Group decision-making (GDM) characterized by complexity and uncertainty is an essential part of various life scenarios. Most existing researches lack tools to fuse information quickly and interpret decision results for partially formed decisions. This limitation is particularly noticeable when there is a need to improve the efficiency of GDM. To address this issue, a novel multi-level sequential three-way decision for group decision-making (S3W-GDM) method is constructed from the perspective of granular computing. This method simultaneously considers the vagueness, hesitation, and variation of GDM problems under double hierarchy hesitant fuzzy linguistic term sets (DHHFLTS) environment. First, for fusing information efficiently, a novel multi-level expert information fusion method is proposed, and the concepts of expert decision table and the extraction/aggregation of decision-leveled information based on the multi-level granularity are defined. Second, the neighborhood theory, outranking relation and regret theory (RT) are utilized to redesign the calculations of conditional probability and relative loss function. Then, the granular structure of DHHFLTS based on the sequential three-way decision (S3WD) is defined to improve the decision-making efficiency, and the decision-making strategy and interpretation of each decision-level are proposed. Furthermore, the algorithm of S3W-GDM is given. Finally, an illustrative example of diagnosis is presented, and the comparative and sensitivity analysis with other methods are performed to verify the efficiency and rationality of the proposed method.

The prosperity of machine learning has also brought people's concerns about data privacy. Among them, inference attacks can implement privacy breaches in various MLaaS scenarios and model training/prediction phases. Specifically, inference attacks can perform privacy inference on undisclosed target training sets based on outputs of the target model, including but not limited to statistics, membership, semantics, data representation, etc. For instance, infer whether the target data has the characteristics of AIDS. In addition, the rapid development of the machine learning community in recent years, especially the surge of model types and application scenarios, has further stimulated the inference attacks' research. Thus, studying inference attacks and analyzing them in depth is urgent and significant. However, there is still a gap in the systematic discussion of inference attacks from taxonomy, global perspective, attack, and defense perspectives. This survey provides an in-depth and comprehensive inference of attacks and corresponding countermeasures in ML-as-a-service based on taxonomy and the latest researches. Without compromising researchers' intuition, we first propose the 3MP taxonomy based on the community research status, trying to normalize the confusing naming system of inference attacks. Also, we analyze the pros and cons of each type of inference attack, their workflow, countermeasure, and how they interact with other attacks. In the end, we point out several promising directions for researchers from a more comprehensive and novel perspective.

The Kalman Filter (KF) is a powerful mathematical tool widely used for state estimation in various domains, including Simultaneous Localization and Mapping (SLAM). This paper presents an in-depth introduction to the Kalman Filter and explores its several extensions: the Extended Kalman Filter (EKF), the Error-State Kalman Filter (ESKF), the Iterated Extended Kalman Filter (IEKF), and the Iterated Error-State Kalman Filter (IESKF). Each variant is meticulously examined, with detailed derivations of their mathematical formulations and discussions on their respective advantages and limitations. By providing a comprehensive overview of these techniques, this paper aims to offer valuable insights into their applications in SLAM and enhance the understanding of state estimation methodologies in complex environments.

Discovering causal structures in data is a challenging task. Ideally, we would like to input the data into an algorithm that outputs one or more plausible causal directed acyclic graphs (DAGs) linking the variables in the data. Such data driven approaches for estimating a causal DAG are known as causal discovery (or causal search, structure learning etc.). While algorithms for causal discovery were first developed in the field of computer science more than twenty years ago [1] and have, since then, continually been generalised and refined [2], their use with biomedical or epidemiological data is still rare (other than in genetics [3]). Exceptions are, for example, two applications of causal discovery to data from cohort studies finding that modifiable risk factors in early childhood or early life have mostly indirect, if any, causal relations with later health outcomes[4, 5]. Similarly, in an analysis of healthcare data considering cardiac surgery it was found that many of the known predictors were in fact only indirect causes of postoperative length of stay [6]. Also, it has been suggested to use causal discovery to improve the quality of care for hip replacement patients by investigating the complex clinical performance of implants with data from large patient registries [7]. Typical causal analyses often aim at causal effect estimation. In contrast to the above, such analyses typically assume the causal structure, i.e. the DAG, to be given, usually derived from domain

Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating population densities in a geographic region, a small Wasserstein distance means that the estimate is able to capture roughly where the population mass is. In this work we study differentially private density estimation in the Wasserstein distance. We design and analyze instance-optimal algorithms for this problem that can adapt to easy instances. For distributions $P$ over $\mathbb{R}$, we consider a strong notion of instance-optimality: an algorithm that uniformly achieves the instance-optimal estimation rate is competitive with an algorithm that is told that the distribution is either $P$ or $Q_P$ for some distribution $Q_P$ whose probability density function (pdf) is within a factor of 2 of the pdf of $P$. For distributions over $\mathbb{R}^2$, we use a different notion of instance optimality. We say that an algorithm is instance-optimal if it is competitive with an algorithm that is given a constant-factor multiplicative approximation of the density of the distribution. We characterize the instance-optimal estimation rates in both these settings and show that they are uniformly achievable (up to polylogarithmic factors). Our approach for $\mathbb{R}^2$ extends to arbitrary metric spaces as it goes via hierarchically separated trees. As a special case our results lead to instance-optimal private learning in TV distance for discrete distributions.

Agent-based models (ABM) provide an excellent framework for modeling outbreaks and interventions in epidemiology by explicitly accounting for diverse individual interactions and environments. However, these models are usually stochastic and highly parametrized, requiring precise calibration for predictive performance. When considering realistic numbers of agents and properly accounting for stochasticity, this high dimensional calibration can be computationally prohibitive. This paper presents a random forest based surrogate modeling technique to accelerate the evaluation of ABMs and demonstrates its use to calibrate an epidemiological ABM named CityCOVID via Markov chain Monte Carlo (MCMC). The technique is first outlined in the context of CityCOVID's quantities of interest, namely hospitalizations and deaths, by exploring dimensionality reduction via temporal decomposition with principal component analysis (PCA) and via sensitivity analysis. The calibration problem is then presented and samples are generated to best match COVID-19 hospitalization and death numbers in Chicago from March to June in 2020. These results are compared with previous approximate Bayesian calibration (IMABC) results and their predictive performance is analyzed showing improved performance with a reduction in computation.

We consider the problem of selecting an optimal subset of information sources for a hypothesis testing/classification task where the goal is to identify the true state of the world from a finite set of hypotheses, based on finite observation samples from the sources. In order to characterize the learning performance, we propose a misclassification penalty framework, which enables nonuniform treatment of different misclassification errors. In a centralized Bayesian learning setting, we study two variants of the subset selection problem: (i) selecting a minimum cost information set to ensure that the maximum penalty of misclassifying the true hypothesis is below a desired bound and (ii) selecting an optimal information set under a limited budget to minimize the maximum penalty of misclassifying the true hypothesis. Under certain assumptions, we prove that the objective (or constraints) of these combinatorial optimization problems are weak (or approximate) submodular, and establish high-probability performance guarantees for greedy algorithms. Further, we propose an alternate metric for information set selection which is based on the total penalty of misclassification. We prove that this metric is submodular and establish near-optimal guarantees for the greedy algorithms for both the information set selection problems. Finally, we present numerical simulations to validate our theoretical results over several randomly generated instances.

In sampling tasks, it is common for target distributions to be known up to a normalising constant. However, in many situations, evaluating even the unnormalised distribution can be costly or infeasible. This issue arises in scenarios such as sampling from the Bayesian posterior for tall datasets and the 'doubly-intractable' distributions. In this paper, we begin by observing that seemingly different Markov chain Monte Carlo (MCMC) algorithms, such as the exchange algorithm, PoissonMH, and TunaMH, can be unified under a simple common procedure. We then extend this procedure into a novel framework that allows the use of auxiliary variables in both the proposal and acceptance-rejection steps. We develop the theory of the new framework, applying it to existing algorithms to simplify and extend their results. Several new algorithms emerge from this framework, with improved performance demonstrated on both synthetic and real datasets.

Determining the chronology of ancient handwritten manuscripts is essential for reconstructing the evolution of ideas. For the Dead Sea Scrolls, this is particularly important. However, there is an almost complete lack of date-bearing manuscripts evenly distributed across the timeline and written in similar scripts available for palaeographic comparison. Here, we present Enoch, a state-of-the-art AI-based date-prediction model, trained on the basis of new radiocarbon-dated samples of the scrolls. Enoch uses established handwriting-style descriptors and applies Bayesian ridge regression. The challenge of this study is that the number of radiocarbon-dated manuscripts is small, while current machine learning requires an abundance of training data. We show that by using combined angular and allographic writing style feature vectors and applying Bayesian ridge regression, Enoch could predict the radiocarbon-based dates from style, supported by leave-one-out validation, with varied MAEs of 27.9 to 30.7 years relative to the radiocarbon dating. Enoch was then used to estimate the dates of 135 unseen manuscripts, revealing that 79 per cent of the samples were considered 'realistic' upon palaeographic post-hoc evaluation. We present a new chronology of the scrolls. The radiocarbon ranges and Enoch's style-based predictions are often older than the traditionally assumed palaeographic estimates. In the range of 300-50 BCE, Enoch's date prediction provides an improved granularity. The study is in line with current developments in multimodal machine-learning techniques, and the methods can be used for date prediction in other partially-dated manuscript collections. This research shows how Enoch's quantitative, probability-based approach can be a tool for palaeographers and historians, re-dating ancient Jewish key texts and contributing to current debates on Jewish and Christian origins.

Accurate segmentation of tumors in PET/CT images is important in computer-aided diagnosis and treatment of cancer. The key issue of such a segmentation problem lies in the effective integration of complementary information from PET and CT images. However, the quality of PET and CT images varies widely in clinical settings, which leads to uncertainty in the modality information extracted by networks. To take the uncertainty into account in multi-modal information fusion, this paper proposes a novel Multi-modal Evidential Fusion Network (MEFN) comprising a Cross-Modal Feature Learning (CFL) module and a Multi-modal Trusted Fusion (MTF) module. The CFL module reduces the domain gap upon modality conversion and highlights common tumor features, thereby alleviating the needs of the segmentation module to handle modality specificity. The MTF module utilizes mutual attention mechanisms and an uncertainty calibrator to fuse modality features based on modality uncertainty and then fuse the segmentation results under the guidance of Dempster-Shafer Theory. Besides, a new uncertainty perceptual loss is introduced to force the model focusing on uncertain features and hence improve its ability to extract trusted modality information. Extensive comparative experiments are conducted on two publicly available PET/CT datasets to evaluate the performance of our proposed method whose results demonstrate that our MEFN significantly outperforms state-of-the-art methods with improvements of 2.15% and 3.23% in DSC scores on the AutoPET dataset and the Hecktor dataset, respectively. More importantly, our model can provide radiologists with credible uncertainty of the segmentation results for their decision in accepting or rejecting the automatic segmentation results, which is particularly important for clinical applications. Our code will be available at https://github.com/QPaws/MEFN.