Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing non-parametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the parameter space of interest if the additional hyper-parameters are chosen well. The No-U-Turn Sampler (NUTS) is a variant of HMC which is extremely effective at selecting these hyper-parameters but is slow to run and is not suited to GPU architectures. An alternative to NUTS, Change in the Estimator of the Expected Square HMC (ChEES-HMC) was shown not only to run faster than NUTS on GPU but also sample from posteriors more efficiently. Sequential Monte Carlo (SMC) samplers are another sampling method which instead output weighted samples from the posterior. They are very amenable to parallelisation and therefore being run on GPUs while having additional flexibility in their choice of proposal over MCMC. We incorporate (ChEEs-HMC) as a proposal into SMC samplers and demonstrate competitive but faster performance than NUTS on a number of tasks.

Detecting localized density differences in multivariate data is a crucial task in computational science. Such anomalies can indicate a critical system failure, lead to a groundbreaking scientific discovery, or reveal unexpected changes in data distribution. We introduce EagleEye, an anomaly detection method to compare two multivariate datasets with the aim of identifying local density anomalies, namely over- or under-densities affecting only localised regions of the feature space. Anomalies are detected by modelling, for each point, the ordered sequence of its neighbours' membership label as a coin-flipping process and monitoring deviations from the expected behaviour of such process. A unique advantage of our method is its ability to provide an accurate, entirely unsupervised estimate of the local signal purity. We demonstrate its effectiveness through experiments on both synthetic and real-world datasets. In synthetic data, EagleEye accurately detects anomalies in multiple dimensions even when they affect a tiny fraction of the data. When applied to a challenging resonant anomaly detection benchmark task in simulated Large Hadron Collider data, EagleEye successfully identifies particle decay events present in just 0.3% of the dataset. In global temperature data, EagleEye uncovers previously unidentified, geographically localised changes in temperature fields that occurred in the most recent years. Thanks to its key advantages of conceptual simplicity, computational efficiency, trivial parallelisation, and scalability, EagleEye is widely applicable across many fields.

Quantum or quantum-inspired Ising machines have recently shown promise in solving combinatorial optimization problems in a short time. Real-world applications, such as time division multiple access (TDMA) scheduling for wireless multi-hop networks and financial trading, require solving those problems sequentially where the size and characteristics change dynamically. However, using Ising machines involves challenges to shorten system-wide latency due to the transfer of large Ising model or the cloud access and to determine the parameters for each problem. Here we show a combinatorial optimization method using embedded Ising machines, which enables solving diverse problems at high speed without runtime parameter tuning. We customize the algorithm and circuit architecture of the simulated bifurcation-based Ising machine to compress the Ising model and accelerate computation and then built a machine learning model to estimate appropriate parameters using extensive training data. In TDMA scheduling for wireless multi-hop networks, our demonstration has shown that the sophisticated system can adapt to changes in the problem and showed that it has a speed advantage over conventional methods.

A new benchmark dataset for functional data analysis (FDA) is presented, focusing on the reconstruction of eye movements from EEG data. The contribution is twofold: first, open challenges and evaluation metrics tailored to FDA applications are proposed. Second, functional neural networks are used to establish baseline results for the primary regression task of reconstructing eye movements from EEG signals. Baseline results are reported for the new dataset, based on consumer-grade hardware, and the EEGEyeNet dataset, based on research-grade hardware.

In recent years, proper scoring rules have emerged as a power ful general approach for estimating probability distributions. In addition to significantly ex panding the range of modeling techniques that can be applied in practice, this has also substantially broadened the conceptual understanding of estimation methods. Originally, proper scoring rules we re conceived in meteorology as summary statistics for describing the performance of probabilisti c forecasts ( Murphy and Winkler, 1984), but they also play an important role in economics as tools for bel ief elicitation ( Schotter and Trevino, 2014). A probabilistic forecast is a probability distribution ove r the space of the possible outcomes of the future event that is stated by the forecaster. The simple st and most popular case of probabilistic forecasts arises when the outcome is binary, so the probabilistic forecast reduces to issuing a predictive probability of success. Brier ( 1950) was the first to consider the problem of devising a scoring rule which could not be "played" by a dishonest fore casting agent. He introduced the quadratic scoring rule and showed that it incentivizes a for ecasting agent to state his most accurate probability estimate when faced with uncertainty.

The integration of high-dimensional genomic data and clinical data into time-to-event prediction models has gained significant attention due to the growing availability of these datasets. Traditionally, a Cox regression model is employed, concatenating various covariate types linearly. Given that much of the data may be redundant or irrelevant, feature selection through penalization is often desirable. A notable characteristic of these datasets is their organization into blocks of distinct data types, such as methylation and clinical predictors, which requires selecting a subset of covariates from each group due to high intra-group correlations. For this reason, we propose utilizing Exclusive Lasso regularization in place of standard Lasso penalization. We apply our methodology to a real-life cancer dataset, demonstrating enhanced survival prediction performance compared to the conventional Cox regression model.

Most knowledge graph embedding (KGE) methods tailored for link prediction focus on the entities and relations in the graph, giving little attention to other literal values, which might encode important information. Therefore, some literal-aware KGE models attempt to either integrate numerical values into the embeddings of the entities or convert these numerics into entities during preprocessing, leading to information loss. Other methods concerned with creating relation-specific numerical features assume completeness of numerical data, which does not apply to real-world graphs. In this work, we propose ReaLitE, a novel relation-centric KGE model that dynamically aggregates and merges entities' numerical attributes with the embeddings of the connecting relations. ReaLitE is designed to complement existing conventional KGE methods while supporting multiple variations for numerical aggregations, including a learnable method. We comprehensively evaluated the proposed relation-centric embedding using several benchmarks for link prediction and node classification tasks. The results showed the superiority of ReaLitE over the state of the art in both tasks.

This work has been submitted to the IEEE for possible publication. Active Learning Design: Modeling Force Output for Axisymmetric Soft Pneumatic Actuators Gregory M. Campbell, Gentian Muhaxheri, Leonardo Ferreira Guilhoto, Christian D. Santangelo, Paris Perdikaris, James Pikul, and Mark Yim Abstract --Soft pneumatic actuators (SPA) made from elas-tomeric materials can provide large strain and large force. The behavior of locally strain-restricted hyperelastic materials under inflation has been investigated thoroughly for shape reconfiguration, but requires further investigation for trajectories involving external force. In this work we model force-pressure-height relationships for a concentrically strain-limited class of soft pneumatic actuators and demonstrate the use of this model to design SPA response for object lifting. We predict relationships under different loadings by solving energy minimization equations and verify this theory by using an automated test rig to collect rich data for n=22 Ecoflex 00-30 membranes. We collect this data using an active learning pipeline to efficiently model the design space. We show that this learned material model outperforms the theory-based model and naive curve-fitting approaches. We use our model to optimize membrane design for different lift tasks and compare this performance to other designs. These contributions represent a step towards understanding the natural response for this class of actuator and embodying intelligent lifts in a single-pressure input actuator system. Keywords: Soft Robot Materials and Design, Hydraulic/Pneumatic Actuators, Active Learning, Hyperelastic Rubbers I. INTRODUCTION Soft actuators are promising for physical human-robot interaction in large part due to their compliance.

Multi-modal optimization involves identifying multiple global and local optima of a function, offering valuable insights into diverse optimal solutions within the search space. Evolutionary algorithms (EAs) excel at finding multiple solutions in a single run, providing a distinct advantage over classical optimization techniques that often require multiple restarts without guarantee of obtaining diverse solutions. Among these EAs, differential evolution (DE) stands out as a powerful and versatile optimizer for continuous parameter spaces. DE has shown significant success in multi-modal optimization by utilizing its population-based search to promote the formation of multiple stable subpopulations, each targeting different optima. Recent advancements in DE for multi-modal optimization have focused on niching methods, parameter adaptation, hybridization with other algorithms including machine learning, and applications across various domains. Given these developments, it is an opportune moment to present a critical review of the latest literature and identify key future research directions. This paper offers a comprehensive overview of recent DE advancements in multimodal optimization, including methods for handling multiple optima, hybridization with EAs, and machine learning, and highlights a range of real-world applications. Additionally, the paper outlines a set of compelling open problems and future research issues from multiple perspectives

Reconstructing and decomposing dynamic urban scenes is crucial for autonomous driving, urban planning, and scene editing. However, existing methods fail to perform instance-aware decomposition without manual annotations, which is crucial for instance-level scene editing.We propose UnIRe, a 3D Gaussian Splatting (3DGS) based approach that decomposes a scene into a static background and individual dynamic instances using only RGB images and LiDAR point clouds. At its core, we introduce 4D superpoints, a novel representation that clusters multi-frame LiDAR points in 4D space, enabling unsupervised instance separation based on spatiotemporal correlations. These 4D superpoints serve as the foundation for our decomposed 4D initialization, i.e., providing spatial and temporal initialization to train a dynamic 3DGS for arbitrary dynamic classes without requiring bounding boxes or object templates.Furthermore, we introduce a smoothness regularization strategy in both 2D and 3D space, further improving the temporal stability.Experiments on benchmark datasets show that our method outperforms existing methods in decomposed dynamic scene reconstruction while enabling accurate and flexible instance-level editing, making it a practical solution for real-world applications.