We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace, e.g., exponential density or distribution based on exponential function. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including Genomics of Drug Sensitivity in Cancer (GDSC $IC_{50}$) and Gene body methylation with different sizes and dimensions, and show that the proposed Bayesian NMF GL$_2^2$ and GL$_\infty$ models lead to robust predictions for different data values and avoid overfitting compared with competitive Bayesian NMF approaches.

Discovering and parameterising latent confounders represent important and challenging problems in causal structure learning and density estimation respectively. In this paper, we focus on both discovering and learning the distribution of latent confounders. This task requires solutions that come from different areas of statistics and machine learning. We combine elements of variational Bayesian methods, expectation-maximisation, hill-climbing search, and structure learning under the assumption of causal insufficiency. We propose two learning strategies; one that maximises model selection accuracy, and another that improves computational efficiency in exchange for minor reductions in accuracy. The former strategy is suitable for small networks and the latter for moderate size networks. Both learning strategies perform well relative to existing solutions. Keywords: Ancestral graphs; EM algorithm; greedy search; hill-climbing search; hidden variables; probabilistic graphical models; variational inference.

Learning a Bayesian network is an NP-hard problem and with an increase in the number of nodes, classical algorithms for learning the structure of Bayesian networks become inefficient. In recent years, some methods and algorithms for learning Bayesian networks with a high number of nodes (more than 50) were developed. But these solutions have their disadvantages, for instance, they only operate one type of data (discrete or continuous) or their algorithm has been created to meet a specific nature of data (medical, social, etc.). The article presents a BigBraveBN algorithm for learning large Bayesian Networks with a high number of nodes (over 100). The algorithm utilizes the Brave coefficient that measures the mutual occurrence of instances in several groups. To form these groups, we use the method of nearest neighbours based on the Mutual information (MI) measure. In the experimental part of the article, we compare the performance of BigBraveBN to other existing solutions on multiple data sets both discrete and continuous. The experimental part also represents tests on real data. The aforementioned experimental results demonstrate the efficiency of the BigBraveBN algorithm in structure learning of Bayesian Networks.

Variational autoencoders (VAEs) often suffer from posterior collapse, which is a phenomenon in which the learned latent space becomes uninformative. This is often related to the hyperparameter resembling the data variance. It can be shown that an inappropriate choice of this hyperparameter causes the oversmoothness in the linearly approximated case and can be empirically verified for the general cases. Moreover, determining such appropriate choice becomes infeasible if the data variance is non-uniform or conditional. Therefore, we propose VAE extensions with generalized parameterizations of the data variance and incorporate maximum likelihood estimation into the objective function to adaptively regularize the decoder smoothness. The images generated from proposed VAE extensions show improved Fr\'echet inception distance (FID) on MNIST and CelebA datasets.

This paper presents Tyche, a Python library to facilitate probabilistic reasoning in uncertain worlds through the construction, querying, and learning of belief models. Tyche uses aleatoric description logic (ADL), which provides computational advantages in its evaluation over other description logics. Tyche belief models can be succinctly created by defining classes of individuals, the probabilistic beliefs about them (concepts), and the probabilistic relationships between them (roles). We also introduce a method of observation propagation to facilitate learning from complex ADL observations. A demonstration of Tyche to predict the author of anonymised messages, and to extract author writing tendencies from anonymised messages, is provided. Tyche has the potential to assist in the development of expert systems, knowledge extraction systems, and agents to play games with incomplete and probabilistic information.

Node classification using Graph Neural Networks (GNNs) has been widely applied in various real-world scenarios. However, in recent years, compelling evidence emerges that the performance of GNN-based node classification may deteriorate substantially by topological perturbation, such as random connections or adversarial attacks. Various solutions, such as topological denoising methods and mechanism design methods, have been proposed to develop robust GNN-based node classifiers but none of these works can fully address the problems related to topological perturbations. Recently, the Bayesian label transition model is proposed to tackle this issue but its slow convergence may lead to inferior performance. In this work, we propose a new label inference model, namely LInDT, which integrates both Bayesian label transition and topology-based label propagation for improving the robustness of GNNs against topological perturbations. LInDT is superior to existing label transition methods as it improves the label prediction of uncertain nodes by utilizing neighborhood-based label propagation leading to better convergence of label inference. Besides, LIndT adopts asymmetric Dirichlet distribution as a prior, which also helps it to improve label inference. Extensive experiments on five graph datasets demonstrate the superiority of LInDT for GNN-based node classification under three scenarios of topological perturbations.

Variational Bayes (VB) applied to latent Dirichlet allocation (LDA) has become the most popular algorithm for aspect modeling. While sufficiently successful in text topic extraction from large corpora, VB is less successful in identifying aspects in the presence of limited data. We present a novel variational message passing algorithm as applied to Latent Dirichlet Allocation (LDA) and compare it with the gold standard VB and collapsed Gibbs sampling. In situations where marginalisation leads to non-conjugate messages, we use ideas from sampling to derive approximate update equations. In cases where conjugacy holds, Loopy Belief update (LBU) (also known as Lauritzen-Spiegelhalter) is used. Our algorithm, ALBU (approximate LBU), has strong similarities with Variational Message Passing (VMP) (which is the message passing variant of VB). To compare the performance of the algorithms in the presence of limited data, we use data sets consisting of tweets and news groups. Using coherence measures we show that ALBU learns latent distributions more accurately than does VB, especially for smaller data sets.

Of late, in order to have better acceptability among various domain, researchers have argued that machine intelligence algorithms must be able to provide explanations that humans can understand causally. This aspect, also known as'causability' achieves a specific level of human-level explainability. A specific class of algorithms known as counterfactuals may be able to provide causability. In statistics, causality has been studied and applied for many years, but not in great detail in artificial intelligence (AI). In a first-of-its-kind study, we employed the principles of causal inference to provide explainability for solving the analytical customer relationship management (ACRM) problems. In the context of banking and insurance, current research on interpretability tries to address causality-related questions like why did this model make such decisions, and was the model's choice influenced by a particular factor? We propose a solution in the form of an intervention, wherein the effect of changing the distribution of features of ACRM datasets is studied on the target feature. Subsequently, a set of counterfactuals is also obtained that may be furnished to any customer who demands an explanation of the decision taken by the bank/insurance company. Except for the credit card churn prediction dataset, good quality counterfactuals were generated for the loan default, insurance fraud detection, and credit card fraud detection datasets, where changes in no more than three features are observed.

Recent progress in machine learning methods, and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs), have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian Process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian Processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. The discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods, and can be particularly impactful for destructive or irreversible measurements.