This paper describes a new approach for learning structures of large Bayesian networks based on blocks resulting from feature space clustering. This clustering is obtained using normalized mutual information. And the subsequent aggregation of blocks is done using classical learning methods except that they are input with compressed information about combinations of feature values for each block. Validation of this approach is done for Hill-Climbing as a graph enumeration algorithm for two score functions: BIC and MI. In this way, potentially parallelizable block learning can be implemented even for those score functions that are considered unsuitable for parallelizable learning. The advantage of the approach is evaluated in terms of speed of work as well as the accuracy of the found structures.

The labels used to train machine learning (ML) models are of paramount importance. Typically for ML classification tasks, datasets contain hard labels, yet learning using soft labels has been shown to yield benefits for model generalization, robustness, and calibration. Earlier work found success in forming soft labels from multiple annotators' hard labels; however, this approach may not converge to the best labels and necessitates many annotators, which can be expensive and inefficient. We focus on efficiently eliciting soft labels from individual annotators. We collect and release a dataset of soft labels (which we call CIFAR-10S) over the CIFAR-10 test set via a crowdsourcing study (N=248). We demonstrate that learning with our labels achieves comparable model performance to prior approaches while requiring far fewer annotators -- albeit with significant temporal costs per elicitation. Our elicitation methodology therefore shows nuanced promise in enabling practitioners to enjoy the benefits of improved model performance and reliability with fewer annotators, and serves as a guide for future dataset curators on the benefits of leveraging richer information, such as categorical uncertainty, from individual annotators.

This paper studies distributed Bayesian learning in a setting encompassing a central server and multiple workers by focusing on the problem of mitigating the impact of stragglers. The standard one-shot, or embarrassingly parallel, Bayesian learning protocol known as consensus Monte Carlo (CMC) is generalized by proposing two straggler-resilient solutions based on grouping and coding. Two main challenges in designing straggler-resilient algorithms for CMC are the need to estimate the statistics of the workers' outputs across multiple shots, and the joint non-linear post-processing of the outputs of the workers carried out at the server. This is in stark contrast to other distributed settings like gradient coding, which only require the per-shot sum of the workers' outputs. The proposed methods, referred to as Group-based CMC (G-CMC) and Coded CMC (C-CMC), leverage redundant computing at the workers in order to enable the estimation of global posterior samples at the server based on partial outputs from the workers. Simulation results show that C-CMC may outperform G-CMC for a small number of workers, while G-CMC is generally preferable for a larger number of workers.

Quantum state tomography (QST), the task of estimating an unknown quantum state given measurement outcomes, is essential to building reliable quantum computing devices. Whereas computing the maximum-likelihood (ML) estimate corresponds to solving a finite-sum convex optimization problem, the objective function is not smooth nor Lipschitz, so most existing convex optimization methods lack sample complexity guarantees; moreover, both the sample size and dimension grow exponentially with the number of qubits in a QST experiment, so a desired algorithm should be highly scalable with respect to the dimension and sample size, just like stochastic gradient descent. In this paper, we propose a stochastic first-order algorithm that computes an $\varepsilon$-approximate ML estimate in $O( ( D \log D ) / \varepsilon ^ 2 )$ iterations with $O( D^3 )$ per-iteration time complexity, where $D$ denotes the dimension of the unknown quantum state and $\varepsilon$ denotes the optimization error. Our algorithm is an extension of Soft-Bayes to the quantum setup.

The understanding of how users in a network update their opinions based on their neighbours opinions has attracted a great deal of interest in the field of network science, and a growing body of literature recognises the significance of this issue. In this research paper, we propose a new dynamic model of opinion formation in directed networks. In this model, the opinion of each node is updated as the weighted average of its neighbours opinions, where the weights represent social influence. We define a new centrality measure as a social influence metric based on both influence and conformity. We measure this new approach using two opinion formation models: (i) the Degroot model and (ii) our own proposed model. Previously published research studies have not considered conformity, and have only considered the influence of the nodes when computing the social influence. In our definition, nodes with low in-degree and high out-degree that were connected to nodes with high out-degree and low in-degree had higher centrality. As the main contribution of this research, we propose an algorithm for finding a small subset of nodes in a social network that can have a significant impact on the opinions of other nodes. Experiments on real-world data demonstrate that the proposed algorithm significantly outperforms previously published state-of-the-art methods.

We develop the compositional theory of active inference by introducing activity, functorially relating statistical games to the dynamical systems which play them, using the new notion of approximate inference doctrine. In order to exhibit such functors, we first develop the necessary theory of dynamical systems, using a generalization of the language of polynomial functors to supply compositional interfaces of the required types: with the resulting polynomially indexed categories of coalgebras, we construct monoidal bicategories of differential and dynamical "hierarchical inference systems", in which approximate inference doctrines have semantics. We then describe "externally parameterized" statistical games, and use them to construct two approximate inference doctrines found in the computational neuroscience literature, which we call the Laplace' and the Hebb-Laplace' doctrines: the former produces dynamical systems which optimize the posteriors of Gaussian models; and the latter produces systems which additionally optimize the parameters (or weights') which determine their predictions.

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This second paper presents a literature review of key enabling technologies of digital twins, with an emphasis on uncertainty quantification, optimization methods, open source datasets and tools, major findings, challenges, and future directions. Discussions focus on current methods of uncertainty quantification and optimization and how they are applied in different dimensions of a digital twin. Additionally, this paper presents a case study where a battery digital twin is constructed and tested to illustrate some of the modeling and twinning methods reviewed in this two-part review. Code and preprocessed data for generating all the results and figures presented in the case study are available on GitHub.

High utility itemset mining approaches discover hidden patterns from large amounts of temporal data. However, an inescapable problem of high utility itemset mining is that its discovered results hide the quantities of patterns, which causes poor interpretability. The results only reflect the shopping trends of customers, which cannot help decision makers quantify collected information. In linguistic terms, computers use mathematical or programming languages that are precisely formalized, but the language used by humans is always ambiguous. In this paper, we propose a novel one-phase temporal fuzzy utility itemset mining approach called TFUM. It revises temporal fuzzy-lists to maintain less but major information about potential high temporal fuzzy utility itemsets in memory, and then discovers a complete set of real interesting patterns in a short time. In particular, the remaining measure is the first adopted in the temporal fuzzy utility itemset mining domain in this paper. The remaining maximal temporal fuzzy utility is a tighter and stronger upper bound than that of previous studies adopted. Hence, it plays an important role in pruning the search space in TFUM. Finally, we also evaluate the efficiency and effectiveness of TFUM on various datasets. Extensive experimental results indicate that TFUM outperforms the state-of-the-art algorithms in terms of runtime cost, memory usage, and scalability. In addition, experiments prove that the remaining measure can significantly prune unnecessary candidates during mining.

We consider learning and compositionality as the key mechanisms towards simulating human-like intelligence. While each mechanism is successfully achieved by neural networks and symbolic AIs, respectively, it is the combination of the two mechanisms that makes human-like intelligence possible. Despite the numerous attempts on building hybrid neuralsymbolic systems, we argue that our true goal should be unifying learning and compositionality, the core mechanisms, instead of neural and symbolic methods, the surface approaches to achieve them. In this work, we review and analyze the strengths and weaknesses of neural and symbolic methods by separating their forms and meanings (structures and semantics), and propose Connectionist Probabilistic Programs (CPPs), a framework that connects connectionist structures (for learning) and probabilistic program semantics (for compositionality). Under the framework, we design a CPP extension for small scale sequence modeling and provide a learning algorithm based on Bayesian inference. Although challenges exist in learning complex patterns without supervision, our early results demonstrate CPP's successful extraction of concepts and relations from raw sequential data, an initial step towards compositional learning.

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance matrix. To circumvent this, mixtures of Gaussian process experts have been considered where data points are assigned to independent experts, reducing the complexity by allowing inference based on smaller, local covariance matrices. Moreover, mixtures of Gaussian process experts substantially enrich the model's flexibility, allowing for behaviors such as non-stationarity, heteroscedasticity, and discontinuities. In this work, we construct a novel inference approach based on nested sequential Monte Carlo samplers to simultaneously infer both the gating network and Gaussian process expert parameters. This greatly improves inference compared to importance sampling, particularly in settings when a stationary Gaussian process is inappropriate, while still being thoroughly parallelizable.