Driven by the critical needs of biomanufacturing 4.0, we introduce a probabilistic knowledge graph hybrid model characterizing the risk- and science-based understanding of bioprocess mechanisms. It can faithfully capture the important properties, including nonlinear reactions, partially observed state, and nonstationary dynamics. Given very limited real process observations, we derive a posterior distribution quantifying model estimation uncertainty. To avoid the evaluation of intractable likelihoods, Approximate Bayesian Computation sampling with Sequential Monte Carlo (ABC-SMC) is utilized to approximate the posterior distribution. Under high stochastic and model uncertainties, it is computationally expensive to match output trajectories. Therefore, we create a linear Gaussian dynamic Bayesian network (LG-DBN) auxiliary likelihood-based ABC-SMC approach. Through matching the summary statistics driven through LG-DBN likelihood that can capture critical interactions and variations, the proposed algorithm can accelerate hybrid model inference, support process monitoring, and facilitate mechanism learning and robust control.

Low-dose computed tomography (LDCT) is an important topic in the field of radiology over the past decades. LDCT reduces ionizing radiation-induced patient health risks but it also results in a low signal-to-noise ratio (SNR) and a potential compromise in the diagnostic performance. In this paper, to improve the LDCT denoising performance, we introduce the conditional denoising diffusion probabilistic model (DDPM) and show encouraging results with a high computational efficiency. Specifically, given the high sampling cost of the original DDPM model, we adapt the fast ordinary differential equation (ODE) solver for a much-improved sampling efficiency. The experiments show that the accelerated DDPM can achieve 20x speedup without compromising image quality.

This paper is concerned with forecast error, particularly in relation to loss reserving. This is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and the likelihood of observed data. A posterior on the model set, conditional on the data, results, and an estimate of model error (contained in a loss reserve) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be thinner than desired, and bootstrapping of the LASSO is used to gain bulk. This provides the bonus of an estimate of parameter error also. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving.

This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical concepts; (2) the potentials and links between fuzzy logic and probability logic that have not been discussed in one document in literature; (3) representation of real-life random and fuzzy uncertainties and ambiguities that arise in data-driven real-life problems, due to uncertain mathematical and vague verbal terms in datasets.

Multilevel data are prevalent in many real-world applications. However, it remains an open research problem to identify and justify a class of models that flexibly capture a wide range of multilevel data. Motivated by the versatility of the mixture of experts (MoE) models in fitting regression data, in this article we extend upon the MoE and study a class of mixed MoE (MMoE) models for multilevel data. Under some regularity conditions, we prove that the MMoE is dense in the space of any continuous mixed effects models in the sense of weak convergence. As a result, the MMoE has a potential to accurately resemble almost all characteristics inherited in multilevel data, including the marginal distributions, dependence structures, regression links, random intercepts and random slopes. In a particular case where the multilevel data is hierarchical, we further show that a nested version of the MMoE universally approximates a broad range of dependence structures of the random effects among different factor levels.

A new index for internal evaluation of clustering is introduced. The index is defined as a mixture of two sub-indices. The first sub-index $ I_a $ is called the Ambiguous Index; the second sub-index $ I_s $ is called the Similarity Index. Calculation of the two sub-indices is based on density estimation to each cluster of a partition of the data. An experiment is conducted to test the performance of the new index, and compared with six other internal clustering evaluation indices -- Calinski-Harabasz index, Silhouette coefficient, Davies-Bouldin index, CDbw, DBCV, and VIASCKDE, on a set of 145 datasets. The result shows the new index significantly improves other internal clustering evaluation indices.

Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on non-probabilistic neural networks which by default do not capture this inherent uncertainty. This well-known problem has led to the development of post-hoc calibration procedures, such as Platt scaling (logistic), isotonic and beta calibration, which transforms the scores into well calibrated empirical probabilities. A plausible alternative to the calibration approach is to use Bayesian neural networks, which directly models a predictive distribution. Although they have been applied to images and text datasets, they have seen limited adoption in the tabular and small data regime. In this paper, we demonstrate that Bayesian neural networks yields competitive performance when compared to calibrated neural networks and conduct experiments across a wide array of datasets.

Search-and-rescue (SaR) in unknown environments requires precise, optimal, and fast decisions. Robots are promising candidates for autonomously performing SaR tasks in unknown environments. While humans use their heuristics to effectively deal with uncertainties, optimisation of multiple objectives in the presence of physical and control constraints is a mathematical challenge that requires machine computations. Thus having both human-inspired and mathematical control capabilities is desired for SaR robots. Moreover, coordinating the decisions of robots with little computation cost in large-scale SaR missions is an open challenge. Finally, in real-life data perceived by SaR robots may be prone to uncertainties. We introduce a hierarchical multi-agent control architecture that exploits non-homogeneous and imperfect perception capabilities of SaR robots, as well as the computational efficiency and robustness to failure of decentralised control methods and global performance improvement of centralised control methods. The integrated structure of the proposed control framework allows to combine human-inspired and mathematical decision making methods in a coordinated and computationally efficient way. The results of various computer-based simulations show that while the area coverage of the proposed approach is comparable to existing heuristic methods that are particularly developed for coverage-oriented SaR, the efficiency of the introduced approach in locating the trapped victims is significantly higher. Furthermore, with comparable computation times, the proposed control approach successfully avoids potential conflicts that exist in non-cooperative methods. These results confirm that the proposed multi-agent control system is capable of combining coverage-oriented and target-oriented SaR in a balanced and coordinated way.

We address object tracking by radar and the robustness of the current state-of-the-art methods to process outliers. The standard tracking algorithms extract detections from radar image space to use it in the filtering stage. Filtering is performed by a Kalman filter, which assumes Gaussian distributed noise. However, this assumption does not account for large modeling errors and results in poor tracking performance during abrupt motions. We take the Gaussian Sum Filter (single-object variant of the Multi Hypothesis Tracker) as our baseline and propose a modification by modelling process noise with a distribution that has heavier tails than a Gaussian. Variational Bayes provides a fast, computationally cheap inference algorithm. Our simulations show that - in the presence of process outliers - the robust tracker outperforms the Gaussian Sum filter when tracking single objects.

Over the course of the last several years, a significant amount of scholarly attention has been drawn to the issue of feature selection. At a high level, feature selection can be considered as a branch of reducing data dimensionality of which the two primary methods are feature learning and feature selection. The problem of feature learning involves the creation of new features from the original data. In contrast, the feature selection problem does not change the original representation of the data variables, so the physical meaning of each variable is preserved. To be more specific, the feature selection problem can be subdivided into two scenarios: supervised and unsupervised. Since we do not have target variables, selecting unsupervised features is more challenging. Typically, the unsupervised feature selection relies on matrix decomposition (Cheng et al., 2005; Liberty et al., 2007; Martinsson et al., 2011; Lu, 2022a), filter (Dash et al., 2002), and embeddings (Dy & Brodley, 2004; Hou et al., 2011). On the other hand, matrix decomposition algorithms such as QR decomposition, and singular value decomposition have been used extensively over the years to reveal hidden structures of data matrices in scientific and engineering areas such as collaborative filtering (Marlin, 2003; Lim & Teh, 2007; Mnih & Salakhutdinov, 2007; Lu, 2022c;a), recommendation systems (Lu, 2022c), clustering and classification (Li et al., 2009; Wang et al., 2013).