes and Measures: Two primary outcomes were evaluated: (1) 30-day ED return prediction accuracy and (2) model interpretability using a novel LLM-enhanced framework integrating SHAP (SHapley Additive exPlanations) values with clinical knowledge. Results: For chief complaint classification, LLaMA 3 (8B) with 10-shot learning outperformed traditional models (accuracy: 0.882, F1-score: 0.86). In SDoH classification, LLM-based models achieved 0.95 accuracy and 0.96 F1-score, with Alcohol, Tobacco, and Substance Abuse performing best (F1: 0.96-0.89), while Exercise and Home Environment showed lower performance (F1: 0.70-0.67). The LLM-based interpretability framework achieved 99% accuracy in translating model predictions into clinically relevant explanations. LLM-extracted features improved XGBoost AUC from 0.74 to 0.76 and AUC-PR from 0.58 to 0.61. Conclusions and Relevance: Integrating LLMs with machine learning models yielded modest but consistent accuracy gains while significantly enhancing interpretability through automated, clinically relevant explanations. This approach provides a framework for translating predictive analytics into actionable clinical insights.

Graph Neural Networks (GNNs) have demonstrated remarkable proficiency in modeling data with graph structures, yet recent research reveals their susceptibility to adversarial attacks. Traditional attack methodologies, which rely on manipulating the original graph or adding links to artificially created nodes, often prove impractical in real-world settings. This paper introduces a novel adversarial scenario involving the injection of an isolated subgraph to deceive both the link recommender and the node classifier within a GNN system. Specifically, the link recommender is mislead to propose links between targeted victim nodes and the subgraph, encouraging users to unintentionally establish connections and that would degrade the node classification accuracy, thereby facilitating a successful attack. To address this, we present the LiSA framework, which employs a dual surrogate model and bi-level optimization to simultaneously meet two adversarial objectives. Extensive experiments on real-world datasets demonstrate the effectiveness of our method.