Conv-PCA is a naive method proposed in Section 4.1.

The integration of artificial intelligence (AI) into the legal domain has revolutionized judicial processes, enabling tasks such as legal judgment prediction (LJP), case summarization, precedent retrieval, and automated legal research. Text extraction, the process of isolating seven semantically meaningful segments--referred to as blocks--from unstructured judicial decisions, is a cornerstone of these applications. These blocks include plaintiff demands, plaintiff arguments, defendant arguments, court evaluation of evidence, judicial reasoning steps, applicable legal norms, and court decision. Accurate extraction is critical, as errors can lead to misinterpretations of case facts, biased predictions, or inefficiencies in judicial workflows, potentially undermining justice delivery in high-stakes contexts. Evaluation metrics are essential for quantifying extraction quality, enabling iterative model improvements and ensuring reliability. Traditional metrics rely on annotated ground truth, which is resource-intensive to produce, particularly for legal texts characterized by verbose narratives, domain-specific terminology, and jurisdiction-specific nuances. The scarcity of annotated legal corpora has driven the development of unsupervised metrics that leverage intrinsic document properties, such as term frequencies, semantic coherence, and structural patterns. These metrics must capture surface-level accuracy, semantic fidelity, logical structure, and legal-specific elements like citations and temporal consistency, while addressing ethical concerns such as fairness and neutrality in AI-driven legal systems [1, 2].

The Weak-form Estimation of Non-linear Dynamics (WENDy) algorithm is extended to accommodate systems of ordinary differential equations that are nonlinear-in-parameters (NiP). The extension rests on derived analytic expressions for a likelihood function, its gradient and its Hessian matrix. WENDy makes use of these to approximate a maximum likelihood estimator based on optimization routines suited for non-convex optimization problems. The resulting parameter estimation algorithm has better accuracy, a substantially larger domain of convergence, and is often orders of magnitude faster than the conventional output error least squares method (based on forward solvers). The WENDy.jl algorithm is efficiently implemented in Julia. We demonstrate the algorithm's ability to accommodate the weak form optimization for both additive normal and multiplicative log-normal noise, and present results on a suite of benchmark systems of ordinary differential equations. In order to demonstrate the practical benefits of our approach, we present extensive comparisons between our method and output error methods in terms of accuracy, precision, bias, and coverage.

Effective utilization of time series data is often constrained by the scarcity of data quantity that reflects complex dynamics, especially under the condition of distributional shifts. Existing datasets may not encompass the full range of statistical properties required for robust and comprehensive analysis. And privacy concerns can further limit their accessibility in domains such as finance and healthcare. This paper presents an approach that utilizes large language models and data source interfaces to explore and collect time series datasets. While obtained from external sources, the collected data share critical statistical properties with primary time series datasets, making it possible to model and adapt to various scenarios. This method enlarges the data quantity when the original data is limited or lacks essential properties. It suggests that collected datasets can effectively supplement existing datasets, especially involving changes in data distribution. We demonstrate the effectiveness of the collected datasets through practical examples and show how time series forecasting foundation models fine-tuned on these datasets achieve comparable performance to those models without fine-tuning.

Background: The accurate prediction of postoperative complication risk using Electronic Health Records (EHR) and artificial intelligence shows great potential. Training a robust artificial intelligence model typically requires large-scale and diverse datasets. In reality, collecting medical data often encounters challenges surrounding privacy protection. Methods: This retrospective cohort study includes adult patients who were admitted to UFH Gainesville (GNV) (n = 79,850) and Jacksonville (JAX) (n = 28,636) for any type of inpatient surgical procedure. Using perioperative and intraoperative features, we developed federated learning models to predict nine major postoperative complications (i.e., prolonged intensive care unit stay and mechanical ventilation). We compared federated learning models with local learning models trained on a single site and central learning models trained on pooled dataset from two centers. Results: Our federated learning models achieved the area under the receiver operating characteristics curve (AUROC) values ranged from 0.81 for wound complications to 0.92 for prolonged ICU stay at UFH GNV center. At UFH JAX center, these values ranged from 0.73-0.74 for wound complications to 0.92-0.93 for hospital mortality. Federated learning models achieved comparable AUROC performance to central learning models, except for prolonged ICU stay, where the performance of federated learning models was slightly higher than central learning models at UFH GNV center, but slightly lower at UFH JAX center. In addition, our federated learning model obtained comparable performance to the best local learning model at each center, demonstrating strong generalizability. Conclusion: Federated learning is shown to be a useful tool to train robust and generalizable models from large scale data across multiple institutions where data protection barriers are high.

We consider a personalized pricing problem in which we have data consisting of feature information, historical pricing decisions, and binary realized demand. The goal is to perform off-policy evaluation for a new personalized pricing policy that maps features to prices. Methods based on inverse propensity weighting (including doubly robust methods) for off-policy evaluation may perform poorly when the logging policy has little exploration or is deterministic, which is common in pricing applications. Building on the balanced policy evaluation framework of Kallus (2018), we propose a new approach tailored to pricing applications. The key idea is to compute an estimate that minimizes the worst-case mean squared error or maximizes a worst-case lower bound on policy performance, where in both cases the worst-case is taken with respect to a set of possible revenue functions. We establish theoretical convergence guarantees and empirically demonstrate the advantage of our approach using a real-world pricing dataset.

Acute kidney injury (AKI) is a common and serious complication after a surgery which is associated with morbidity and mortality. The majority of existing perioperative AKI risk score prediction models are limited in their generalizability and do not fully utilize the physiological intraoperative time-series data. Thus, there is a need for intelligent, accurate, and robust systems, able to leverage information from large-scale data to predict patient's risk of developing postoperative AKI. A retrospective single-center cohort of 2,911 adult patients who underwent surgery at the University of Florida Health has been used for this study. We used machine learning and statistical analysis techniques to develop perioperative models to predict the risk of AKI (risk during the first 3 days, 7 days, and until the discharge day) before and after the surgery. In particular, we examined the improvement in risk prediction by incorporating three intraoperative physiologic time series data, i.e., mean arterial blood pressure, minimum alveolar concentration, and heart rate. For an individual patient, the preoperative model produces a probabilistic AKI risk score, which will be enriched by integrating intraoperative statistical features through a machine learning stacking approach inside a random forest classifier. We compared the performance of our model based on the area under the receiver operating characteristics curve (AUROC), accuracy and net reclassification improvement (NRI). The predictive performance of the proposed model is better than the preoperative data only model. For AKI-7day outcome: The AUC was 0.86 (accuracy was 0.78) in the proposed model, while the preoperative AUC was 0.84 (accuracy 0.76). Furthermore, with the integration of intraoperative features, we were able to classify patients who were misclassified in the preoperative model.

Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we propose a framework for optimizing orthogonal matrices, that is the parallel of coordinate-descent in Euclidean spaces. It is based on {\em Givens-rotations}, a fast-to-compute operation that affects a small number of entries in the learned matrix, and preserves orthogonality. We show two applications of this approach: an algorithm for tensor decomposition that is used in learning mixture models, and an algorithm for sparse-PCA. We study the parameter regime where a Givens rotation approach converges faster and achieves a superior model on a genome-wide brain-wide mRNA expression dataset.

In supervised learning scenarios, feature selection has been studied widely in the literature. Selecting features in unsupervised learning scenarios is a much harder problem, due to the absence of class labels that would guide the search for relevant information. And, almost all of previous unsupervised feature selection methods are "wrapper" techniques that require a learning algorithm to evaluate the candidate feature subsets. In this paper, we propose a "filter" method for feature selection which is independent of any learning algorithm. Our method can be performed in either supervised or unsupervised fashion. The proposed method is based on the observation that, in many real world classification problems, data from the same class are often close to each other. The importance of a feature is evaluated by its power of locality preserving, or, Laplacian Score. We compare our method with data variance (unsupervised) and Fisher score (supervised) on two data sets. Experimental results demonstrate the effectiveness and efficiency of our algorithm.