Clinical data informs the personalization of health care with a potential for more effective disease management. In practice, this is achieved by subgrouping, whereby clusters with similar patient characteristics are identified and then receive customized treatment plans with the goal of targeting subgroup-specific disease dynamics. In this paper, we propose a novel mixture hidden Markov model for subgrouping patient trajectories from chronic diseases. Our model is probabilistic and carefully designed to capture different trajectory phases of chronic diseases (i.e., "severe", "moderate", and "mild") through tailored latent states. We demonstrate our subgrouping framework based on a longitudinal study across 847 patients with non-specific low back pain. Here, our subgrouping framework identifies 8 subgroups. Further, we show that our subgrouping framework outperforms common baselines in terms of cluster validity indices. Finally, we discuss the applicability of the model to other chronic and long-lasting diseases.

This paper presents a novel approach to optimizing profit margins in non-life insurance markets through a gradient descent-based method, targeting three key objectives: 1) maximizing profit margins, 2) ensuring conversion rates, and 3) enforcing fairness criteria such as demographic parity (DP). Traditional pricing optimization, which heavily lean on linear and semi definite programming, encounter challenges in balancing profitability and fairness. These challenges become especially pronounced in situations that necessitate continuous rate adjustments and the incorporation of fairness criteria. Specifically, indirect Ratebook optimization, a widely-used method for new business price setting, relies on predictor models such as XGBoost or GLMs/GAMs to estimate on downstream individually optimized prices. However, this strategy is prone to sequential errors and struggles to effectively manage optimizations for continuous rate scenarios. In practice, to save time actuaries frequently opt for optimization within discrete intervals (e.g., range of [-20\%, +20\%] with fix increments) leading to approximate estimations. Moreover, to circumvent infeasible solutions they often use relaxed constraints leading to suboptimal pricing strategies. The reverse-engineered nature of traditional models complicates the enforcement of fairness and can lead to biased outcomes. Our method addresses these challenges by employing a direct optimization strategy in the continuous space of rates and by embedding fairness through an adversarial predictor model. This innovation not only reduces sequential errors and simplifies the complexities found in traditional models but also directly integrates fairness measures into the commercial premium calculation. We demonstrate improved margin performance and stronger enforcement of fairness highlighting the critical need to evolve existing pricing strategies.

For natural language understanding and generation, embedding concepts using an order-based representation is an essential task. Unlike traditional point vector based representation, an order-based representation imposes geometric constraints on the representation vectors for explicitly capturing various semantic relationships that may exist between a pair of concepts. In existing literature, several approaches on order-based embedding have been proposed, mostly focusing on capturing hierarchical relationships; examples include vectors in Euclidean space, complex, Hyperbolic, order, and Box Embedding. Box embedding creates region-based rich representation of concepts, but along the process it sacrifices simplicity, requiring a custom-made optimization scheme for learning the representation. Hyperbolic embedding improves embedding quality by exploiting the ever-expanding property of Hyperbolic space, but it also suffers from the same fate as box embedding as gradient descent like optimization is not simple in the Hyperbolic space. In this work, we propose Binder, a novel approach for order-based representation. Binder uses binary vectors for embedding, so the embedding vectors are compact with an order of magnitude smaller footprint than other methods. Binder uses a simple and efficient optimization scheme for learning representation vectors with a linear time complexity. Our comprehensive experimental results show that Binder is very accurate, yielding competitive results on the representation task. But Binder stands out from its competitors on the transitive closure link prediction task as it can learn concept embeddings just from the direct edges, whereas all existing order-based approaches rely on the indirect edges.

Task-oriented grasping (TOG), which refers to the problem of synthesizing grasps on an object that are configurationally compatible with the downstream manipulation task, is the first milestone towards tool manipulation. Analogous to the activation of two brain regions responsible for semantic and geometric reasoning during cognitive processes, modeling the complex relationship between objects, tasks, and grasps requires rich prior knowledge about objects and tasks. Existing methods typically limit the prior knowledge to a closed-set scope and cannot support the generalization to novel objects and tasks out of the training set. To address such a limitation, we propose FoundationGrasp, a foundation model-based TOG framework that leverages the open-ended knowledge from foundation models to learn generalizable TOG skills. Comprehensive experiments are conducted on the contributed Language and Vision Augmented TaskGrasp (LaViA-TaskGrasp) dataset, demonstrating the superiority of FoudationGrasp over existing methods when generalizing to novel object instances, object classes, and tasks out of the training set. Furthermore, the effectiveness of FoudationGrasp is validated in real-robot grasping and manipulation experiments on a 7 DoF robotic arm. Our code, data, appendix, and video are publicly available at https://sites.google.com/view/foundationgrasp.

Standard Unsupervised Domain Adaptation (UDA) aims to transfer knowledge from a labeled source domain to an unlabeled target but usually requires simultaneous access to both source and target data. Moreover, UDA approaches commonly assume that source and target domains share the same labels space. Yet, these two assumptions are hardly satisfied in real-world scenarios. This paper considers the more challenging Source-Free Open-set Domain Adaptation (SF-OSDA) setting, where both assumptions are dropped. We propose a novel approach for SF-OSDA that exploits the granularity of target-private categories by segregating their samples into multiple unknown classes. Starting from an initial clustering-based assignment, our method progressively improves the segregation of target-private samples by refining their pseudo-labels with the guide of an uncertainty-based sample selection module. Additionally, we propose a novel contrastive loss, named NL-InfoNCELoss, that, integrating negative learning into self-supervised contrastive learning, enhances the model robustness to noisy pseudo-labels. Extensive experiments on benchmark datasets demonstrate the superiority of the proposed method over existing approaches, establishing new state-of-the-art performance. Notably, additional analyses show that our method is able to learn the underlying semantics of novel classes, opening the possibility to perform novel class discovery.

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood function by leveraging the fact that data can be quickly simulated from the model, but converge slowly and/or poorly in high-dimensional settings. In this paper, we propose a framework for Bayesian posterior estimation by mapping data to posteriors of parameters using a neural network trained on data simulated from the complex model. Posterior distributions of model parameters are efficiently obtained by feeding observed data into the trained neural network. We show theoretically that our posteriors converge to the true posteriors in Kullback-Leibler divergence. Our approach yields computationally efficient and theoretically justified uncertainty quantification, which is lacking in existing simulation-based neural network approaches. Comprehensive simulation studies highlight our method's robustness and accuracy.

This paper studies the geometry of binary hyperdimensional computing (HDC), a computational scheme in which data are encoded using high-dimensional binary vectors. We establish a result about the similarity structure induced by the HDC binding operator and show that the Laplace kernel naturally arises in this setting, motivating our new encoding method Laplace-HDC, which improves upon previous methods. We describe how our results indicate limitations of binary HDC in encoding spatial information from images and discuss potential solutions, including using Haar convolutional features and the definition of a translation-equivariant HDC encoding. Several numerical experiments highlighting the improved accuracy of Laplace-HDC in contrast to alternative methods are presented. We also numerically study other aspects of the proposed framework such as robustness and the underlying translation-equivariant encoding.

We propose an analytical solution for approximating the gradient of the Evidence Lower Bound (ELBO) in variational inference problems where the statistical model is a Bayesian network consisting of observations drawn from a mixture of a Gaussian distribution embedded in unrelated clutter, known as the clutter problem. The method employs the reparameterization trick to move the gradient operator inside the expectation and relies on the assumption that, because the likelihood factorizes over the observed data, the variational distribution is generally more compactly supported than the Gaussian distribution in the likelihood factors. This allows efficient local approximation of the individual likelihood factors, which leads to an analytical solution for the integral defining the gradient expectation. We integrate the proposed gradient approximation as the expectation step in an EM (Expectation Maximization) algorithm for maximizing ELBO and test against classical deterministic approaches in Bayesian inference, such as the Laplace approximation, Expectation Propagation and Mean-Field Variational Inference. The proposed method demonstrates good accuracy and rate of convergence together with linear computational complexity.

This paper explores the field of semi-supervised Fr\'echet regression, driven by the significant costs associated with obtaining non-Euclidean labels. Methodologically, we propose two novel methods: semi-supervised NW Fr\'echet regression and semi-supervised kNN Fr\'echet regression, both based on graph distance acquired from all feature instances. These methods extend the scope of existing semi-supervised Euclidean regression methods. We establish their convergence rates with limited labeled data and large amounts of unlabeled data, taking into account the low-dimensional manifold structure of the feature space. Through comprehensive simulations across diverse settings and applications to real data, we demonstrate the superior performance of our methods over their supervised counterparts. This study addresses existing research gaps and paves the way for further exploration and advancements in the field of semi-supervised Fr\'echet regression.

Relative Validity Indices (RVIs) such as the Silhouette Width Criterion, Calinski-Harabasz and Davie's Bouldin indices are the most popular tools for evaluating and optimising applications of clustering. Their ability to rank collections of candidate partitions has been used to guide the selection of the number of clusters, and to compare partitions from different clustering algorithms. Beyond these more conventional tasks, many examples can be found in the literature where RVIs have been used to compare and select other aspects of clustering approaches such as data normalisation procedures, data representation methods, and distance measures. The authors are not aware of any studies that have attempted to establish the suitability of RVIs for such comparisons. Moreover, given the impact of these aspects on pairwise similarities, it is not even immediately obvious how RVIs should be implemented when comparing these aspects. In this study, we conducted experiments with seven common RVIs on over 2.7 million clustering partitions for both synthetic and real-world datasets, encompassing feature-vector and time-series data. Our findings suggest that RVIs are not well-suited to these unconventional tasks, and that conclusions drawn from such applications may be misleading. It is recommended that normalisation procedures, representation methods, and distance measures instead be selected using external validation on high quality labelled datasets or carefully designed outcome-oriented objective criteria, both of which should be informed by relevant domain knowledge and clustering aims.