Cluster weighted models with multivariate skewed distributions for functional data Cristina Anton, 1 Roy Shivam Ram Shreshtth 2 1 Department of Mathematics and Statistics, MacEwan University, 103C, 10700-104 Ave., Edmonton, AB T5J 4S2, Canada, email: popescuc@macewan.ca 2 Department of Mathematics and Statistics, Indian Institute of Technology Kanpur Abstract We propose a clustering method, funWeightClustSkew, based on mixtures of functional linear regression models and three skewed multivariate distributions: the variance-gamma distribution, the skew-t distribution, and the normal-inverse Gaussian distribution. Our approach follows the framework of the functional high dimensional data clustering (funHDDC) method, and we extend to functional data the cluster weighted models based on skewed distributions used for finite dimensional multivariate data. We consider several parsimonious models, and to estimate the parameters we construct an expectation maximization (EM) algorithm. We illustrate the performance of funWeightClustSkew for simulated data and for the Air Quality dataset. Keywords: Cluster weighted models, Functional linear regression, EM algorithm, Skewed distributions, Multivariate functional principal component analysis 1 Introduction Smart devices and other modern technologies record huge amounts of data measured continuously in time. These data are better represented as curves instead of finite-dimensional vectors, and they are analyzed using statistical methods specific to functional data (Ramsay and Silverman, 2006; Ferraty and Vieu, 2006; Horv ath and Kokoszka, 2012). Many times more than one curve is collected for one individual, e.g.

The performance of modern reinforcement learning algorithms critically relies on tuning ever increasing numbers of hyperparameters. Often, small changes in a hyperparameter can lead to drastic changes in performance, and different environments require very different hyperparameter settings to achieve state-of-the-art performance reported in the literature. We currently lack a scalable and widely accepted approach to characterizing these complex interactions. This work proposes a new empirical methodology for studying, comparing, and quantifying the sensitivity of an algorithm's performance to hyperparameter tuning for a given set of environments. We then demonstrate the utility of this methodology by assessing the hyperparameter sensitivity of several commonly used normalization variants of PPO. The results suggest that several algorithmic performance improvements may, in fact, be a result of an increased reliance on hyperparameter tuning.

Survival prediction often involves estimating the time-to-event distribution from censored datasets. Previous approaches have focused on enhancing discrimination and marginal calibration. In this paper, we highlight the significance of conditional calibration for real-world applications - especially its role in individual decision-making. We propose a method based on conformal prediction that uses the model's predicted individual survival probability at that instance's observed time. This method effectively improves the model's marginal and conditional calibration, without compromising discrimination. We provide asymptotic theoretical guarantees for both marginal and conditional calibration and test it extensively across 15 diverse real-world datasets, demonstrating the method's practical effectiveness and versatility in various settings.

In recent times, reinforcement learning (RL) with physical robots has attracted the attention of a wide range of researchers. However, state-of-the-art RL algorithms do not consider that physical environments do not wait for the RL agent to make decisions or updates. RL agents learn by periodically conducting computationally expensive gradient updates. When decision-making and gradient update tasks are carried out sequentially by the RL agent in a physical robot, it significantly increases the agent's response time. In a rapidly changing environment, this increased response time may be detrimental to the performance of the learning agent. Asynchronous RL methods, which separate the computation of decision-making and gradient updates, are a potential solution to this problem. However, only a few comparisons between asynchronous and synchronous RL have been made with physical robots. For this reason, the exact performance benefits of using asynchronous RL methods over synchronous RL methods are still unclear. In this study, we provide a performance comparison between asynchronous and synchronous RL using a physical robotic arm called Franka Emika Panda. Our experiments show that the agents learn faster and attain significantly more returns using asynchronous RL. Our experiments also demonstrate that the learning agent with a faster response time performs better than the agent with a slower response time, even if the agent with a slower response time performs a higher number of gradient updates.

Large language models (LLMs) are among the best methods for processing natural language, partly due to their versatility. At the same time, domain-specific LLMs are more practical in real-life applications. This work introduces a novel natural language dataset created by acquired data from official legislative authorities' websites. The study focuses on formulating three natural language processing (NLP) tasks to evaluate the effectiveness of LLMs on legislative content analysis within the context of the Polish legal system. Key findings highlight the potential of LLMs in automating and enhancing legislative content analysis while emphasizing specific challenges, such as understanding legal context. The research contributes to the advancement of NLP in the legal field, particularly in the Polish language. It has been demonstrated that even commonly accessible data can be practically utilized for legislative content analysis.

Dynamic Treatment Regimes (DTRs) provide a systematic approach for making sequential treatment decisions that adapt to individual patient characteristics, particularly in clinical contexts where survival outcomes are of interest. Censoring-Aware Tree-Based Reinforcement Learning (CA-TRL) is a novel framework to address the complexities associated with censored data when estimating optimal DTRs. We explore ways to learn effective DTRs, from observational data. By enhancing traditional tree-based reinforcement learning methods with augmented inverse probability weighting (AIPW) and censoring-aware modifications, CA-TRL delivers robust and interpretable treatment strategies. We demonstrate its effectiveness through extensive simulations and real-world applications using the SANAD epilepsy dataset, where it outperformed the recently proposed ASCL method in key metrics such as restricted mean survival time (RMST) and decision-making accuracy. This work represents a step forward in advancing personalized and data-driven treatment strategies across diverse healthcare settings.

We propose a method, funWeightClust, based on a family of parsimonious models for clustering heterogeneous functional linear regression data. These models extend cluster weighted models to functional data, and they allow for multivariate functional responses and predictors. The proposed methodology follows the approach used by the the functional high dimensional data clustering (funHDDC) method. We construct an expectation maximization (EM) algorithm for parameter estimation. Using simulated and benchmark data we show that funWeightClust outperforms funHDDC and several two-steps clustering methods. We also use funWeightClust to analyze traffic patterns in Edmonton, Canada.

Deep reinforcement learning (DRL)-based frameworks, featuring Transformer-style policy networks, have demonstrated their efficacy across various vehicle routing problem (VRP) variants. However, the application of these methods to the multi-trip time-dependent vehicle routing problem (MTTDVRP) with maximum working hours constraints -- a pivotal element of urban logistics -- remains largely unexplored. This paper introduces a DRL-based method called the Simultaneous Encoder and Dual Decoder Attention Model (SED2AM), tailored for the MTTDVRP with maximum working hours constraints. The proposed method introduces a temporal locality inductive bias to the encoding module of the policy networks, enabling it to effectively account for the time-dependency in travel distance or time. The decoding module of SED2AM includes a vehicle selection decoder that selects a vehicle from the fleet, effectively associating trips with vehicles for functional multi-trip routing. Additionally, this decoding module is equipped with a trip construction decoder leveraged for constructing trips for the vehicles. This policy model is equipped with two classes of state representations, fleet state and routing state, providing the information needed for effective route construction in the presence of maximum working hours constraints. Experimental results using real-world datasets from two major Canadian cities not only show that SED2AM outperforms the current state-of-the-art DRL-based and metaheuristic-based baselines but also demonstrate its generalizability to solve larger-scale problems.

Legal case documents play a critical role in judicial proceedings. As the number of cases continues to rise, the reliance on manual drafting of legal case documents is facing increasing pressure and challenges. The development of large language models (LLMs) offers a promising solution for automating document generation. However, existing benchmarks fail to fully capture the complexities involved in drafting legal case documents in real-world scenarios. To address this gap, we introduce CaseGen, the benchmark for multi-stage legal case documents generation in the Chinese legal domain. CaseGen is based on 500 real case samples annotated by legal experts and covers seven essential case sections. It supports four key tasks: drafting defense statements, writing trial facts, composing legal reasoning, and generating judgment results. To the best of our knowledge, CaseGen is the first benchmark designed to evaluate LLMs in the context of legal case document generation. To ensure an accurate and comprehensive evaluation, we design the LLM-as-a-judge evaluation framework and validate its effectiveness through human annotations. We evaluate several widely used general-domain LLMs and legal-specific LLMs, highlighting their limitations in case document generation and pinpointing areas for potential improvement. This work marks a step toward a more effective framework for automating legal case documents drafting, paving the way for the reliable application of AI in the legal field. The dataset and code are publicly available at https://github.com/CSHaitao/CaseGen.

The recent application of LLMs to the legal field has spurred the creation of benchmarks across various jurisdictions and languages. However, no benchmark has yet been specifically designed for the Portuguese legal system. In this work, we present LegalBench.PT, the first comprehensive legal benchmark covering key areas of Portuguese law. To develop LegalBench.PT, we first collect long-form questions and answers from real law exams, and then use GPT-4o to convert them into multiple-choice, true/false, and matching formats. Once generated, the questions are filtered and processed to improve the quality of the dataset. To ensure accuracy and relevance, we validate our approach by having a legal professional review a sample of the generated questions. Although the questions are synthetically generated, we show that their basis in human-created exams and our rigorous filtering and processing methods applied result in a reliable benchmark for assessing LLMs' legal knowledge and reasoning abilities. Finally, we evaluate the performance of leading LLMs on LegalBench.PT and investigate potential biases in GPT-4o's responses. We also assess the performance of Portuguese lawyers on a sample of questions to establish a baseline for model comparison and validate the benchmark.