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.

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.

In recent years, there has been a significant increase in applications of multimodal signal processing and analysis, largely driven by the increased availability of multimodal datasets and the rapid progress in multimodal learning systems. Well-known examples include autonomous vehicles, audiovisual generative systems, vision-language systems, and so on. Such systems integrate multiple signal modalities: text, speech, images, video, LiDAR, etc., to perform various tasks. A key issue for understanding such systems is the relationship between various modalities and how it impacts task performance. In this paper, we employ the concept of mutual information (MI) to gain insight into this issue. Taking advantage of the recent progress in entropy modeling and estimation, we develop a system called InfoMeter to estimate MI between modalities in a multimodal learning system. We then apply InfoMeter to analyze a multimodal 3D object detection system over a large-scale dataset for autonomous driving. Our experiments on this system suggest that a lower MI between modalities is beneficial for detection accuracy. This new insight may facilitate improvements in the development of future multimodal learning systems.

This research paper explores ways to apply Federated Learning (FL) and Differential Privacy (DP) techniques to population-scale Electrocardiogram (ECG) data. The study learns a multi-label ECG classification model using FL and DP based on 1,565,849 ECG tracings from 7 hospitals in Alberta, Canada. The FL approach allowed collaborative model training without sharing raw data between hospitals while building robust ECG classification models for diagnosing various cardiac conditions. These accurate ECG classification models can facilitate the diagnoses while preserving patient confidentiality using FL and DP techniques. Our results show that the performance achieved using our implementation of the FL approach is comparable to that of the pooled approach, where the model is trained over the aggregating data from all hospitals. Furthermore, our findings suggest that hospitals with limited ECGs for training can benefit from adopting the FL model compared to single-site training. In addition, this study showcases the trade-off between model performance and data privacy by employing DP during model training. Our code is available at https://github.com/vikhyatt/Hospital-FL-DP.

The end-to-end learning pipeline is gradually creating a paradigm shift in the ongoing development of highly autonomous vehicles, largely due to advances in deep learning, the availability of large-scale training datasets, and improvements in integrated sensor devices. However, a lack of interpretability in real-time decisions with contemporary learning methods impedes user trust and attenuates the widespread deployment and commercialization of such vehicles. Moreover, the issue is exacerbated when these cars are involved in or cause traffic accidents. Such drawback raises serious safety concerns from societal and legal perspectives. Consequently, explainability in end-to-end autonomous driving is essential to build trust in vehicular automation. However, the safety and explainability aspects of end-to-end driving have generally been investigated disjointly by researchers in today's state of the art. This survey aims to bridge the gaps between these topics and seeks to answer the following research question: When and how can explanations improve safety of end-to-end autonomous driving? In this regard, we first revisit established safety and state-of-the-art explainability techniques in end-to-end driving. Furthermore, we present three critical case studies and show the pivotal role of explanations in enhancing self-driving safety. Finally, we describe insights from empirical studies and reveal potential value, limitations, and caveats of practical explainable AI methods with respect to their safety assurance in end-to-end autonomous driving.