Data increasingly take the form of a multi-way array, or tensor, in several biomedical domains. Such tensors are often incompletely observed. For example, we are motivated by longitudinal microbiome studies in which several timepoints are missing for several subjects. There is a growing literature on missing data imputation for tensors. However, existing methods give a point estimate for missing values without capturing uncertainty. We propose a multiple imputation approach for tensors in a flexible Bayesian framework, that yields realistic simulated values for missing entries and can propagate uncertainty through subsequent analyses. Our model uses efficient and widely applicable conjugate priors for a CANDECOMP/PARAFAC (CP) factorization, with a separable residual covariance structure. This approach is shown to perform well with respect to both imputation accuracy and uncertainty calibration, for scenarios in which either single entries or entire fibers of the tensor are missing. For two microbiome applications, it is shown to accurately capture uncertainty in the full microbiome profile at missing timepoints and used to infer trends in species diversity for the population. Documented R code to perform our multiple imputation approach is available at https://github.com/lockEF/MultiwayImputation .

BART Bayesian Additive Regression Trees (BART) is a nonparametric Bayesian regression method, introduced by Chipman, George, and McCulloch (2006, 2010). It defines a prior distribution over the space of functions by representing them as a sum of binary decision trees, and then specifying a stochastic tree generation process. The posterior is then obtained with Metropolis-Gibbs sampling over the trees. See Hill, Linero, and Murray (2020) for a review, and Daniels, Linero, and Roy (2023, ch. 5) for a textbook treatment. BART's success BART has proven empirically effective, and is gaining popularity (consider, e.g., Tan and Roy 2019). The Atlantic Causal Inference Conference (ACIC) Data Challenge has confirmed BART as one of the best regression methods for causal inference (Dorie et al. 2019; Gruber et al. 2019; Hahn, Dorie, and Murray 2019; Thal and Finucane 2023). Many BART variants have been developed throughout the years, adding features such as variable selection (Linero 2018).

Causal discovery is essential for understanding relationships among variables of interest in many scientific domains. In this paper, we focus on permutation-based methods for learning causal graphs in Linear Gaussian Acyclic Models (LiGAMs), where the permutation encodes a causal ordering of the variables. Existing methods in this setting are not scalable due to their high computational complexity. These methods are comprised of two main components: (i) constructing a specific DAG, $\mathcal{G}^\pi$, for a given permutation $\pi$, which represents the best structure that can be learned from the available data while adhering to $\pi$, and (ii) searching over the space of permutations (i.e., causal orders) to minimize the number of edges in $\mathcal{G}^\pi$. We introduce QWO, a novel approach that significantly enhances the efficiency of computing $\mathcal{G}^\pi$ for a given permutation $\pi$. QWO has a speed-up of $O(n^2)$ ($n$ is the number of variables) compared to the state-of-the-art BIC-based method, making it highly scalable. We show that our method is theoretically sound and can be integrated into existing search strategies such as GRASP and hill-climbing-based methods to improve their performance.

Stein variational gradient descent (SVGD) [Liu and Wang, 2016] performs approximate Bayesian inference by representing the posterior with a set of particles. However, SVGD suffers from variance collapse, i.e. poor predictions due to underestimating uncertainty [Ba et al., 2021], even for moderately-dimensional models such as small Bayesian neural networks (BNNs). To address this issue, we generalize SVGD by letting each particle parameterize a component distribution in a mixture model. Our method, Stein Mixture Inference (SMI), optimizes a lower bound to the evidence (ELBO) and introduces user-specified guides parameterized by particles. SMI extends the Nonlinear SVGD framework [Wang and Liu, 2019] to the case of variational Bayes. SMI effectively avoids variance collapse, judging by a previously described test developed for this purpose, and performs well on standard data sets. In addition, SMI requires considerably fewer particles than SVGD to accurately estimate uncertainty for small BNNs. The synergistic combination of NSVGD, ELBO optimization and user-specified guides establishes a promising approach towards variational Bayesian inference in the case of tall and wide data.

Hyperparameters are configuration variables controlling the behavior of machine learning algorithms. They are ubiquitous in machine learning and artificial intelligence and the choice of their values determine the effectiveness of systems based on these technologies. Manual hyperparameter search is often unsatisfactory and becomes unfeasible when the number of hyperparameters is large. Automating the search is an important step towards automating machine learning, freeing researchers and practitioners alike from the burden of finding a good set of hyperparameters by trial and error. In this survey, we present a unified treatment of hyperparameter optimization, providing the reader with examples and insights into the state-of-the-art. We cover the main families of techniques to automate hyperparameter search, often referred to as hyperparameter optimization or tuning, including random and quasi-random search, bandit-, model- and gradient- based approaches. We further discuss extensions, including online, constrained, and multi-objective formulations, touch upon connections with other fields such as meta-learning and neural architecture search, and conclude with open questions and future research directions.

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable flexible representations of complex relationships between variables. They serve as a mechanism for efficiently transferring the representation of a distribution downstream to other tasks, such as hypothesis testing or causal effect estimation. In the context of causal inference, the main challenges include identifying causal associations and estimating the average treatment effect from observational data, where confounding variables may obscure direct cause-and-effect relationships. Kernel embeddings provide a robust nonparametric framework for addressing these challenges. They allow for the representations of distributions of observational data and their seamless transformation into representations of interventional distributions to estimate relevant causal quantities.

In complex systems, processes operate across multiple time scales, such as rapid fluctuations in environmental conditions, intermediate responses like population dynamics, and slower shifts such as ecosystem succession or climate change. These dynamics are often nested, with fast processes embedded within slower ones. Fine-scale, rapid changes can accumulate over time to influence large-scale trends, while slower processes provide the conditions for fast dynamics to unfold. This interplay between processes at different time scales can lead to transient behaviors, where a system remains in one dynamic state for an extended period before abruptly shifting to another [4]. In ecological systems, these dynamics often manifest as long transients--periods of apparent stability followed by sudden regime shifts. These shifts can occur without any obvious external trigger, driven instead by internal processes or responses to environmental variability [6]. During these phases, a system may exhibit consistent behavior over time before transitioning to a different dynamic regime, which could involve altered oscillatory patterns or a completely new structure. Such transitions are difficult to predict, as they are nonlinear, involve systems operating at multiple interacting scales, and are influenced by stochasticity [5, 2]. Understanding these multiscale and nonlinear interactions is essential for anticipating regime shifts, which are often most consequential at the coarsest time scales, where changes in slow-moving processes like ecosystem succession or long-term climate changes lead to impactful, irreversible transitions [6].

Integrating symbolic techniques with statistical ones is a long-standing problem in artificial intelligence. The motivation is that the strengths of either area match the weaknesses of the other, and $\unicode{x2013}$ by combining the two $\unicode{x2013}$ the weaknesses of either method can be limited. Neuro-symbolic AI focuses on this integration where the statistical methods are in particular neural networks. In recent years, there has been significant progress in this research field, where neuro-symbolic systems outperformed logical or neural models alone. Yet, neuro-symbolic AI is, comparatively speaking, still in its infancy and has not been widely adopted by machine learning practitioners. In this survey, we present the first mapping of neuro-symbolic techniques into families of frameworks based on their architectures, with several benefits: Firstly, it allows us to link different strengths of frameworks to their respective architectures. Secondly, it allows us to illustrate how engineers can augment their neural networks while treating the symbolic methods as black-boxes. Thirdly, it allows us to map most of the field so that future researchers can identify closely related frameworks.

Uncontrolled cell division in the brain is what gives rise to brain tumors. If the tumor size increases by more than half, there is little hope for the patient's recovery. This emphasizes the need of rapid and precise brain tumor diagnosis. When it comes to analyzing, diagnosing, and planning therapy for brain tumors, MRI imaging plays a crucial role. A brain tumor's development history is crucial information for doctors to have. When it comes to distinguishing between human soft tissues, MRI scans are superior. In order to get reliable classification results from MRI scans quickly, deep learning is one of the most practical methods. Early human illness diagnosis has been demonstrated to be more accurate when deep learning methods are used. In the case of diagnosing a brain tumor, when even a little misdiagnosis might have serious consequences, accuracy is especially important. Disclosure of brain tumors in medical images is still a difficult task. Brain MRIs are notoriously imprecise in revealing the presence or absence of tumors. Using MRI scans of the brain, a Convolutional Neural Network (CNN) was trained to identify the presence of a tumor in this research. Results from the CNN model showed an accuracy of 99.17%. The CNN model's characteristics were also retrieved. In order to evaluate the CNN model's capability for processing images, we applied the features via the following machine learning models: KNN, Logistic regression, SVM, Random Forest, Naive Bayes, and Perception. CNN and machine learning models were also evaluated using the standard metrics of Precision, Recall, Specificity, and F1 score. The significance of the doctor's diagnosis enhanced the accuracy of the CNN model's assistance in identifying the existence of tumor and treating the patient.

Like many chronic diseases, human immunodeficiency virus (HIV) is managed over time at regular clinic visits. At each visit, patient features are assessed, treatments are prescribed, and a subsequent visit is scheduled. There is a need for data-driven methods for both predicting retention and recommending scheduling decisions that optimize retention. Prediction models can be useful for estimating retention rates across a range of scheduling options. However, training such models with electronic health records (EHR) involves several complexities. First, formal causal inference methods are needed to adjust for observed confounding when estimating retention rates under counterfactual scheduling decisions. Second, competing events such as death preclude retention, while censoring events render retention missing. Third, inconsistent monitoring of features such as viral load and CD4 count lead to covariate missingness. This paper presents an all-in-one approach for both predicting HIV retention and optimizing scheduling while accounting for these complexities. We formulate and identify causal retention estimands in terms of potential return-time under a hypothetical scheduling decision. Flexible Bayesian approaches are used to model the observed return-time distribution while accounting for competing and censoring events and form posterior point and uncertainty estimates for these estimands. We address the urgent need for data-driven decision support in HIV care by applying our method to EHR from the Academic Model Providing Access to Healthcare (AMPATH) - a consortium of clinics that treat HIV in Western Kenya.