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.

We provide the largest compiled publicly available dictionaries of first, middle, and last names for the purpose of imputing race and ethnicity using, for example, Bayesian Improved Surname Geocoding (BISG). The dictionaries are based on the voter files of six Southern states that collect self-reported racial data upon voter registration. Our data cover a much larger scope of names than any comparable dataset, containing roughly one million first names, 1.1 million middle names, and 1.4 million surnames. Individuals are categorized into five mutually exclusive racial and ethnic groups -- White, Black, Hispanic, Asian, and Other -- and racial/ethnic counts by name are provided for every name in each dictionary. Counts can then be normalized row-wise or column-wise to obtain conditional probabilities of race given name or name given race. These conditional probabilities can then be deployed for imputation in a data analytic task for which ground truth racial and ethnic data is not available.

The purpose of this review is to introduce the reader to graph kernels and the corresponding literature, with an emphasis on those with direct application to chemoinformatics. Graph kernels are functions that allow for the inference of properties of molecules and compounds, which can help with tasks such as finding suitable compounds in drug design. The use of kernel methods is but one particular way two quantify similarity between graphs. We restrict our discussion to this one method, although popular alternatives have emerged in recent years, most notably graph neural networks.

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.

Rail breaks are one of the most common causes of derailments internationally. This is no different for the South African Iron Ore line. Many rail breaks occur as a heavy-haul train passes over a crack, large defect or defective weld. In such cases, it is usually too late for the train to slow down in time to prevent a de-railment. Knowing the risk of a rail break occurring associated with a train passing over a section of rail allows for better implementation of maintenance initiatives and mitigating measures. In this paper the Ore Line's specific challenges are discussed and the currently available data that can be used to create a rail break risk prediction model is reviewed. The development of a basic rail break risk prediction model for the Ore Line is then presented. Finally the insight gained from the model is demonstrated by means of discussing various scenarios of various rail break risk. In future work, we are planning on extending this basic model to allow input from live monitoring systems such as the ultrasonic broken rail detection system.

The eigendecomposition of a matrix is the central procedure in probabilistic models based on matrix factorization, for instance principal component analysis and topic models. Quantifying the uncertainty of such a decomposition based on a finite sample estimate is essential to reasoning under uncertainty when employing such models. This paper tackles the challenge of computing confidence bounds on the individual entries of eigenvectors of a covariance matrix of fixed dimension. Moreover, we derive a method to bound the entries of the inverse covariance matrix, the so-called precision matrix. The assumptions behind our method are minimal and require that the covariance matrix exists, and its empirical estimator converges to the true covariance. We make use of the theory of U-statistics to bound the $L_2$ perturbation of the empirical covariance matrix. From this result, we obtain bounds on the eigenvectors using Weyl's theorem and the eigenvalue-eigenvector identity and we derive confidence intervals on the entries of the precision matrix using matrix inversion perturbation bounds. As an application of these results, we demonstrate a new statistical test, which allows us to test for non-zero values of the precision matrix. We compare this test to the well-known Fisher-z test for partial correlations, and demonstrate the soundness and scalability of the proposed statistical test, as well as its application to real-world data from medical and physics domains.